Merge branch 'master' of github.com:TheAlgorithms/Python into bug-fix-expression-tree

updates:
- [github.com/astral-sh/ruff-pre-commit: v0.0.280 → v0.0.281](https://github.com/astral-sh/ruff-pre-commit/compare/v0.0.280...v0.0.281)

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

.devcontainer/Dockerfile

@@ -0,0 +1,8 @@
+# https://github.com/microsoft/vscode-dev-containers/blob/main/containers/python-3/README.md
+ARG VARIANT=3.11-bookworm
+FROM mcr.microsoft.com/vscode/devcontainers/python:${VARIANT}
+COPY requirements.txt /tmp/pip-tmp/
+RUN python3 -m pip install --upgrade pip \
+  && python3 -m pip install --no-cache-dir install -r /tmp/pip-tmp/requirements.txt \
+  && pipx install pre-commit ruff \
+  && pre-commit install

.devcontainer/devcontainer.json

@@ -0,0 +1,42 @@
+{
+	"name": "Python 3",
+	"build": {
+		"dockerfile": "Dockerfile",
+		"context": "..",
+		"args": {
+			// Update 'VARIANT' to pick a Python version: 3, 3.10, 3.9, 3.8, 3.7, 3.6
+			// Append -bullseye or -buster to pin to an OS version.
+			// Use -bullseye variants on local on arm64/Apple Silicon.
+			"VARIANT": "3.11-bookworm",
+		}
+	},
+
+	// Configure tool-specific properties.
+	"customizations": {
+		// Configure properties specific to VS Code.
+		"vscode": {
+			// Set *default* container specific settings.json values on container create.
+			"settings": {
+				"python.defaultInterpreterPath": "/usr/local/bin/python",
+				"python.linting.enabled": true,
+				"python.formatting.blackPath": "/usr/local/py-utils/bin/black",
+				"python.linting.mypyPath": "/usr/local/py-utils/bin/mypy"
+			},
+
+			// Add the IDs of extensions you want installed when the container is created.
+			"extensions": [
+				"ms-python.python",
+				"ms-python.vscode-pylance"
+			]
+		}
+	},
+
+	// Use 'forwardPorts' to make a list of ports inside the container available locally.
+	// "forwardPorts": [],
+
+	// Use 'postCreateCommand' to run commands after the container is created.
+	// "postCreateCommand": "pip3 install --user -r requirements.txt",
+
+	// Comment out to connect as root instead. More info: https://aka.ms/vscode-remote/containers/non-root.
+	"remoteUser": "vscode"
+}

.github/pull_request_template.md

@@ -17,4 +17,4 @@
 * [ ] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
 * [ ] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
 * [ ] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
-* [ ] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
+* [ ] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

.github/workflows/build.yml

@@ -22,11 +22,9 @@ jobs:
           python -m pip install --upgrade pip setuptools six wheel
           python -m pip install pytest-cov -r requirements.txt
       - name: Run tests
-        # See: #6591 for re-enabling tests on Python v3.11
+        # TODO: #8818 Re-enable quantum tests
         run: pytest
-            --ignore=computer_vision/cnn_classification.py
-            --ignore=machine_learning/lstm/lstm_prediction.py
-            --ignore=quantum/
+            --ignore=quantum/q_fourier_transform.py
             --ignore=project_euler/
             --ignore=scripts/validate_solutions.py
             --cov-report=term-missing:skip-covered

.pre-commit-config.yaml

@@ -15,25 +15,25 @@ repos:
     hooks:
     -   id: auto-walrus
 
-  - repo: https://github.com/charliermarsh/ruff-pre-commit
-    rev: v0.0.262
+  - repo: https://github.com/astral-sh/ruff-pre-commit
+    rev: v0.0.281
     hooks:
       - id: ruff
 
   - repo: https://github.com/psf/black
-    rev: 23.3.0
+    rev: 23.7.0
     hooks:
       - id: black
 
   - repo: https://github.com/codespell-project/codespell
-    rev: v2.2.4
+    rev: v2.2.5
     hooks:
       - id: codespell
         additional_dependencies:
           - tomli
 
   - repo: https://github.com/tox-dev/pyproject-fmt
-    rev: "0.10.0"
+    rev: "0.13.0"
     hooks:
       - id: pyproject-fmt
 
@@ -46,12 +46,12 @@ repos:
         pass_filenames: false
 
   - repo: https://github.com/abravalheri/validate-pyproject
-    rev: v0.12.2
+    rev: v0.13
     hooks:
       - id: validate-pyproject
 
   - repo: https://github.com/pre-commit/mirrors-mypy
-    rev: v1.2.0
+    rev: v1.4.1
     hooks:
       - id: mypy
         args:

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+    "githubPullRequests.ignoredPullRequestBranches": [
+        "master"
+    ]
+}

CONTRIBUTING.md

@@ -25,7 +25,14 @@ We appreciate any contribution, from fixing a grammar mistake in a comment to im
 
 Your contribution will be tested by our [automated testing on GitHub Actions](https://github.com/TheAlgorithms/Python/actions) to save time and mental energy.  After you have submitted your pull request, you should see the GitHub Actions tests start to run at the bottom of your submission page.  If those tests fail, then click on the ___details___ button try to read through the GitHub Actions output to understand the failure.  If you do not understand, please leave a comment on your submission page and a community member will try to help.
 
-Please help us keep our issue list small by adding fixes: #{$ISSUE_NO} to the commit message of pull requests that resolve open issues. GitHub will use this tag to auto-close the issue when the PR is merged.
+If you are interested in resolving an [open issue](https://github.com/TheAlgorithms/Python/issues), simply make a pull request with your proposed fix. __We do not assign issues in this repo__ so please do not ask for permission to work on an issue.
+
+Please help us keep our issue list small by adding `Fixes #{$ISSUE_NUMBER}` to the description of pull requests that resolve open issues.
+For example, if your pull request fixes issue #10, then please add the following to its description:
+```
+Fixes #10
+```
+GitHub will use this tag to [auto-close the issue](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue) if and when the PR is merged.
 
 #### What is an Algorithm?
 

DIRECTORY.md

@@ -29,6 +29,7 @@
   * [Minmax](backtracking/minmax.py)
   * [N Queens](backtracking/n_queens.py)
   * [N Queens Math](backtracking/n_queens_math.py)
+  * [Power Sum](backtracking/power_sum.py)
   * [Rat In Maze](backtracking/rat_in_maze.py)
   * [Sudoku](backtracking/sudoku.py)
   * [Sum Of Subsets](backtracking/sum_of_subsets.py)
@@ -146,6 +147,7 @@
   * [Decimal To Binary Recursion](conversions/decimal_to_binary_recursion.py)
   * [Decimal To Hexadecimal](conversions/decimal_to_hexadecimal.py)
   * [Decimal To Octal](conversions/decimal_to_octal.py)
+  * [Energy Conversions](conversions/energy_conversions.py)
   * [Excel Title To Column](conversions/excel_title_to_column.py)
   * [Hex To Bin](conversions/hex_to_bin.py)
   * [Hexadecimal To Decimal](conversions/hexadecimal_to_decimal.py)
@@ -166,6 +168,7 @@
   * Arrays
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
+    * [Product Sum](data_structures/arrays/product_sum.py)
   * Binary Tree
     * [Avl Tree](data_structures/binary_tree/avl_tree.py)
     * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py)
@@ -233,8 +236,8 @@
     * [Double Ended Queue](data_structures/queue/double_ended_queue.py)
     * [Linked Queue](data_structures/queue/linked_queue.py)
     * [Priority Queue Using List](data_structures/queue/priority_queue_using_list.py)
+    * [Queue By List](data_structures/queue/queue_by_list.py)
     * [Queue By Two Stacks](data_structures/queue/queue_by_two_stacks.py)
-    * [Queue On List](data_structures/queue/queue_on_list.py)
     * [Queue On Pseudo Stack](data_structures/queue/queue_on_pseudo_stack.py)
   * Stacks
     * [Balanced Parentheses](data_structures/stacks/balanced_parentheses.py)
@@ -290,7 +293,7 @@
   * [Inversions](divide_and_conquer/inversions.py)
   * [Kth Order Statistic](divide_and_conquer/kth_order_statistic.py)
   * [Max Difference Pair](divide_and_conquer/max_difference_pair.py)
-  * [Max Subarray Sum](divide_and_conquer/max_subarray_sum.py)
+  * [Max Subarray](divide_and_conquer/max_subarray.py)
   * [Mergesort](divide_and_conquer/mergesort.py)
   * [Peak](divide_and_conquer/peak.py)
   * [Power](divide_and_conquer/power.py)
@@ -321,8 +324,7 @@
   * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py)
   * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py)
   * [Max Product Subarray](dynamic_programming/max_product_subarray.py)
-  * [Max Sub Array](dynamic_programming/max_sub_array.py)
-  * [Max Sum Contiguous Subsequence](dynamic_programming/max_sum_contiguous_subsequence.py)
+  * [Max Subarray Sum](dynamic_programming/max_subarray_sum.py)
   * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py)
   * [Minimum Coin Change](dynamic_programming/minimum_coin_change.py)
   * [Minimum Cost Path](dynamic_programming/minimum_cost_path.py)
@@ -363,6 +365,7 @@
 ## Financial
   * [Equated Monthly Installments](financial/equated_monthly_installments.py)
   * [Interest](financial/interest.py)
+  * [Present Value](financial/present_value.py)
   * [Price Plus Tax](financial/price_plus_tax.py)
 
 ## Fractals
@@ -409,6 +412,7 @@
   * [Dijkstra 2](graphs/dijkstra_2.py)
   * [Dijkstra Algorithm](graphs/dijkstra_algorithm.py)
   * [Dijkstra Alternate](graphs/dijkstra_alternate.py)
+  * [Dijkstra Binary Grid](graphs/dijkstra_binary_grid.py)
   * [Dinic](graphs/dinic.py)
   * [Directed And Undirected (Weighted) Graph](graphs/directed_and_undirected_(weighted)_graph.py)
   * [Edmonds Karp Multiple Source And Sink](graphs/edmonds_karp_multiple_source_and_sink.py)
@@ -418,8 +422,9 @@
   * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py)
   * [G Topological Sort](graphs/g_topological_sort.py)
   * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py)
+  * [Graph Adjacency List](graphs/graph_adjacency_list.py)
+  * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py)
   * [Graph List](graphs/graph_list.py)
-  * [Graph Matrix](graphs/graph_matrix.py)
   * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py)
   * [Greedy Best First](graphs/greedy_best_first.py)
   * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py)
@@ -448,6 +453,7 @@
 ## Greedy Methods
   * [Fractional Knapsack](greedy_methods/fractional_knapsack.py)
   * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py)
+  * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py)
   * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py)
 
 ## Hashes
@@ -477,11 +483,15 @@
     * [Lib](linear_algebra/src/lib.py)
     * [Polynom For Points](linear_algebra/src/polynom_for_points.py)
     * [Power Iteration](linear_algebra/src/power_iteration.py)
+    * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py)
     * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py)
     * [Schur Complement](linear_algebra/src/schur_complement.py)
     * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py)
     * [Transformations 2D](linear_algebra/src/transformations_2d.py)
 
+## Linear Programming
+  * [Simplex](linear_programming/simplex.py)
+
 ## Machine Learning
   * [Astar](machine_learning/astar.py)
   * [Data Transformations](machine_learning/data_transformations.py)
@@ -501,7 +511,7 @@
   * Lstm
     * [Lstm Prediction](machine_learning/lstm/lstm_prediction.py)
   * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py)
-  * [Polymonial Regression](machine_learning/polymonial_regression.py)
+  * [Polynomial Regression](machine_learning/polynomial_regression.py)
   * [Scoring Functions](machine_learning/scoring_functions.py)
   * [Self Organizing Map](machine_learning/self_organizing_map.py)
   * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py)
@@ -512,7 +522,6 @@
   * [Xgboost Regressor](machine_learning/xgboost_regressor.py)
 
 ## Maths
-  * [3N Plus 1](maths/3n_plus_1.py)
   * [Abs](maths/abs.py)
   * [Add](maths/add.py)
   * [Addition Without Arithmetic](maths/addition_without_arithmetic.py)
@@ -548,6 +557,7 @@
   * [Dodecahedron](maths/dodecahedron.py)
   * [Double Factorial Iterative](maths/double_factorial_iterative.py)
   * [Double Factorial Recursive](maths/double_factorial_recursive.py)
+  * [Dual Number Automatic Differentiation](maths/dual_number_automatic_differentiation.py)
   * [Entropy](maths/entropy.py)
   * [Euclidean Distance](maths/euclidean_distance.py)
   * [Euclidean Gcd](maths/euclidean_gcd.py)
@@ -575,16 +585,15 @@
   * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py)
   * [Hexagonal Number](maths/hexagonal_number.py)
   * [Integration By Simpson Approx](maths/integration_by_simpson_approx.py)
+  * [Is Int Palindrome](maths/is_int_palindrome.py)
   * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py)
   * [Is Square Free](maths/is_square_free.py)
   * [Jaccard Similarity](maths/jaccard_similarity.py)
   * [Juggler Sequence](maths/juggler_sequence.py)
-  * [Kadanes](maths/kadanes.py)
   * [Karatsuba](maths/karatsuba.py)
   * [Krishnamurthy Number](maths/krishnamurthy_number.py)
   * [Kth Lexicographic Permutation](maths/kth_lexicographic_permutation.py)
   * [Largest Of Very Large Numbers](maths/largest_of_very_large_numbers.py)
-  * [Largest Subarray Sum](maths/largest_subarray_sum.py)
   * [Least Common Multiple](maths/least_common_multiple.py)
   * [Line Length](maths/line_length.py)
   * [Liouville Lambda](maths/liouville_lambda.py)
@@ -604,6 +613,7 @@
   * [Newton Raphson](maths/newton_raphson.py)
   * [Number Of Digits](maths/number_of_digits.py)
   * [Numerical Integration](maths/numerical_integration.py)
+  * [Odd Sieve](maths/odd_sieve.py)
   * [Perfect Cube](maths/perfect_cube.py)
   * [Perfect Number](maths/perfect_number.py)
   * [Perfect Square](maths/perfect_square.py)
@@ -630,6 +640,7 @@
   * [Radians](maths/radians.py)
   * [Radix2 Fft](maths/radix2_fft.py)
   * [Relu](maths/relu.py)
+  * [Remove Digit](maths/remove_digit.py)
   * [Runge Kutta](maths/runge_kutta.py)
   * [Segmented Sieve](maths/segmented_sieve.py)
   * Series
@@ -645,6 +656,7 @@
   * [Sigmoid Linear Unit](maths/sigmoid_linear_unit.py)
   * [Signum](maths/signum.py)
   * [Simpson Rule](maths/simpson_rule.py)
+  * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py)
   * [Sin](maths/sin.py)
   * [Sock Merchant](maths/sock_merchant.py)
   * [Softmax](maths/softmax.py)
@@ -655,6 +667,7 @@
   * [Sum Of Harmonic Series](maths/sum_of_harmonic_series.py)
   * [Sumset](maths/sumset.py)
   * [Sylvester Sequence](maths/sylvester_sequence.py)
+  * [Tanh](maths/tanh.py)
   * [Test Prime Check](maths/test_prime_check.py)
   * [Trapezoidal Rule](maths/trapezoidal_rule.py)
   * [Triplet Sum](maths/triplet_sum.py)
@@ -669,6 +682,7 @@
 ## Matrix
   * [Binary Search Matrix](matrix/binary_search_matrix.py)
   * [Count Islands In Matrix](matrix/count_islands_in_matrix.py)
+  * [Count Negative Numbers In Sorted Matrix](matrix/count_negative_numbers_in_sorted_matrix.py)
   * [Count Paths](matrix/count_paths.py)
   * [Cramers Rule 2X2](matrix/cramers_rule_2x2.py)
   * [Inverse Of Matrix](matrix/inverse_of_matrix.py)
@@ -691,6 +705,8 @@
 
 ## Neural Network
   * [2 Hidden Layers Neural Network](neural_network/2_hidden_layers_neural_network.py)
+  * Activation Functions
+    * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py)
   * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py)
   * [Convolution Neural Network](neural_network/convolution_neural_network.py)
   * [Input Data](neural_network/input_data.py)
@@ -707,13 +723,16 @@
   * [Gauss Easter](other/gauss_easter.py)
   * [Graham Scan](other/graham_scan.py)
   * [Greedy](other/greedy.py)
+  * [Guess The Number Search](other/guess_the_number_search.py)
+  * [H Index](other/h_index.py)
   * [Least Recently Used](other/least_recently_used.py)
   * [Lfu Cache](other/lfu_cache.py)
   * [Linear Congruential Generator](other/linear_congruential_generator.py)
   * [Lru Cache](other/lru_cache.py)
   * [Magicdiamondpattern](other/magicdiamondpattern.py)
-  * [Maximum Subarray](other/maximum_subarray.py)
+  * [Maximum Subsequence](other/maximum_subsequence.py)
   * [Nested Brackets](other/nested_brackets.py)
+  * [Number Container System](other/number_container_system.py)
   * [Password](other/password.py)
   * [Quine](other/quine.py)
   * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -721,7 +740,9 @@
   * [Tower Of Hanoi](other/tower_of_hanoi.py)
 
 ## Physics
+  * [Altitude Pressure](physics/altitude_pressure.py)
   * [Archimedes Principle](physics/archimedes_principle.py)
+  * [Basic Orbital Capture](physics/basic_orbital_capture.py)
   * [Casimir Effect](physics/casimir_effect.py)
   * [Centripetal Force](physics/centripetal_force.py)
   * [Grahams Law](physics/grahams_law.py)
@@ -737,6 +758,7 @@
   * [Potential Energy](physics/potential_energy.py)
   * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py)
   * [Shear Stress](physics/shear_stress.py)
+  * [Speed Of Sound](physics/speed_of_sound.py)
 
 ## Project Euler
   * Problem 001
@@ -1042,7 +1064,6 @@
   * [Q Fourier Transform](quantum/q_fourier_transform.py)
   * [Q Full Adder](quantum/q_full_adder.py)
   * [Quantum Entanglement](quantum/quantum_entanglement.py)
-  * [Quantum Random](quantum/quantum_random.py)
   * [Quantum Teleportation](quantum/quantum_teleportation.py)
   * [Ripple Adder Classic](quantum/ripple_adder_classic.py)
   * [Single Qubit Measure](quantum/single_qubit_measure.py)
@@ -1076,6 +1097,7 @@
 
 ## Sorts
   * [Bead Sort](sorts/bead_sort.py)
+  * [Binary Insertion Sort](sorts/binary_insertion_sort.py)
   * [Bitonic Sort](sorts/bitonic_sort.py)
   * [Bogo Sort](sorts/bogo_sort.py)
   * [Bubble Sort](sorts/bubble_sort.py)
@@ -1144,7 +1166,6 @@
   * [Indian Phone Validator](strings/indian_phone_validator.py)
   * [Is Contains Unique Chars](strings/is_contains_unique_chars.py)
   * [Is Isogram](strings/is_isogram.py)
-  * [Is Palindrome](strings/is_palindrome.py)
   * [Is Pangram](strings/is_pangram.py)
   * [Is Spain National Id](strings/is_spain_national_id.py)
   * [Is Srilankan Phone Number](strings/is_srilankan_phone_number.py)
@@ -1166,7 +1187,9 @@
   * [Reverse Words](strings/reverse_words.py)
   * [Snake Case To Camel Pascal Case](strings/snake_case_to_camel_pascal_case.py)
   * [Split](strings/split.py)
+  * [String Switch Case](strings/string_switch_case.py)
   * [Text Justification](strings/text_justification.py)
+  * [Top K Frequent Words](strings/top_k_frequent_words.py)
   * [Upper](strings/upper.py)
   * [Wave](strings/wave.py)
   * [Wildcard Pattern Matching](strings/wildcard_pattern_matching.py)
@@ -1186,7 +1209,6 @@
   * [Daily Horoscope](web_programming/daily_horoscope.py)
   * [Download Images From Google Query](web_programming/download_images_from_google_query.py)
   * [Emails From Url](web_programming/emails_from_url.py)
-  * [Fetch Anime And Play](web_programming/fetch_anime_and_play.py)
   * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
   * [Fetch Github Info](web_programming/fetch_github_info.py)
   * [Fetch Jobs](web_programming/fetch_jobs.py)

README.md

@@ -13,7 +13,7 @@
     <img src="https://img.shields.io/static/v1.svg?label=Contributions&message=Welcome&color=0059b3&style=flat-square" height="20" alt="Contributions Welcome">
   </a>
   <img src="https://img.shields.io/github/repo-size/TheAlgorithms/Python.svg?label=Repo%20size&style=flat-square" height="20">
-  <a href="https://discord.gg/c7MnfGFGa6">
+  <a href="https://the-algorithms.com/discord">
     <img src="https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square" height="20" alt="Discord chat">
   </a>
   <a href="https://gitter.im/TheAlgorithms/community">
@@ -42,7 +42,7 @@ Read through our [Contribution Guidelines](CONTRIBUTING.md) before you contribut
 
 ## Community Channels
 
-We are on [Discord](https://discord.gg/c7MnfGFGa6) and [Gitter](https://gitter.im/TheAlgorithms/community)! Community channels are a great way for you to ask questions and get help. Please join us!
+We are on [Discord](https://the-algorithms.com/discord) and [Gitter](https://gitter.im/TheAlgorithms/community)! Community channels are a great way for you to ask questions and get help. Please join us!
 
 ## List of Algorithms
 

arithmetic_analysis/jacobi_iteration_method.py

@@ -49,7 +49,9 @@ def jacobi_iteration_method(
     >>> constant = np.array([[2], [-6]])
     >>> init_val = [0.5, -0.5, -0.5]
     >>> iterations = 3
-    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    >>> jacobi_iteration_method(
+    ...     coefficient, constant, init_val, iterations
+    ... )  # doctest: +NORMALIZE_WHITESPACE
     Traceback (most recent call last):
         ...
     ValueError: Coefficient and constant matrices dimensions must be nxn and nx1 but
@@ -59,7 +61,9 @@ def jacobi_iteration_method(
     >>> constant = np.array([[2], [-6], [-4]])
     >>> init_val = [0.5, -0.5]
     >>> iterations = 3
-    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    >>> jacobi_iteration_method(
+    ...     coefficient, constant, init_val, iterations
+    ... )  # doctest: +NORMALIZE_WHITESPACE
     Traceback (most recent call last):
         ...
     ValueError: Number of initial values must be equal to number of rows in coefficient
@@ -79,24 +83,26 @@ def jacobi_iteration_method(
     rows2, cols2 = constant_matrix.shape
 
     if rows1 != cols1:
-        raise ValueError(
-            f"Coefficient matrix dimensions must be nxn but received {rows1}x{cols1}"
-        )
+        msg = f"Coefficient matrix dimensions must be nxn but received {rows1}x{cols1}"
+        raise ValueError(msg)
 
     if cols2 != 1:
-        raise ValueError(f"Constant matrix must be nx1 but received {rows2}x{cols2}")
+        msg = f"Constant matrix must be nx1 but received {rows2}x{cols2}"
+        raise ValueError(msg)
 
     if rows1 != rows2:
-        raise ValueError(
-            f"""Coefficient and constant matrices dimensions must be nxn and nx1 but
-            received {rows1}x{cols1} and {rows2}x{cols2}"""
+        msg = (
+            "Coefficient and constant matrices dimensions must be nxn and nx1 but "
+            f"received {rows1}x{cols1} and {rows2}x{cols2}"
         )
+        raise ValueError(msg)
 
     if len(init_val) != rows1:
-        raise ValueError(
-            f"""Number of initial values must be equal to number of rows in coefficient
-            matrix but received {len(init_val)} and {rows1}"""
+        msg = (
+            "Number of initial values must be equal to number of rows in coefficient "
+            f"matrix but received {len(init_val)} and {rows1}"
         )
+        raise ValueError(msg)
 
     if iterations <= 0:
         raise ValueError("Iterations must be at least 1")

arithmetic_analysis/lu_decomposition.py

@@ -80,10 +80,11 @@ def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray
     # Ensure that table is a square array
     rows, columns = np.shape(table)
     if rows != columns:
-        raise ValueError(
-            f"'table' has to be of square shaped array but got a "
+        msg = (
+            "'table' has to be of square shaped array but got a "
             f"{rows}x{columns} array:\n{table}"
         )
+        raise ValueError(msg)
 
     lower = np.zeros((rows, columns))
     upper = np.zeros((rows, columns))

arithmetic_analysis/newton_raphson.py

@@ -25,9 +25,11 @@ def newton_raphson(
     """
     x = a
     while True:
-        x = Decimal(x) - (Decimal(eval(func)) / Decimal(eval(str(diff(func)))))
+        x = Decimal(x) - (
+            Decimal(eval(func)) / Decimal(eval(str(diff(func))))  # noqa: S307
+        )
         # This number dictates the accuracy of the answer
-        if abs(eval(func)) < precision:
+        if abs(eval(func)) < precision:  # noqa: S307
             return float(x)
 
 

audio_filters/iir_filter.py

@@ -50,16 +50,18 @@ class IIRFilter:
             a_coeffs = [1.0, *a_coeffs]
 
         if len(a_coeffs) != self.order + 1:
-            raise ValueError(
-                f"Expected a_coeffs to have {self.order + 1} elements for {self.order}"
-                f"-order filter, got {len(a_coeffs)}"
+            msg = (
+                f"Expected a_coeffs to have {self.order + 1} elements "
+                f"for {self.order}-order filter, got {len(a_coeffs)}"
             )
+            raise ValueError(msg)
 
         if len(b_coeffs) != self.order + 1:
-            raise ValueError(
-                f"Expected b_coeffs to have {self.order + 1} elements for {self.order}"
-                f"-order filter, got {len(a_coeffs)}"
+            msg = (
+                f"Expected b_coeffs to have {self.order + 1} elements "
+                f"for {self.order}-order filter, got {len(a_coeffs)}"
             )
+            raise ValueError(msg)
 
         self.a_coeffs = a_coeffs
         self.b_coeffs = b_coeffs

backtracking/knight_tour.py

@@ -91,7 +91,8 @@ def open_knight_tour(n: int) -> list[list[int]]:
                 return board
             board[i][j] = 0
 
-    raise ValueError(f"Open Kight Tour cannot be performed on a board of size {n}")
+    msg = f"Open Kight Tour cannot be performed on a board of size {n}"
+    raise ValueError(msg)
 
 
 if __name__ == "__main__":

backtracking/power_sum.py

@@ -0,0 +1,93 @@
+"""
+Problem source: https://www.hackerrank.com/challenges/the-power-sum/problem
+Find the number of ways that a given integer X, can be expressed as the sum
+of the Nth powers of unique, natural numbers. For example, if X=13 and N=2.
+We have to find all combinations of unique squares adding up to 13.
+The only solution is 2^2+3^2. Constraints: 1<=X<=1000, 2<=N<=10.
+"""
+
+from math import pow
+
+
+def backtrack(
+    needed_sum: int,
+    power: int,
+    current_number: int,
+    current_sum: int,
+    solutions_count: int,
+) -> tuple[int, int]:
+    """
+    >>> backtrack(13, 2, 1, 0, 0)
+    (0, 1)
+    >>> backtrack(100, 2, 1, 0, 0)
+    (0, 3)
+    >>> backtrack(100, 3, 1, 0, 0)
+    (0, 1)
+    >>> backtrack(800, 2, 1, 0, 0)
+    (0, 561)
+    >>> backtrack(1000, 10, 1, 0, 0)
+    (0, 0)
+    >>> backtrack(400, 2, 1, 0, 0)
+    (0, 55)
+    >>> backtrack(50, 1, 1, 0, 0)
+    (0, 3658)
+    """
+    if current_sum == needed_sum:
+        # If the sum of the powers is equal to needed_sum, then we have a solution.
+        solutions_count += 1
+        return current_sum, solutions_count
+
+    i_to_n = int(pow(current_number, power))
+    if current_sum + i_to_n <= needed_sum:
+        # If the sum of the powers is less than needed_sum, then continue adding powers.
+        current_sum += i_to_n
+        current_sum, solutions_count = backtrack(
+            needed_sum, power, current_number + 1, current_sum, solutions_count
+        )
+        current_sum -= i_to_n
+    if i_to_n < needed_sum:
+        # If the power of i is less than needed_sum, then try with the next power.
+        current_sum, solutions_count = backtrack(
+            needed_sum, power, current_number + 1, current_sum, solutions_count
+        )
+    return current_sum, solutions_count
+
+
+def solve(needed_sum: int, power: int) -> int:
+    """
+    >>> solve(13, 2)
+    1
+    >>> solve(100, 2)
+    3
+    >>> solve(100, 3)
+    1
+    >>> solve(800, 2)
+    561
+    >>> solve(1000, 10)
+    0
+    >>> solve(400, 2)
+    55
+    >>> solve(50, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid input
+    needed_sum must be between 1 and 1000, power between 2 and 10.
+    >>> solve(-10, 5)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid input
+    needed_sum must be between 1 and 1000, power between 2 and 10.
+    """
+    if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
+        raise ValueError(
+            "Invalid input\n"
+            "needed_sum must be between 1 and 1000, power between 2 and 10."
+        )
+
+    return backtrack(needed_sum, power, 1, 0, 0)[1]  # Return the solutions_count
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

bit_manipulation/reverse_bits.py

@@ -14,10 +14,11 @@ def get_reverse_bit_string(number: int) -> str:
     TypeError: operation can not be conducted on a object of type str
     """
     if not isinstance(number, int):
-        raise TypeError(
+        msg = (
             "operation can not be conducted on a object of type "
             f"{type(number).__name__}"
         )
+        raise TypeError(msg)
     bit_string = ""
     for _ in range(0, 32):
         bit_string += str(number % 2)

boolean_algebra/and_gate.py

@@ -43,6 +43,8 @@ def test_and_gate() -> None:
 
 
 if __name__ == "__main__":
+    test_and_gate()
+    print(and_gate(1, 0))
     print(and_gate(0, 0))
     print(and_gate(0, 1))
     print(and_gate(1, 1))

cellular_automata/game_of_life.py

@@ -10,7 +10,7 @@ Python:
   - 3.5
 
 Usage:
-  - $python3 game_o_life <canvas_size:int>
+  - $python3 game_of_life <canvas_size:int>
 
 Game-Of-Life Rules:
 
@@ -34,7 +34,7 @@ import numpy as np
 from matplotlib import pyplot as plt
 from matplotlib.colors import ListedColormap
 
-usage_doc = "Usage of script: script_nama <size_of_canvas:int>"
+usage_doc = "Usage of script: script_name <size_of_canvas:int>"
 
 choice = [0] * 100 + [1] * 10
 random.shuffle(choice)
@@ -52,7 +52,8 @@ def seed(canvas: list[list[bool]]) -> None:
 
 
 def run(canvas: list[list[bool]]) -> list[list[bool]]:
-    """This  function runs the rules of game through all points, and changes their
+    """
+    This function runs the rules of game through all points, and changes their
     status accordingly.(in the same canvas)
     @Args:
     --
@@ -60,7 +61,7 @@ def run(canvas: list[list[bool]]) -> list[list[bool]]:
 
     @returns:
     --
-    None
+    canvas of population after one step
     """
     current_canvas = np.array(canvas)
     next_gen_canvas = np.array(create_canvas(current_canvas.shape[0]))
@@ -70,10 +71,7 @@ def run(canvas: list[list[bool]]) -> list[list[bool]]:
                 pt, current_canvas[r - 1 : r + 2, c - 1 : c + 2]
             )
 
-    current_canvas = next_gen_canvas
-    del next_gen_canvas  # cleaning memory as we move on.
-    return_canvas: list[list[bool]] = current_canvas.tolist()
-    return return_canvas
+    return next_gen_canvas.tolist()
 
 
 def __judge_point(pt: bool, neighbours: list[list[bool]]) -> bool:
@@ -98,7 +96,7 @@ def __judge_point(pt: bool, neighbours: list[list[bool]]) -> bool:
     if pt:
         if alive < 2:
             state = False
-        elif alive == 2 or alive == 3:
+        elif alive in {2, 3}:
             state = True
         elif alive > 3:
             state = False

ciphers/base64.py

@@ -34,9 +34,8 @@ def base64_encode(data: bytes) -> bytes:
     """
     # Make sure the supplied data is a bytes-like object
     if not isinstance(data, bytes):
-        raise TypeError(
-            f"a bytes-like object is required, not '{data.__class__.__name__}'"
-        )
+        msg = f"a bytes-like object is required, not '{data.__class__.__name__}'"
+        raise TypeError(msg)
 
     binary_stream = "".join(bin(byte)[2:].zfill(8) for byte in data)
 
@@ -88,10 +87,11 @@ def base64_decode(encoded_data: str) -> bytes:
     """
     # Make sure encoded_data is either a string or a bytes-like object
     if not isinstance(encoded_data, bytes) and not isinstance(encoded_data, str):
-        raise TypeError(
-            "argument should be a bytes-like object or ASCII string, not "
-            f"'{encoded_data.__class__.__name__}'"
+        msg = (
+            "argument should be a bytes-like object or ASCII string, "
+            f"not '{encoded_data.__class__.__name__}'"
         )
+        raise TypeError(msg)
 
     # In case encoded_data is a bytes-like object, make sure it contains only
     # ASCII characters so we convert it to a string object

ciphers/beaufort_cipher.py

@@ -5,7 +5,7 @@ Author: Mohit Radadiya
 from string import ascii_uppercase
 
 dict1 = {char: i for i, char in enumerate(ascii_uppercase)}
-dict2 = {i: char for i, char in enumerate(ascii_uppercase)}
+dict2 = dict(enumerate(ascii_uppercase))
 
 
 # This function generates the key in

ciphers/cryptomath_module.py

@@ -6,7 +6,8 @@ def gcd(a: int, b: int) -> int:
 
 def find_mod_inverse(a: int, m: int) -> int:
     if gcd(a, m) != 1:
-        raise ValueError(f"mod inverse of {a!r} and {m!r} does not exist")
+        msg = f"mod inverse of {a!r} and {m!r} does not exist"
+        raise ValueError(msg)
     u1, u2, u3 = 1, 0, a
     v1, v2, v3 = 0, 1, m
     while v3 != 0:

ciphers/diffie_hellman.py

@@ -10,13 +10,13 @@ primes = {
     5: {
         "prime": int(
             "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
-            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
-            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
-            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
-            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
-            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
-            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
-            + "670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
+            "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+            "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+            "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+            "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+            "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+            "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+            "670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
             base=16,
         ),
         "generator": 2,
@@ -25,16 +25,16 @@ primes = {
     14: {
         "prime": int(
             "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
-            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
-            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
-            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
-            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
-            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
-            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
-            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
-            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
-            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
-            + "15728E5A8AACAA68FFFFFFFFFFFFFFFF",
+            "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+            "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+            "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+            "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+            "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+            "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+            "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+            "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+            "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+            "15728E5A8AACAA68FFFFFFFFFFFFFFFF",
             base=16,
         ),
         "generator": 2,
@@ -43,21 +43,21 @@ primes = {
     15: {
         "prime": int(
             "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
-            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
-            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
-            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
-            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
-            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
-            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
-            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
-            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
-            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
-            + "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
-            + "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
-            + "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
-            + "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
-            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
-            + "43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
+            "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+            "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+            "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+            "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+            "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+            "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+            "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+            "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+            "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+            "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+            "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+            "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+            "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+            "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+            "43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
             base=16,
         ),
         "generator": 2,
@@ -66,27 +66,27 @@ primes = {
     16: {
         "prime": int(
             "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
-            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
-            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
-            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
-            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
-            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
-            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
-            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
-            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
-            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
-            + "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
-            + "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
-            + "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
-            + "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
-            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
-            + "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
-            + "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
-            + "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
-            + "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
-            + "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
-            + "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199"
-            + "FFFFFFFFFFFFFFFF",
+            "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+            "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+            "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+            "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+            "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+            "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+            "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+            "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+            "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+            "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+            "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+            "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+            "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+            "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+            "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
+            "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
+            "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
+            "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
+            "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
+            "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199"
+            "FFFFFFFFFFFFFFFF",
             base=16,
         ),
         "generator": 2,
@@ -95,33 +95,33 @@ primes = {
     17: {
         "prime": int(
             "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08"
-            + "8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
-            + "302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
-            + "A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
-            + "49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8"
-            + "FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D"
-            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C"
-            + "180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718"
-            + "3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D"
-            + "04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D"
-            + "B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226"
-            + "1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
-            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC"
-            + "E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26"
-            + "99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB"
-            + "04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2"
-            + "233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127"
-            + "D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
-            + "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406"
-            + "AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918"
-            + "DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151"
-            + "2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03"
-            + "F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F"
-            + "BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
-            + "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B"
-            + "B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632"
-            + "387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E"
-            + "6DCC4024FFFFFFFFFFFFFFFF",
+            "8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
+            "302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
+            "A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
+            "49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8"
+            "FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+            "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C"
+            "180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718"
+            "3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D"
+            "04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D"
+            "B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226"
+            "1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+            "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC"
+            "E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26"
+            "99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB"
+            "04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2"
+            "233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127"
+            "D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
+            "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406"
+            "AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918"
+            "DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151"
+            "2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03"
+            "F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F"
+            "BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
+            "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B"
+            "B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632"
+            "387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E"
+            "6DCC4024FFFFFFFFFFFFFFFF",
             base=16,
         ),
         "generator": 2,
@@ -130,48 +130,48 @@ primes = {
     18: {
         "prime": int(
             "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
-            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
-            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
-            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
-            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
-            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
-            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
-            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
-            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
-            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
-            + "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
-            + "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
-            + "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
-            + "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
-            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
-            + "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
-            + "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
-            + "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
-            + "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
-            + "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
-            + "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
-            + "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD"
-            + "F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831"
-            + "179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B"
-            + "DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF"
-            + "5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6"
-            + "D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3"
-            + "23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
-            + "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328"
-            + "06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C"
-            + "DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE"
-            + "12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4"
-            + "38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300"
-            + "741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568"
-            + "3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9"
-            + "22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B"
-            + "4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A"
-            + "062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36"
-            + "4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1"
-            + "B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92"
-            + "4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47"
-            + "9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71"
-            + "60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
+            "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+            "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+            "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+            "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+            "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+            "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+            "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+            "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+            "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+            "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+            "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+            "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+            "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+            "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+            "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
+            "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
+            "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
+            "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
+            "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
+            "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
+            "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD"
+            "F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831"
+            "179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B"
+            "DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF"
+            "5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6"
+            "D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3"
+            "23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
+            "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328"
+            "06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C"
+            "DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE"
+            "12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4"
+            "38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300"
+            "741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568"
+            "3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9"
+            "22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B"
+            "4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A"
+            "062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36"
+            "4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1"
+            "B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92"
+            "4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47"
+            "9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71"
+            "60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
             base=16,
         ),
         "generator": 2,

ciphers/enigma_machine2.py

@@ -87,22 +87,20 @@ def _validator(
     # Checks if there are 3 unique rotors
 
     if (unique_rotsel := len(set(rotsel))) < 3:
-        raise Exception(f"Please use 3 unique rotors (not {unique_rotsel})")
+        msg = f"Please use 3 unique rotors (not {unique_rotsel})"
+        raise Exception(msg)
 
     # Checks if rotor positions are valid
     rotorpos1, rotorpos2, rotorpos3 = rotpos
     if not 0 < rotorpos1 <= len(abc):
-        raise ValueError(
-            "First rotor position is not within range of 1..26 (" f"{rotorpos1}"
-        )
+        msg = f"First rotor position is not within range of 1..26 ({rotorpos1}"
+        raise ValueError(msg)
     if not 0 < rotorpos2 <= len(abc):
-        raise ValueError(
-            "Second rotor position is not within range of 1..26 (" f"{rotorpos2})"
-        )
+        msg = f"Second rotor position is not within range of 1..26 ({rotorpos2})"
+        raise ValueError(msg)
     if not 0 < rotorpos3 <= len(abc):
-        raise ValueError(
-            "Third rotor position is not within range of 1..26 (" f"{rotorpos3})"
-        )
+        msg = f"Third rotor position is not within range of 1..26 ({rotorpos3})"
+        raise ValueError(msg)
 
     # Validates string and returns dict
     pbdict = _plugboard(pb)
@@ -130,9 +128,11 @@ def _plugboard(pbstring: str) -> dict[str, str]:
     # a) is type string
     # b) has even length (so pairs can be made)
     if not isinstance(pbstring, str):
-        raise TypeError(f"Plugboard setting isn't type string ({type(pbstring)})")
+        msg = f"Plugboard setting isn't type string ({type(pbstring)})"
+        raise TypeError(msg)
     elif len(pbstring) % 2 != 0:
-        raise Exception(f"Odd number of symbols ({len(pbstring)})")
+        msg = f"Odd number of symbols ({len(pbstring)})"
+        raise Exception(msg)
     elif pbstring == "":
         return {}
 
@@ -142,9 +142,11 @@ def _plugboard(pbstring: str) -> dict[str, str]:
     tmppbl = set()
     for i in pbstring:
         if i not in abc:
-            raise Exception(f"'{i}' not in list of symbols")
+            msg = f"'{i}' not in list of symbols"
+            raise Exception(msg)
         elif i in tmppbl:
-            raise Exception(f"Duplicate symbol ({i})")
+            msg = f"Duplicate symbol ({i})"
+            raise Exception(msg)
         else:
             tmppbl.add(i)
     del tmppbl

ciphers/hill_cipher.py

@@ -104,10 +104,11 @@ class HillCipher:
 
         req_l = len(self.key_string)
         if greatest_common_divisor(det, len(self.key_string)) != 1:
-            raise ValueError(
-                f"determinant modular {req_l} of encryption key({det}) is not co prime "
-                f"w.r.t {req_l}.\nTry another key."
+            msg = (
+                f"determinant modular {req_l} of encryption key({det}) "
+                f"is not co prime w.r.t {req_l}.\nTry another key."
             )
+            raise ValueError(msg)
 
     def process_text(self, text: str) -> str:
         """

ciphers/mixed_keyword_cypher.py

@@ -1,7 +1,11 @@
-def mixed_keyword(key: str = "college", pt: str = "UNIVERSITY") -> str:
-    """
+from string import ascii_uppercase
 
-    For key:hello
+
+def mixed_keyword(
+    keyword: str, plaintext: str, verbose: bool = False, alphabet: str = ascii_uppercase
+) -> str:
+    """
+    For keyword: hello
 
     H E L O
     A B C D
@@ -12,57 +16,60 @@ def mixed_keyword(key: str = "college", pt: str = "UNIVERSITY") -> str:
     Y Z
     and map vertically
 
-    >>> mixed_keyword("college", "UNIVERSITY")  # doctest: +NORMALIZE_WHITESPACE
+    >>> mixed_keyword("college", "UNIVERSITY", True)  # doctest: +NORMALIZE_WHITESPACE
     {'A': 'C', 'B': 'A', 'C': 'I', 'D': 'P', 'E': 'U', 'F': 'Z', 'G': 'O', 'H': 'B',
      'I': 'J', 'J': 'Q', 'K': 'V', 'L': 'L', 'M': 'D', 'N': 'K', 'O': 'R', 'P': 'W',
      'Q': 'E', 'R': 'F', 'S': 'M', 'T': 'S', 'U': 'X', 'V': 'G', 'W': 'H', 'X': 'N',
      'Y': 'T', 'Z': 'Y'}
     'XKJGUFMJST'
+
+    >>> mixed_keyword("college", "UNIVERSITY", False)  # doctest: +NORMALIZE_WHITESPACE
+    'XKJGUFMJST'
     """
-    key = key.upper()
-    pt = pt.upper()
-    temp = []
-    for i in key:
-        if i not in temp:
-            temp.append(i)
-    len_temp = len(temp)
-    # print(temp)
-    alpha = []
-    modalpha = []
-    for j in range(65, 91):
-        t = chr(j)
-        alpha.append(t)
-        if t not in temp:
-            temp.append(t)
-    # print(temp)
-    r = int(26 / 4)
-    # print(r)
-    k = 0
-    for _ in range(r):
-        s = []
-        for _ in range(len_temp):
-            s.append(temp[k])
-            if k >= 25:
+    keyword = keyword.upper()
+    plaintext = plaintext.upper()
+    alphabet_set = set(alphabet)
+
+    # create a list of unique characters in the keyword - their order matters
+    # it determines how we will map plaintext characters to the ciphertext
+    unique_chars = []
+    for char in keyword:
+        if char in alphabet_set and char not in unique_chars:
+            unique_chars.append(char)
+    # the number of those unique characters will determine the number of rows
+    num_unique_chars_in_keyword = len(unique_chars)
+
+    # create a shifted version of the alphabet
+    shifted_alphabet = unique_chars + [
+        char for char in alphabet if char not in unique_chars
+    ]
+
+    # create a modified alphabet by splitting the shifted alphabet into rows
+    modified_alphabet = [
+        shifted_alphabet[k : k + num_unique_chars_in_keyword]
+        for k in range(0, 26, num_unique_chars_in_keyword)
+    ]
+
+    # map the alphabet characters to the modified alphabet characters
+    # going 'vertically' through the modified alphabet - consider columns first
+    mapping = {}
+    letter_index = 0
+    for column in range(num_unique_chars_in_keyword):
+        for row in modified_alphabet:
+            # if current row (the last one) is too short, break out of loop
+            if len(row) <= column:
                 break
-            k += 1
-        modalpha.append(s)
-    # print(modalpha)
-    d = {}
-    j = 0
-    k = 0
-    for j in range(len_temp):
-        for m in modalpha:
-            if not len(m) - 1 >= j:
-                break
-            d[alpha[k]] = m[j]
-            if not k < 25:
-                break
-            k += 1
-    print(d)
-    cypher = ""
-    for i in pt:
-        cypher += d[i]
-    return cypher
+
+            # map current letter to letter in modified alphabet
+            mapping[alphabet[letter_index]] = row[column]
+            letter_index += 1
+
+    if verbose:
+        print(mapping)
+    # create the encrypted text by mapping the plaintext to the modified alphabet
+    return "".join(mapping[char] if char in mapping else char for char in plaintext)
 
 
-print(mixed_keyword("college", "UNIVERSITY"))
+if __name__ == "__main__":
+    # example use
+    print(mixed_keyword("college", "UNIVERSITY"))

compression/burrows_wheeler.py

@@ -150,7 +150,7 @@ def reverse_bwt(bwt_string: str, idx_original_string: int) -> str:
         raise ValueError("The parameter idx_original_string must not be lower than 0.")
     if idx_original_string >= len(bwt_string):
         raise ValueError(
-            "The parameter idx_original_string must be lower than" " len(bwt_string)."
+            "The parameter idx_original_string must be lower than len(bwt_string)."
         )
 
     ordered_rotations = [""] * len(bwt_string)

conversions/astronomical_length_scale_conversion.py

@@ -77,15 +77,17 @@ def length_conversion(value: float, from_type: str, to_type: str) -> float:
     to_sanitized = UNIT_SYMBOL.get(to_sanitized, to_sanitized)
 
     if from_sanitized not in METRIC_CONVERSION:
-        raise ValueError(
+        msg = (
             f"Invalid 'from_type' value: {from_type!r}.\n"
             f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
         )
+        raise ValueError(msg)
     if to_sanitized not in METRIC_CONVERSION:
-        raise ValueError(
+        msg = (
             f"Invalid 'to_type' value: {to_type!r}.\n"
             f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
         )
+        raise ValueError(msg)
     from_exponent = METRIC_CONVERSION[from_sanitized]
     to_exponent = METRIC_CONVERSION[to_sanitized]
     exponent = 1

conversions/energy_conversions.py

@@ -0,0 +1,114 @@
+"""
+Conversion of energy units.
+
+Available units: joule, kilojoule, megajoule, gigajoule,\
+      wattsecond, watthour, kilowatthour, newtonmeter, calorie_nutr,\
+          kilocalorie_nutr, electronvolt, britishthermalunit_it, footpound
+
+USAGE :
+-> Import this file into their respective project.
+-> Use the function energy_conversion() for conversion of energy units.
+-> Parameters :
+    -> from_type : From which type you want to convert
+    -> to_type : To which type you want to convert
+    -> value : the value which you want to convert
+
+REFERENCES :
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Units_of_energy
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Joule
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Kilowatt-hour
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Newton-metre
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Calorie
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Electronvolt
+-> Wikipedia reference: https://en.wikipedia.org/wiki/British_thermal_unit
+-> Wikipedia reference: https://en.wikipedia.org/wiki/Foot-pound_(energy)
+-> Unit converter reference: https://www.unitconverters.net/energy-converter.html
+"""
+
+ENERGY_CONVERSION: dict[str, float] = {
+    "joule": 1.0,
+    "kilojoule": 1_000,
+    "megajoule": 1_000_000,
+    "gigajoule": 1_000_000_000,
+    "wattsecond": 1.0,
+    "watthour": 3_600,
+    "kilowatthour": 3_600_000,
+    "newtonmeter": 1.0,
+    "calorie_nutr": 4_186.8,
+    "kilocalorie_nutr": 4_186_800.00,
+    "electronvolt": 1.602_176_634e-19,
+    "britishthermalunit_it": 1_055.055_85,
+    "footpound": 1.355_818,
+}
+
+
+def energy_conversion(from_type: str, to_type: str, value: float) -> float:
+    """
+    Conversion of energy units.
+    >>> energy_conversion("joule", "joule", 1)
+    1.0
+    >>> energy_conversion("joule", "kilojoule", 1)
+    0.001
+    >>> energy_conversion("joule", "megajoule", 1)
+    1e-06
+    >>> energy_conversion("joule", "gigajoule", 1)
+    1e-09
+    >>> energy_conversion("joule", "wattsecond", 1)
+    1.0
+    >>> energy_conversion("joule", "watthour", 1)
+    0.0002777777777777778
+    >>> energy_conversion("joule", "kilowatthour", 1)
+    2.7777777777777776e-07
+    >>> energy_conversion("joule", "newtonmeter", 1)
+    1.0
+    >>> energy_conversion("joule", "calorie_nutr", 1)
+    0.00023884589662749592
+    >>> energy_conversion("joule", "kilocalorie_nutr", 1)
+    2.388458966274959e-07
+    >>> energy_conversion("joule", "electronvolt", 1)
+    6.241509074460763e+18
+    >>> energy_conversion("joule", "britishthermalunit_it", 1)
+    0.0009478171226670134
+    >>> energy_conversion("joule", "footpound", 1)
+    0.7375621211696556
+    >>> energy_conversion("joule", "megajoule", 1000)
+    0.001
+    >>> energy_conversion("calorie_nutr", "kilocalorie_nutr", 1000)
+    1.0
+    >>> energy_conversion("kilowatthour", "joule", 10)
+    36000000.0
+    >>> energy_conversion("britishthermalunit_it", "footpound", 1)
+    778.1692306784539
+    >>> energy_conversion("watthour", "joule", "a") # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    TypeError: unsupported operand type(s) for /: 'str' and 'float'
+    >>> energy_conversion("wrongunit", "joule", 1) # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    ValueError: Incorrect 'from_type' or 'to_type' value: 'wrongunit', 'joule'
+    Valid values are: joule, ... footpound
+    >>> energy_conversion("joule", "wrongunit", 1) # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    ValueError: Incorrect 'from_type' or 'to_type' value: 'joule', 'wrongunit'
+    Valid values are: joule, ... footpound
+    >>> energy_conversion("123", "abc", 1) # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    ValueError: Incorrect 'from_type' or 'to_type' value: '123', 'abc'
+    Valid values are: joule, ... footpound
+    """
+    if to_type not in ENERGY_CONVERSION or from_type not in ENERGY_CONVERSION:
+        msg = (
+            f"Incorrect 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
+            f"Valid values are: {', '.join(ENERGY_CONVERSION)}"
+        )
+        raise ValueError(msg)
+    return value * ENERGY_CONVERSION[from_type] / ENERGY_CONVERSION[to_type]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

conversions/length_conversion.py

@@ -104,15 +104,17 @@ def length_conversion(value: float, from_type: str, to_type: str) -> float:
     new_to = to_type.lower().rstrip("s")
     new_to = TYPE_CONVERSION.get(new_to, new_to)
     if new_from not in METRIC_CONVERSION:
-        raise ValueError(
+        msg = (
             f"Invalid 'from_type' value: {from_type!r}.\n"
             f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
         )
+        raise ValueError(msg)
     if new_to not in METRIC_CONVERSION:
-        raise ValueError(
+        msg = (
             f"Invalid 'to_type' value: {to_type!r}.\n"
             f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
         )
+        raise ValueError(msg)
     return value * METRIC_CONVERSION[new_from].from_ * METRIC_CONVERSION[new_to].to
 
 

conversions/prefix_conversions_string.py

@@ -96,7 +96,7 @@ def add_si_prefix(value: float) -> str:
     for name_prefix, value_prefix in prefixes.items():
         numerical_part = value / (10**value_prefix)
         if numerical_part > 1:
-            return f"{str(numerical_part)} {name_prefix}"
+            return f"{numerical_part!s} {name_prefix}"
     return str(value)
 
 
@@ -111,7 +111,7 @@ def add_binary_prefix(value: float) -> str:
     for prefix in BinaryUnit:
         numerical_part = value / (2**prefix.value)
         if numerical_part > 1:
-            return f"{str(numerical_part)} {prefix.name}"
+            return f"{numerical_part!s} {prefix.name}"
     return str(value)
 
 

conversions/rgb_hsv_conversion.py

@@ -121,8 +121,8 @@ def rgb_to_hsv(red: int, green: int, blue: int) -> list[float]:
     float_red = red / 255
     float_green = green / 255
     float_blue = blue / 255
-    value = max(max(float_red, float_green), float_blue)
-    chroma = value - min(min(float_red, float_green), float_blue)
+    value = max(float_red, float_green, float_blue)
+    chroma = value - min(float_red, float_green, float_blue)
     saturation = 0 if value == 0 else chroma / value
 
     if chroma == 0:

conversions/speed_conversions.py

@@ -57,10 +57,11 @@ def convert_speed(speed: float, unit_from: str, unit_to: str) -> float:
     115.078
     """
     if unit_to not in speed_chart or unit_from not in speed_chart_inverse:
-        raise ValueError(
+        msg = (
             f"Incorrect 'from_type' or 'to_type' value: {unit_from!r}, {unit_to!r}\n"
             f"Valid values are: {', '.join(speed_chart_inverse)}"
         )
+        raise ValueError(msg)
     return round(speed * speed_chart[unit_from] * speed_chart_inverse[unit_to], 3)
 
 

conversions/weight_conversion.py

@@ -299,10 +299,11 @@ def weight_conversion(from_type: str, to_type: str, value: float) -> float:
     1.999999998903455
     """
     if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
-        raise ValueError(
+        msg = (
             f"Invalid 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
             f"Supported values are: {', '.join(WEIGHT_TYPE_CHART)}"
         )
+        raise ValueError(msg)
     return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]
 
 

data_structures/arrays/permutations.py

@@ -1,7 +1,6 @@
 def permute(nums: list[int]) -> list[list[int]]:
     """
     Return all permutations.
-
     >>> from itertools import permutations
     >>> numbers= [1,2,3]
     >>> all(list(nums) in permute(numbers) for nums in permutations(numbers))
@@ -20,7 +19,32 @@ def permute(nums: list[int]) -> list[list[int]]:
     return result
 
 
+def permute2(nums):
+    """
+    Return all permutations of the given list.
+
+    >>> permute2([1, 2, 3])
+    [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1], [3, 1, 2]]
+    """
+
+    def backtrack(start):
+        if start == len(nums) - 1:
+            output.append(nums[:])
+        else:
+            for i in range(start, len(nums)):
+                nums[start], nums[i] = nums[i], nums[start]
+                backtrack(start + 1)
+                nums[start], nums[i] = nums[i], nums[start]  # backtrack
+
+    output = []
+    backtrack(0)
+    return output
+
+
 if __name__ == "__main__":
     import doctest
 
+    # use res to print the data in permute2 function
+    res = permute2([1, 2, 3])
+    print(res)
     doctest.testmod()

data_structures/arrays/product_sum.py

@@ -0,0 +1,98 @@
+"""
+Calculate the Product Sum from a Special Array.
+reference: https://dev.to/sfrasica/algorithms-product-sum-from-an-array-dc6
+
+Python doctests can be run with the following command:
+python -m doctest -v product_sum.py
+
+Calculate the product sum of a "special" array which can contain integers or nested
+arrays. The product sum is obtained by adding all elements and multiplying by their
+respective depths.
+
+For example, in the array [x, y], the product sum is (x + y). In the array [x, [y, z]],
+the product sum is x + 2 * (y + z). In the array [x, [y, [z]]],
+the product sum is x + 2 * (y + 3z).
+
+Example Input:
+[5, 2, [-7, 1], 3, [6, [-13, 8], 4]]
+Output: 12
+
+"""
+
+
+def product_sum(arr: list[int | list], depth: int) -> int:
+    """
+    Recursively calculates the product sum of an array.
+
+    The product sum of an array is defined as the sum of its elements multiplied by
+    their respective depths.  If an element is a list, its product sum is calculated
+    recursively by multiplying the sum of its elements with its depth plus one.
+
+    Args:
+        arr: The array of integers and nested lists.
+        depth: The current depth level.
+
+    Returns:
+        int: The product sum of the array.
+
+    Examples:
+        >>> product_sum([1, 2, 3], 1)
+        6
+        >>> product_sum([-1, 2, [-3, 4]], 2)
+        8
+        >>> product_sum([1, 2, 3], -1)
+        -6
+        >>> product_sum([1, 2, 3], 0)
+        0
+        >>> product_sum([1, 2, 3], 7)
+        42
+        >>> product_sum((1, 2, 3), 7)
+        42
+        >>> product_sum({1, 2, 3}, 7)
+        42
+        >>> product_sum([1, -1], 1)
+        0
+        >>> product_sum([1, -2], 1)
+        -1
+        >>> product_sum([-3.5, [1, [0.5]]], 1)
+        1.5
+
+    """
+    total_sum = 0
+    for ele in arr:
+        total_sum += product_sum(ele, depth + 1) if isinstance(ele, list) else ele
+    return total_sum * depth
+
+
+def product_sum_array(array: list[int | list]) -> int:
+    """
+    Calculates the product sum of an array.
+
+    Args:
+        array (List[Union[int, List]]): The array of integers and nested lists.
+
+    Returns:
+        int: The product sum of the array.
+
+    Examples:
+        >>> product_sum_array([1, 2, 3])
+        6
+        >>> product_sum_array([1, [2, 3]])
+        11
+        >>> product_sum_array([1, [2, [3, 4]]])
+        47
+        >>> product_sum_array([0])
+        0
+        >>> product_sum_array([-3.5, [1, [0.5]]])
+        1.5
+        >>> product_sum_array([1, -2])
+        -1
+
+    """
+    return product_sum(array, 1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

data_structures/binary_tree/binary_search_tree.py

@@ -40,7 +40,7 @@ class BinarySearchTree:
             else:
                 node.parent.left = new_children
         else:
-            self.root = None
+            self.root = new_children
 
     def is_right(self, node: Node) -> bool:
         if node.parent and node.parent.right:

data_structures/binary_tree/binary_search_tree_recursive.py

@@ -77,7 +77,8 @@ class BinarySearchTree:
             elif label > node.label:
                 node.right = self._put(node.right, label, node)
             else:
-                raise Exception(f"Node with label {label} already exists")
+                msg = f"Node with label {label} already exists"
+                raise Exception(msg)
 
         return node
 
@@ -100,7 +101,8 @@ class BinarySearchTree:
 
     def _search(self, node: Node | None, label: int) -> Node:
         if node is None:
-            raise Exception(f"Node with label {label} does not exist")
+            msg = f"Node with label {label} does not exist"
+            raise Exception(msg)
         else:
             if label < node.label:
                 node = self._search(node.left, label)

data_structures/binary_tree/binary_tree_mirror.py

@@ -31,7 +31,8 @@ def binary_tree_mirror(binary_tree: dict, root: int = 1) -> dict:
     if not binary_tree:
         raise ValueError("binary tree cannot be empty")
     if root not in binary_tree:
-        raise ValueError(f"root {root} is not present in the binary_tree")
+        msg = f"root {root} is not present in the binary_tree"
+        raise ValueError(msg)
     binary_tree_mirror_dictionary = dict(binary_tree)
     binary_tree_mirror_dict(binary_tree_mirror_dictionary, root)
     return binary_tree_mirror_dictionary

data_structures/binary_tree/binary_tree_traversals.py

@@ -58,6 +58,19 @@ def inorder(root: Node | None) -> list[int]:
     return [*inorder(root.left), root.data, *inorder(root.right)] if root else []
 
 
+def reverse_inorder(root: Node | None) -> list[int]:
+    """
+    Reverse in-order traversal visits right subtree, root node, left subtree.
+    >>> reverse_inorder(make_tree())
+    [3, 1, 5, 2, 4]
+    """
+    return (
+        [*reverse_inorder(root.right), root.data, *reverse_inorder(root.left)]
+        if root
+        else []
+    )
+
+
 def height(root: Node | None) -> int:
     """
     Recursive function for calculating the height of the binary tree.
@@ -161,15 +174,12 @@ def zigzag(root: Node | None) -> Sequence[Node | None] | list[Any]:
 
 
 def main() -> None:  # Main function for testing.
-    """
-    Create binary tree.
-    """
+    # Create binary tree.
     root = make_tree()
-    """
-    All Traversals of the binary are as follows:
-    """
 
+    # All Traversals of the binary are as follows:
     print(f"In-order Traversal: {inorder(root)}")
+    print(f"Reverse In-order Traversal: {reverse_inorder(root)}")
     print(f"Pre-order Traversal: {preorder(root)}")
     print(f"Post-order Traversal: {postorder(root)}", "\n")
 

data_structures/binary_tree/red_black_tree.py

@@ -152,7 +152,7 @@ class RedBlackTree:
                     self.grandparent.color = 1
                     self.grandparent._insert_repair()
 
-    def remove(self, label: int) -> RedBlackTree:
+    def remove(self, label: int) -> RedBlackTree:  # noqa: PLR0912
         """Remove label from this tree."""
         if self.label == label:
             if self.left and self.right:

data_structures/binary_tree/segment_tree.py

@@ -7,7 +7,8 @@ class SegmentTree:
         self.st = [0] * (
             4 * self.N
         )  # approximate the overall size of segment tree with array N
-        self.build(1, 0, self.N - 1)
+        if self.N:
+            self.build(1, 0, self.N - 1)
 
     def left(self, idx):
         return idx * 2

data_structures/disjoint_set/disjoint_set.py

@@ -56,7 +56,8 @@ def find_python_set(node: Node) -> set:
     for s in sets:
         if node.data in s:
             return s
-    raise ValueError(f"{node.data} is not in {sets}")
+    msg = f"{node.data} is not in {sets}"
+    raise ValueError(msg)
 
 
 def test_disjoint_set() -> None:

data_structures/heap/heap.py

@@ -1,9 +1,28 @@
 from __future__ import annotations
 
+from abc import abstractmethod
 from collections.abc import Iterable
+from typing import Generic, Protocol, TypeVar
 
 
-class Heap:
+class Comparable(Protocol):
+    @abstractmethod
+    def __lt__(self: T, other: T) -> bool:
+        pass
+
+    @abstractmethod
+    def __gt__(self: T, other: T) -> bool:
+        pass
+
+    @abstractmethod
+    def __eq__(self: T, other: object) -> bool:
+        pass
+
+
+T = TypeVar("T", bound=Comparable)
+
+
+class Heap(Generic[T]):
     """A Max Heap Implementation
 
     >>> unsorted = [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5]
@@ -27,7 +46,7 @@ class Heap:
     """
 
     def __init__(self) -> None:
-        self.h: list[float] = []
+        self.h: list[T] = []
         self.heap_size: int = 0
 
     def __repr__(self) -> str:
@@ -79,7 +98,7 @@ class Heap:
                 # fix the subsequent violation recursively if any
                 self.max_heapify(violation)
 
-    def build_max_heap(self, collection: Iterable[float]) -> None:
+    def build_max_heap(self, collection: Iterable[T]) -> None:
         """build max heap from an unsorted array"""
         self.h = list(collection)
         self.heap_size = len(self.h)
@@ -88,7 +107,7 @@ class Heap:
             for i in range(self.heap_size // 2 - 1, -1, -1):
                 self.max_heapify(i)
 
-    def extract_max(self) -> float:
+    def extract_max(self) -> T:
         """get and remove max from heap"""
         if self.heap_size >= 2:
             me = self.h[0]
@@ -102,7 +121,7 @@ class Heap:
         else:
             raise Exception("Empty heap")
 
-    def insert(self, value: float) -> None:
+    def insert(self, value: T) -> None:
         """insert a new value into the max heap"""
         self.h.append(value)
         idx = (self.heap_size - 1) // 2
@@ -144,7 +163,7 @@ if __name__ == "__main__":
     ]:
         print(f"unsorted array: {unsorted}")
 
-        heap = Heap()
+        heap: Heap[int] = Heap()
         heap.build_max_heap(unsorted)
         print(f"after build heap: {heap}")
 

data_structures/linked_list/circular_linked_list.py

@@ -94,25 +94,25 @@ def test_circular_linked_list() -> None:
 
     try:
         circular_linked_list.delete_front()
-        raise AssertionError()  # This should not happen
+        raise AssertionError  # This should not happen
     except IndexError:
         assert True  # This should happen
 
     try:
         circular_linked_list.delete_tail()
-        raise AssertionError()  # This should not happen
+        raise AssertionError  # This should not happen
     except IndexError:
         assert True  # This should happen
 
     try:
         circular_linked_list.delete_nth(-1)
-        raise AssertionError()
+        raise AssertionError
     except IndexError:
         assert True
 
     try:
         circular_linked_list.delete_nth(0)
-        raise AssertionError()
+        raise AssertionError
     except IndexError:
         assert True
 

data_structures/linked_list/doubly_linked_list.py

@@ -198,13 +198,13 @@ def test_doubly_linked_list() -> None:
 
     try:
         linked_list.delete_head()
-        raise AssertionError()  # This should not happen.
+        raise AssertionError  # This should not happen.
     except IndexError:
         assert True  # This should happen.
 
     try:
         linked_list.delete_tail()
-        raise AssertionError()  # This should not happen.
+        raise AssertionError  # This should not happen.
     except IndexError:
         assert True  # This should happen.
 

data_structures/linked_list/singly_linked_list.py

@@ -353,13 +353,13 @@ def test_singly_linked_list() -> None:
 
     try:
         linked_list.delete_head()
-        raise AssertionError()  # This should not happen.
+        raise AssertionError  # This should not happen.
     except IndexError:
         assert True  # This should happen.
 
     try:
         linked_list.delete_tail()
-        raise AssertionError()  # This should not happen.
+        raise AssertionError  # This should not happen.
     except IndexError:
         assert True  # This should happen.
 

data_structures/queue/double_ended_queue.py

@@ -32,7 +32,7 @@ class Deque:
         the number of nodes
     """
 
-    __slots__ = ["_front", "_back", "_len"]
+    __slots__ = ("_front", "_back", "_len")
 
     @dataclass
     class _Node:
@@ -54,7 +54,7 @@ class Deque:
             the current node of the iteration.
         """
 
-        __slots__ = ["_cur"]
+        __slots__ = ("_cur",)
 
         def __init__(self, cur: Deque._Node | None) -> None:
             self._cur = cur

data_structures/queue/queue_by_list.py

@@ -0,0 +1,141 @@
+"""Queue represented by a Python list"""
+
+from collections.abc import Iterable
+from typing import Generic, TypeVar
+
+_T = TypeVar("_T")
+
+
+class QueueByList(Generic[_T]):
+    def __init__(self, iterable: Iterable[_T] | None = None) -> None:
+        """
+        >>> QueueByList()
+        Queue(())
+        >>> QueueByList([10, 20, 30])
+        Queue((10, 20, 30))
+        >>> QueueByList((i**2 for i in range(1, 4)))
+        Queue((1, 4, 9))
+        """
+        self.entries: list[_T] = list(iterable or [])
+
+    def __len__(self) -> int:
+        """
+        >>> len(QueueByList())
+        0
+        >>> from string import ascii_lowercase
+        >>> len(QueueByList(ascii_lowercase))
+        26
+        >>> queue = QueueByList()
+        >>> for i in range(1, 11):
+        ...     queue.put(i)
+        >>> len(queue)
+        10
+        >>> for i in range(2):
+        ...   queue.get()
+        1
+        2
+        >>> len(queue)
+        8
+        """
+
+        return len(self.entries)
+
+    def __repr__(self) -> str:
+        """
+        >>> queue = QueueByList()
+        >>> queue
+        Queue(())
+        >>> str(queue)
+        'Queue(())'
+        >>> queue.put(10)
+        >>> queue
+        Queue((10,))
+        >>> queue.put(20)
+        >>> queue.put(30)
+        >>> queue
+        Queue((10, 20, 30))
+        """
+
+        return f"Queue({tuple(self.entries)})"
+
+    def put(self, item: _T) -> None:
+        """Put `item` to the Queue
+
+        >>> queue = QueueByList()
+        >>> queue.put(10)
+        >>> queue.put(20)
+        >>> len(queue)
+        2
+        >>> queue
+        Queue((10, 20))
+        """
+
+        self.entries.append(item)
+
+    def get(self) -> _T:
+        """
+        Get `item` from the Queue
+
+        >>> queue = QueueByList((10, 20, 30))
+        >>> queue.get()
+        10
+        >>> queue.put(40)
+        >>> queue.get()
+        20
+        >>> queue.get()
+        30
+        >>> len(queue)
+        1
+        >>> queue.get()
+        40
+        >>> queue.get()
+        Traceback (most recent call last):
+            ...
+        IndexError: Queue is empty
+        """
+
+        if not self.entries:
+            raise IndexError("Queue is empty")
+        return self.entries.pop(0)
+
+    def rotate(self, rotation: int) -> None:
+        """Rotate the items of the Queue `rotation` times
+
+        >>> queue = QueueByList([10, 20, 30, 40])
+        >>> queue
+        Queue((10, 20, 30, 40))
+        >>> queue.rotate(1)
+        >>> queue
+        Queue((20, 30, 40, 10))
+        >>> queue.rotate(2)
+        >>> queue
+        Queue((40, 10, 20, 30))
+        """
+
+        put = self.entries.append
+        get = self.entries.pop
+
+        for _ in range(rotation):
+            put(get(0))
+
+    def get_front(self) -> _T:
+        """Get the front item from the Queue
+
+        >>> queue = QueueByList((10, 20, 30))
+        >>> queue.get_front()
+        10
+        >>> queue
+        Queue((10, 20, 30))
+        >>> queue.get()
+        10
+        >>> queue.get_front()
+        20
+        """
+
+        return self.entries[0]
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()

data_structures/queue/queue_on_list.py

@@ -1,52 +0,0 @@
-"""Queue represented by a Python list"""
-
-
-class Queue:
-    def __init__(self):
-        self.entries = []
-        self.length = 0
-        self.front = 0
-
-    def __str__(self):
-        printed = "<" + str(self.entries)[1:-1] + ">"
-        return printed
-
-    """Enqueues {@code item}
-    @param item
-        item to enqueue"""
-
-    def put(self, item):
-        self.entries.append(item)
-        self.length = self.length + 1
-
-    """Dequeues {@code item}
-    @requirement: |self.length| > 0
-    @return dequeued
-        item that was dequeued"""
-
-    def get(self):
-        self.length = self.length - 1
-        dequeued = self.entries[self.front]
-        # self.front-=1
-        # self.entries = self.entries[self.front:]
-        self.entries = self.entries[1:]
-        return dequeued
-
-    """Rotates the queue {@code rotation} times
-    @param rotation
-        number of times to rotate queue"""
-
-    def rotate(self, rotation):
-        for _ in range(rotation):
-            self.put(self.get())
-
-    """Enqueues {@code item}
-    @return item at front of self.entries"""
-
-    def get_front(self):
-        return self.entries[0]
-
-    """Returns the length of this.entries"""
-
-    def size(self):
-        return self.length

data_structures/stacks/stack.py

@@ -92,13 +92,13 @@ def test_stack() -> None:
 
     try:
         _ = stack.pop()
-        raise AssertionError()  # This should not happen
+        raise AssertionError  # This should not happen
     except StackUnderflowError:
         assert True  # This should happen
 
     try:
         _ = stack.peek()
-        raise AssertionError()  # This should not happen
+        raise AssertionError  # This should not happen
     except StackUnderflowError:
         assert True  # This should happen
 
@@ -118,7 +118,7 @@ def test_stack() -> None:
 
     try:
         stack.push(200)
-        raise AssertionError()  # This should not happen
+        raise AssertionError  # This should not happen
     except StackOverflowError:
         assert True  # This should happen
 

data_structures/trie/radix_tree.py

@@ -54,10 +54,17 @@ class RadixNode:
             word (str): word to insert
 
         >>> RadixNode("myprefix").insert("mystring")
+
+        >>> root = RadixNode()
+        >>> root.insert_many(['myprefix', 'myprefixA', 'myprefixAA'])
+        >>> root.print_tree()
+        - myprefix   (leaf)
+        -- A   (leaf)
+        --- A   (leaf)
         """
         # Case 1: If the word is the prefix of the node
         # Solution: We set the current node as leaf
-        if self.prefix == word:
+        if self.prefix == word and not self.is_leaf:
             self.is_leaf = True
 
         # Case 2: The node has no edges that have a prefix to the word
@@ -156,7 +163,7 @@ class RadixNode:
                         del self.nodes[word[0]]
                         # We merge the current node with its only child
                         if len(self.nodes) == 1 and not self.is_leaf:
-                            merging_node = list(self.nodes.values())[0]
+                            merging_node = next(iter(self.nodes.values()))
                             self.is_leaf = merging_node.is_leaf
                             self.prefix += merging_node.prefix
                             self.nodes = merging_node.nodes
@@ -165,7 +172,7 @@ class RadixNode:
                         incoming_node.is_leaf = False
                     # If there is 1 edge, we merge it with its child
                     else:
-                        merging_node = list(incoming_node.nodes.values())[0]
+                        merging_node = next(iter(incoming_node.nodes.values()))
                         incoming_node.is_leaf = merging_node.is_leaf
                         incoming_node.prefix += merging_node.prefix
                         incoming_node.nodes = merging_node.nodes

digital_image_processing/dithering/burkes.py

@@ -21,7 +21,8 @@ class Burkes:
         self.max_threshold = int(self.get_greyscale(255, 255, 255))
 
         if not self.min_threshold < threshold < self.max_threshold:
-            raise ValueError(f"Factor value should be from 0 to {self.max_threshold}")
+            msg = f"Factor value should be from 0 to {self.max_threshold}"
+            raise ValueError(msg)
 
         self.input_img = input_img
         self.threshold = threshold
@@ -38,9 +39,18 @@ class Burkes:
     def get_greyscale(cls, blue: int, green: int, red: int) -> float:
         """
         >>> Burkes.get_greyscale(3, 4, 5)
-        3.753
+        4.185
+        >>> Burkes.get_greyscale(0, 0, 0)
+        0.0
+        >>> Burkes.get_greyscale(255, 255, 255)
+        255.0
         """
-        return 0.114 * blue + 0.587 * green + 0.2126 * red
+        """
+        Formula from https://en.wikipedia.org/wiki/HSL_and_HSV
+        cf Lightness section, and Fig 13c.
+        We use the first of four possible.
+        """
+        return 0.114 * blue + 0.587 * green + 0.299 * red
 
     def process(self) -> None:
         for y in range(self.height):
@@ -48,10 +58,10 @@ class Burkes:
                 greyscale = int(self.get_greyscale(*self.input_img[y][x]))
                 if self.threshold > greyscale + self.error_table[y][x]:
                     self.output_img[y][x] = (0, 0, 0)
-                    current_error = greyscale + self.error_table[x][y]
+                    current_error = greyscale + self.error_table[y][x]
                 else:
                     self.output_img[y][x] = (255, 255, 255)
-                    current_error = greyscale + self.error_table[x][y] - 255
+                    current_error = greyscale + self.error_table[y][x] - 255
                 """
                 Burkes error propagation (`*` is current pixel):
 

digital_image_processing/test_digital_image_processing.py

@@ -96,7 +96,7 @@ def test_nearest_neighbour(
 
 
 def test_local_binary_pattern():
-    file_path: str = "digital_image_processing/image_data/lena.jpg"
+    file_path = "digital_image_processing/image_data/lena.jpg"
 
     # Reading the image and converting it to grayscale.
     image = imread(file_path, 0)

divide_and_conquer/convex_hull.py

@@ -174,12 +174,12 @@ def _validate_input(points: list[Point] | list[list[float]]) -> list[Point]:
     """
 
     if not hasattr(points, "__iter__"):
-        raise ValueError(
-            f"Expecting an iterable object but got an non-iterable type {points}"
-        )
+        msg = f"Expecting an iterable object but got an non-iterable type {points}"
+        raise ValueError(msg)
 
     if not points:
-        raise ValueError(f"Expecting a list of points but got {points}")
+        msg = f"Expecting a list of points but got {points}"
+        raise ValueError(msg)
 
     return _construct_points(points)
 
@@ -266,7 +266,7 @@ def convex_hull_bf(points: list[Point]) -> list[Point]:
             points_left_of_ij = points_right_of_ij = False
             ij_part_of_convex_hull = True
             for k in range(n):
-                if k != i and k != j:
+                if k not in {i, j}:
                     det_k = _det(points[i], points[j], points[k])
 
                     if det_k > 0:

divide_and_conquer/max_subarray.py

@@ -0,0 +1,112 @@
+"""
+The maximum subarray problem is the task of finding the continuous subarray that has the
+maximum sum within a given array of numbers. For example, given the array
+[-2, 1, -3, 4, -1, 2, 1, -5, 4], the contiguous subarray with the maximum sum is
+[4, -1, 2, 1], which has a sum of 6.
+
+This divide-and-conquer algorithm finds the maximum subarray in O(n log n) time.
+"""
+from __future__ import annotations
+
+import time
+from collections.abc import Sequence
+from random import randint
+
+from matplotlib import pyplot as plt
+
+
+def max_subarray(
+    arr: Sequence[float], low: int, high: int
+) -> tuple[int | None, int | None, float]:
+    """
+    Solves the maximum subarray problem using divide and conquer.
+    :param arr:     the given array of numbers
+    :param low:     the start index
+    :param high:    the end index
+    :return:        the start index of the maximum subarray, the end index of the
+                    maximum subarray, and the maximum subarray sum
+
+    >>> nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
+    >>> max_subarray(nums, 0, len(nums) - 1)
+    (3, 6, 6)
+    >>> nums = [2, 8, 9]
+    >>> max_subarray(nums, 0, len(nums) - 1)
+    (0, 2, 19)
+    >>> nums = [0, 0]
+    >>> max_subarray(nums, 0, len(nums) - 1)
+    (0, 0, 0)
+    >>> nums = [-1.0, 0.0, 1.0]
+    >>> max_subarray(nums, 0, len(nums) - 1)
+    (2, 2, 1.0)
+    >>> nums = [-2, -3, -1, -4, -6]
+    >>> max_subarray(nums, 0, len(nums) - 1)
+    (2, 2, -1)
+    >>> max_subarray([], 0, 0)
+    (None, None, 0)
+    """
+    if not arr:
+        return None, None, 0
+    if low == high:
+        return low, high, arr[low]
+
+    mid = (low + high) // 2
+    left_low, left_high, left_sum = max_subarray(arr, low, mid)
+    right_low, right_high, right_sum = max_subarray(arr, mid + 1, high)
+    cross_left, cross_right, cross_sum = max_cross_sum(arr, low, mid, high)
+    if left_sum >= right_sum and left_sum >= cross_sum:
+        return left_low, left_high, left_sum
+    elif right_sum >= left_sum and right_sum >= cross_sum:
+        return right_low, right_high, right_sum
+    return cross_left, cross_right, cross_sum
+
+
+def max_cross_sum(
+    arr: Sequence[float], low: int, mid: int, high: int
+) -> tuple[int, int, float]:
+    left_sum, max_left = float("-inf"), -1
+    right_sum, max_right = float("-inf"), -1
+
+    summ: int | float = 0
+    for i in range(mid, low - 1, -1):
+        summ += arr[i]
+        if summ > left_sum:
+            left_sum = summ
+            max_left = i
+
+    summ = 0
+    for i in range(mid + 1, high + 1):
+        summ += arr[i]
+        if summ > right_sum:
+            right_sum = summ
+            max_right = i
+
+    return max_left, max_right, (left_sum + right_sum)
+
+
+def time_max_subarray(input_size: int) -> float:
+    arr = [randint(1, input_size) for _ in range(input_size)]
+    start = time.time()
+    max_subarray(arr, 0, input_size - 1)
+    end = time.time()
+    return end - start
+
+
+def plot_runtimes() -> None:
+    input_sizes = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
+    runtimes = [time_max_subarray(input_size) for input_size in input_sizes]
+    print("No of Inputs\t\tTime Taken")
+    for input_size, runtime in zip(input_sizes, runtimes):
+        print(input_size, "\t\t", runtime)
+    plt.plot(input_sizes, runtimes)
+    plt.xlabel("Number of Inputs")
+    plt.ylabel("Time taken in seconds")
+    plt.show()
+
+
+if __name__ == "__main__":
+    """
+    A random simulation of this algorithm.
+    """
+    from doctest import testmod
+
+    testmod()

divide_and_conquer/max_subarray_sum.py

@@ -1,78 +0,0 @@
-"""
-Given a array of length n, max_subarray_sum() finds
-the maximum of sum of contiguous sub-array using divide and conquer method.
-
-Time complexity : O(n log n)
-
-Ref : INTRODUCTION TO ALGORITHMS THIRD EDITION
-(section : 4, sub-section : 4.1, page : 70)
-
-"""
-
-
-def max_sum_from_start(array):
-    """This function finds the maximum contiguous sum of array from 0 index
-
-    Parameters :
-    array (list[int]) : given array
-
-    Returns :
-    max_sum (int) : maximum contiguous sum of array from 0 index
-
-    """
-    array_sum = 0
-    max_sum = float("-inf")
-    for num in array:
-        array_sum += num
-        if array_sum > max_sum:
-            max_sum = array_sum
-    return max_sum
-
-
-def max_cross_array_sum(array, left, mid, right):
-    """This function finds the maximum contiguous sum of left and right arrays
-
-    Parameters :
-    array, left, mid, right (list[int], int, int, int)
-
-    Returns :
-    (int) :  maximum of sum of contiguous sum of left and right arrays
-
-    """
-
-    max_sum_of_left = max_sum_from_start(array[left : mid + 1][::-1])
-    max_sum_of_right = max_sum_from_start(array[mid + 1 : right + 1])
-    return max_sum_of_left + max_sum_of_right
-
-
-def max_subarray_sum(array, left, right):
-    """Maximum contiguous sub-array sum, using divide and conquer method
-
-    Parameters :
-    array, left, right (list[int], int, int) :
-    given array, current left index and current right index
-
-    Returns :
-    int :  maximum of sum of contiguous sub-array
-
-    """
-
-    # base case: array has only one element
-    if left == right:
-        return array[right]
-
-    # Recursion
-    mid = (left + right) // 2
-    left_half_sum = max_subarray_sum(array, left, mid)
-    right_half_sum = max_subarray_sum(array, mid + 1, right)
-    cross_sum = max_cross_array_sum(array, left, mid, right)
-    return max(left_half_sum, right_half_sum, cross_sum)
-
-
-if __name__ == "__main__":
-    array = [-2, -5, 6, -2, -3, 1, 5, -6]
-    array_length = len(array)
-    print(
-        "Maximum sum of contiguous subarray:",
-        max_subarray_sum(array, 0, array_length - 1),
-    )

divide_and_conquer/strassen_matrix_multiplication.py

@@ -112,17 +112,19 @@ def strassen(matrix1: list, matrix2: list) -> list:
     [[139, 163], [121, 134], [100, 121]]
     """
     if matrix_dimensions(matrix1)[1] != matrix_dimensions(matrix2)[0]:
-        raise Exception(
-            "Unable to multiply these matrices, please check the dimensions. \n"
-            f"Matrix A:{matrix1} \nMatrix B:{matrix2}"
+        msg = (
+            "Unable to multiply these matrices, please check the dimensions.\n"
+            f"Matrix A: {matrix1}\n"
+            f"Matrix B: {matrix2}"
         )
+        raise Exception(msg)
     dimension1 = matrix_dimensions(matrix1)
     dimension2 = matrix_dimensions(matrix2)
 
     if dimension1[0] == dimension1[1] and dimension2[0] == dimension2[1]:
         return [matrix1, matrix2]
 
-    maximum = max(max(dimension1), max(dimension2))
+    maximum = max(*dimension1, *dimension2)
     maxim = int(math.pow(2, math.ceil(math.log2(maximum))))
     new_matrix1 = matrix1
     new_matrix2 = matrix2

dynamic_programming/fibonacci.py

@@ -24,7 +24,7 @@ class Fibonacci:
         return self.sequence[:index]
 
 
-def main():
+def main() -> None:
     print(
         "Fibonacci Series Using Dynamic Programming\n",
         "Enter the index of the Fibonacci number you want to calculate ",

dynamic_programming/knapsack.py

@@ -78,17 +78,18 @@ def knapsack_with_example_solution(w: int, wt: list, val: list):
 
     num_items = len(wt)
     if num_items != len(val):
-        raise ValueError(
-            "The number of weights must be the "
-            "same as the number of values.\nBut "
-            f"got {num_items} weights and {len(val)} values"
+        msg = (
+            "The number of weights must be the same as the number of values.\n"
+            f"But got {num_items} weights and {len(val)} values"
         )
+        raise ValueError(msg)
     for i in range(num_items):
         if not isinstance(wt[i], int):
-            raise TypeError(
-                "All weights must be integers but "
-                f"got weight of type {type(wt[i])} at index {i}"
+            msg = (
+                "All weights must be integers but got weight of "
+                f"type {type(wt[i])} at index {i}"
             )
+            raise TypeError(msg)
 
     optimal_val, dp_table = knapsack(w, wt, val, num_items)
     example_optional_set: set = set()

dynamic_programming/max_sub_array.py

@@ -1,93 +0,0 @@
-"""
-author : Mayank Kumar Jha (mk9440)
-"""
-from __future__ import annotations
-
-
-def find_max_sub_array(a, low, high):
-    if low == high:
-        return low, high, a[low]
-    else:
-        mid = (low + high) // 2
-        left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
-        right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
-        cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
-        if left_sum >= right_sum and left_sum >= cross_sum:
-            return left_low, left_high, left_sum
-        elif right_sum >= left_sum and right_sum >= cross_sum:
-            return right_low, right_high, right_sum
-        else:
-            return cross_left, cross_right, cross_sum
-
-
-def find_max_cross_sum(a, low, mid, high):
-    left_sum, max_left = -999999999, -1
-    right_sum, max_right = -999999999, -1
-    summ = 0
-    for i in range(mid, low - 1, -1):
-        summ += a[i]
-        if summ > left_sum:
-            left_sum = summ
-            max_left = i
-    summ = 0
-    for i in range(mid + 1, high + 1):
-        summ += a[i]
-        if summ > right_sum:
-            right_sum = summ
-            max_right = i
-    return max_left, max_right, (left_sum + right_sum)
-
-
-def max_sub_array(nums: list[int]) -> int:
-    """
-    Finds the contiguous subarray which has the largest sum and return its sum.
-
-    >>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
-    6
-
-    An empty (sub)array has sum 0.
-    >>> max_sub_array([])
-    0
-
-    If all elements are negative, the largest subarray would be the empty array,
-    having the sum 0.
-    >>> max_sub_array([-1, -2, -3])
-    0
-    >>> max_sub_array([5, -2, -3])
-    5
-    >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
-    187
-    """
-    best = 0
-    current = 0
-    for i in nums:
-        current += i
-        current = max(current, 0)
-        best = max(best, current)
-    return best
-
-
-if __name__ == "__main__":
-    """
-    A random simulation of this algorithm.
-    """
-    import time
-    from random import randint
-
-    from matplotlib import pyplot as plt
-
-    inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
-    tim = []
-    for i in inputs:
-        li = [randint(1, i) for j in range(i)]
-        strt = time.time()
-        (find_max_sub_array(li, 0, len(li) - 1))
-        end = time.time()
-        tim.append(end - strt)
-    print("No of Inputs       Time Taken")
-    for i in range(len(inputs)):
-        print(inputs[i], "\t\t", tim[i])
-    plt.plot(inputs, tim)
-    plt.xlabel("Number of Inputs")
-    plt.ylabel("Time taken in seconds ")
-    plt.show()

dynamic_programming/max_subarray_sum.py

@@ -0,0 +1,60 @@
+"""
+The maximum subarray sum problem is the task of finding the maximum sum that can be
+obtained from a contiguous subarray within a given array of numbers. For example, given
+the array [-2, 1, -3, 4, -1, 2, 1, -5, 4], the contiguous subarray with the maximum sum
+is [4, -1, 2, 1], so the maximum subarray sum is 6.
+
+Kadane's algorithm is a simple dynamic programming algorithm that solves the maximum
+subarray sum problem in O(n) time and O(1) space.
+
+Reference: https://en.wikipedia.org/wiki/Maximum_subarray_problem
+"""
+from collections.abc import Sequence
+
+
+def max_subarray_sum(
+    arr: Sequence[float], allow_empty_subarrays: bool = False
+) -> float:
+    """
+    Solves the maximum subarray sum problem using Kadane's algorithm.
+    :param arr: the given array of numbers
+    :param allow_empty_subarrays: if True, then the algorithm considers empty subarrays
+
+    >>> max_subarray_sum([2, 8, 9])
+    19
+    >>> max_subarray_sum([0, 0])
+    0
+    >>> max_subarray_sum([-1.0, 0.0, 1.0])
+    1.0
+    >>> max_subarray_sum([1, 2, 3, 4, -2])
+    10
+    >>> max_subarray_sum([-2, 1, -3, 4, -1, 2, 1, -5, 4])
+    6
+    >>> max_subarray_sum([2, 3, -9, 8, -2])
+    8
+    >>> max_subarray_sum([-2, -3, -1, -4, -6])
+    -1
+    >>> max_subarray_sum([-2, -3, -1, -4, -6], allow_empty_subarrays=True)
+    0
+    >>> max_subarray_sum([])
+    0
+    """
+    if not arr:
+        return 0
+
+    max_sum = 0 if allow_empty_subarrays else float("-inf")
+    curr_sum = 0.0
+    for num in arr:
+        curr_sum = max(0 if allow_empty_subarrays else num, curr_sum + num)
+        max_sum = max(max_sum, curr_sum)
+
+    return max_sum
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+
+    nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
+    print(f"{max_subarray_sum(nums) = }")

dynamic_programming/max_sum_contiguous_subsequence.py

@@ -1,20 +0,0 @@
-def max_subarray_sum(nums: list) -> int:
-    """
-    >>> max_subarray_sum([6 , 9, -1, 3, -7, -5, 10])
-    17
-    """
-    if not nums:
-        return 0
-    n = len(nums)
-
-    res, s, s_pre = nums[0], nums[0], nums[0]
-    for i in range(1, n):
-        s = max(nums[i], s_pre + nums[i])
-        s_pre = s
-        res = max(res, s)
-    return res
-
-
-if __name__ == "__main__":
-    nums = [6, 9, -1, 3, -7, -5, 10]
-    print(max_subarray_sum(nums))

dynamic_programming/minimum_steps_to_one.py

@@ -42,7 +42,8 @@ def min_steps_to_one(number: int) -> int:
     """
 
     if number <= 0:
-        raise ValueError(f"n must be greater than 0. Got n = {number}")
+        msg = f"n must be greater than 0. Got n = {number}"
+        raise ValueError(msg)
 
     table = [number + 1] * (number + 1)
 

dynamic_programming/rod_cutting.py

@@ -177,13 +177,15 @@ def _enforce_args(n: int, prices: list):
     the rod
     """
     if n < 0:
-        raise ValueError(f"n must be greater than or equal to 0. Got n = {n}")
+        msg = f"n must be greater than or equal to 0. Got n = {n}"
+        raise ValueError(msg)
 
     if n > len(prices):
-        raise ValueError(
-            "Each integral piece of rod must have a corresponding "
-            f"price. Got n = {n} but length of prices = {len(prices)}"
+        msg = (
+            "Each integral piece of rod must have a corresponding price. "
+            f"Got n = {n} but length of prices = {len(prices)}"
         )
+        raise ValueError(msg)
 
 
 def main():

dynamic_programming/viterbi.py

@@ -297,11 +297,13 @@ def _validate_list(_object: Any, var_name: str) -> None:
 
     """
     if not isinstance(_object, list):
-        raise ValueError(f"{var_name} must be a list")
+        msg = f"{var_name} must be a list"
+        raise ValueError(msg)
     else:
         for x in _object:
             if not isinstance(x, str):
-                raise ValueError(f"{var_name} must be a list of strings")
+                msg = f"{var_name} must be a list of strings"
+                raise ValueError(msg)
 
 
 def _validate_dicts(
@@ -384,14 +386,15 @@ def _validate_dict(
     ValueError: mock_name nested dictionary all values must be float
     """
     if not isinstance(_object, dict):
-        raise ValueError(f"{var_name} must be a dict")
+        msg = f"{var_name} must be a dict"
+        raise ValueError(msg)
     if not all(isinstance(x, str) for x in _object):
-        raise ValueError(f"{var_name} all keys must be strings")
+        msg = f"{var_name} all keys must be strings"
+        raise ValueError(msg)
     if not all(isinstance(x, value_type) for x in _object.values()):
         nested_text = "nested dictionary " if nested else ""
-        raise ValueError(
-            f"{var_name} {nested_text}all values must be {value_type.__name__}"
-        )
+        msg = f"{var_name} {nested_text}all values must be {value_type.__name__}"
+        raise ValueError(msg)
 
 
 if __name__ == "__main__":

electronics/resistor_equivalence.py

@@ -23,7 +23,8 @@ def resistor_parallel(resistors: list[float]) -> float:
     index = 0
     for resistor in resistors:
         if resistor <= 0:
-            raise ValueError(f"Resistor at index {index} has a negative or zero value!")
+            msg = f"Resistor at index {index} has a negative or zero value!"
+            raise ValueError(msg)
         first_sum += 1 / float(resistor)
         index += 1
     return 1 / first_sum
@@ -47,7 +48,8 @@ def resistor_series(resistors: list[float]) -> float:
     for resistor in resistors:
         sum_r += resistor
         if resistor < 0:
-            raise ValueError(f"Resistor at index {index} has a negative value!")
+            msg = f"Resistor at index {index} has a negative value!"
+            raise ValueError(msg)
         index += 1
     return sum_r
 

financial/interest.py

@@ -4,7 +4,7 @@ from __future__ import annotations
 
 
 def simple_interest(
-    principal: float, daily_interest_rate: float, days_between_payments: int
+    principal: float, daily_interest_rate: float, days_between_payments: float
 ) -> float:
     """
     >>> simple_interest(18000.0, 0.06, 3)
@@ -42,7 +42,7 @@ def simple_interest(
 def compound_interest(
     principal: float,
     nominal_annual_interest_rate_percentage: float,
-    number_of_compounding_periods: int,
+    number_of_compounding_periods: float,
 ) -> float:
     """
     >>> compound_interest(10000.0, 0.05, 3)
@@ -77,6 +77,43 @@ def compound_interest(
     )
 
 
+def apr_interest(
+    principal: float,
+    nominal_annual_percentage_rate: float,
+    number_of_years: float,
+) -> float:
+    """
+    >>> apr_interest(10000.0, 0.05, 3)
+    1618.223072263547
+    >>> apr_interest(10000.0, 0.05, 1)
+    512.6749646744732
+    >>> apr_interest(0.5, 0.05, 3)
+    0.08091115361317736
+    >>> apr_interest(10000.0, 0.06, -4)
+    Traceback (most recent call last):
+        ...
+    ValueError: number_of_years must be > 0
+    >>> apr_interest(10000.0, -3.5, 3.0)
+    Traceback (most recent call last):
+        ...
+    ValueError: nominal_annual_percentage_rate must be >= 0
+    >>> apr_interest(-5500.0, 0.01, 5)
+    Traceback (most recent call last):
+        ...
+    ValueError: principal must be > 0
+    """
+    if number_of_years <= 0:
+        raise ValueError("number_of_years must be > 0")
+    if nominal_annual_percentage_rate < 0:
+        raise ValueError("nominal_annual_percentage_rate must be >= 0")
+    if principal <= 0:
+        raise ValueError("principal must be > 0")
+
+    return compound_interest(
+        principal, nominal_annual_percentage_rate / 365, number_of_years * 365
+    )
+
+
 if __name__ == "__main__":
     import doctest
 

financial/present_value.py

@@ -0,0 +1,42 @@
+"""
+Reference: https://www.investopedia.com/terms/p/presentvalue.asp
+
+An algorithm that calculates the present value of a stream of yearly cash flows given...
+1. The discount rate (as a decimal, not a percent)
+2. An array of cash flows, with the index of the cash flow being the associated year
+
+Note: This algorithm assumes that cash flows are paid at the end of the specified year
+"""
+
+
+def present_value(discount_rate: float, cash_flows: list[float]) -> float:
+    """
+    >>> present_value(0.13, [10, 20.70, -293, 297])
+    4.69
+    >>> present_value(0.07, [-109129.39, 30923.23, 15098.93, 29734,39])
+    -42739.63
+    >>> present_value(0.07, [109129.39, 30923.23, 15098.93, 29734,39])
+    175519.15
+    >>> present_value(-1, [109129.39, 30923.23, 15098.93, 29734,39])
+    Traceback (most recent call last):
+        ...
+    ValueError: Discount rate cannot be negative
+    >>> present_value(0.03, [])
+    Traceback (most recent call last):
+        ...
+    ValueError: Cash flows list cannot be empty
+    """
+    if discount_rate < 0:
+        raise ValueError("Discount rate cannot be negative")
+    if not cash_flows:
+        raise ValueError("Cash flows list cannot be empty")
+    present_value = sum(
+        cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(cash_flows)
+    )
+    return round(present_value, ndigits=2)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

fractals/sierpinski_triangle.py

@@ -82,3 +82,4 @@ if __name__ == "__main__":
 
     vertices = [(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
     triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))
+    turtle.Screen().exitonclick()

genetic_algorithm/basic_string.py

@@ -21,6 +21,54 @@ MUTATION_PROBABILITY = 0.4
 random.seed(random.randint(0, 1000))
 
 
+def evaluate(item: str, main_target: str) -> tuple[str, float]:
+    """
+    Evaluate how similar the item is with the target by just
+    counting each char in the right position
+    >>> evaluate("Helxo Worlx", "Hello World")
+    ('Helxo Worlx', 9.0)
+    """
+    score = len([g for position, g in enumerate(item) if g == main_target[position]])
+    return (item, float(score))
+
+
+def crossover(parent_1: str, parent_2: str) -> tuple[str, str]:
+    """Slice and combine two string at a random point."""
+    random_slice = random.randint(0, len(parent_1) - 1)
+    child_1 = parent_1[:random_slice] + parent_2[random_slice:]
+    child_2 = parent_2[:random_slice] + parent_1[random_slice:]
+    return (child_1, child_2)
+
+
+def mutate(child: str, genes: list[str]) -> str:
+    """Mutate a random gene of a child with another one from the list."""
+    child_list = list(child)
+    if random.uniform(0, 1) < MUTATION_PROBABILITY:
+        child_list[random.randint(0, len(child)) - 1] = random.choice(genes)
+    return "".join(child_list)
+
+
+# Select, crossover and mutate a new population.
+def select(
+    parent_1: tuple[str, float],
+    population_score: list[tuple[str, float]],
+    genes: list[str],
+) -> list[str]:
+    """Select the second parent and generate new population"""
+    pop = []
+    # Generate more children proportionally to the fitness score.
+    child_n = int(parent_1[1] * 100) + 1
+    child_n = 10 if child_n >= 10 else child_n
+    for _ in range(child_n):
+        parent_2 = population_score[random.randint(0, N_SELECTED)][0]
+
+        child_1, child_2 = crossover(parent_1[0], parent_2)
+        # Append new string to the population list.
+        pop.append(mutate(child_1, genes))
+        pop.append(mutate(child_2, genes))
+    return pop
+
+
 def basic(target: str, genes: list[str], debug: bool = True) -> tuple[int, int, str]:
     """
     Verify that the target contains no genes besides the ones inside genes variable.
@@ -48,13 +96,13 @@ def basic(target: str, genes: list[str], debug: bool = True) -> tuple[int, int,
 
     # Verify if N_POPULATION is bigger than N_SELECTED
     if N_POPULATION < N_SELECTED:
-        raise ValueError(f"{N_POPULATION} must be bigger than {N_SELECTED}")
+        msg = f"{N_POPULATION} must be bigger than {N_SELECTED}"
+        raise ValueError(msg)
     # Verify that the target contains no genes besides the ones inside genes variable.
     not_in_genes_list = sorted({c for c in target if c not in genes})
     if not_in_genes_list:
-        raise ValueError(
-            f"{not_in_genes_list} is not in genes list, evolution cannot converge"
-        )
+        msg = f"{not_in_genes_list} is not in genes list, evolution cannot converge"
+        raise ValueError(msg)
 
     # Generate random starting population.
     population = []
@@ -70,17 +118,6 @@ def basic(target: str, genes: list[str], debug: bool = True) -> tuple[int, int,
         total_population += len(population)
 
         # Random population created. Now it's time to evaluate.
-        def evaluate(item: str, main_target: str = target) -> tuple[str, float]:
-            """
-            Evaluate how similar the item is with the target by just
-            counting each char in the right position
-            >>> evaluate("Helxo Worlx", Hello World)
-            ["Helxo Worlx", 9]
-            """
-            score = len(
-                [g for position, g in enumerate(item) if g == main_target[position]]
-            )
-            return (item, float(score))
 
         # Adding a bit of concurrency can make everything faster,
         #
@@ -94,7 +131,7 @@ def basic(target: str, genes: list[str], debug: bool = True) -> tuple[int, int,
         #
         # but with a simple algorithm like this, it will probably be slower.
         # We just need to call evaluate for every item inside the population.
-        population_score = [evaluate(item) for item in population]
+        population_score = [evaluate(item, target) for item in population]
 
         # Check if there is a matching evolution.
         population_score = sorted(population_score, key=lambda x: x[1], reverse=True)
@@ -121,41 +158,9 @@ def basic(target: str, genes: list[str], debug: bool = True) -> tuple[int, int,
             (item, score / len(target)) for item, score in population_score
         ]
 
-        # Select, crossover and mutate a new population.
-        def select(parent_1: tuple[str, float]) -> list[str]:
-            """Select the second parent and generate new population"""
-            pop = []
-            # Generate more children proportionally to the fitness score.
-            child_n = int(parent_1[1] * 100) + 1
-            child_n = 10 if child_n >= 10 else child_n
-            for _ in range(child_n):
-                parent_2 = population_score[  # noqa: B023
-                    random.randint(0, N_SELECTED)
-                ][0]
-
-                child_1, child_2 = crossover(parent_1[0], parent_2)
-                # Append new string to the population list.
-                pop.append(mutate(child_1))
-                pop.append(mutate(child_2))
-            return pop
-
-        def crossover(parent_1: str, parent_2: str) -> tuple[str, str]:
-            """Slice and combine two string at a random point."""
-            random_slice = random.randint(0, len(parent_1) - 1)
-            child_1 = parent_1[:random_slice] + parent_2[random_slice:]
-            child_2 = parent_2[:random_slice] + parent_1[random_slice:]
-            return (child_1, child_2)
-
-        def mutate(child: str) -> str:
-            """Mutate a random gene of a child with another one from the list."""
-            child_list = list(child)
-            if random.uniform(0, 1) < MUTATION_PROBABILITY:
-                child_list[random.randint(0, len(child)) - 1] = random.choice(genes)
-            return "".join(child_list)
-
         # This is selection
         for i in range(N_SELECTED):
-            population.extend(select(population_score[int(i)]))
+            population.extend(select(population_score[int(i)], population_score, genes))
             # Check if the population has already reached the maximum value and if so,
             # break the cycle.  If this check is disabled, the algorithm will take
             # forever to compute large strings, but will also calculate small strings in

graphics/vector3_for_2d_rendering.py

@@ -28,9 +28,8 @@ def convert_to_2d(
     TypeError: Input values must either be float or int: ['1', 2, 3, 10, 10]
     """
     if not all(isinstance(val, (float, int)) for val in locals().values()):
-        raise TypeError(
-            "Input values must either be float or int: " f"{list(locals().values())}"
-        )
+        msg = f"Input values must either be float or int: {list(locals().values())}"
+        raise TypeError(msg)
     projected_x = ((x * distance) / (z + distance)) * scale
     projected_y = ((y * distance) / (z + distance)) * scale
     return projected_x, projected_y
@@ -71,10 +70,11 @@ def rotate(
     input_variables = locals()
     del input_variables["axis"]
     if not all(isinstance(val, (float, int)) for val in input_variables.values()):
-        raise TypeError(
+        msg = (
             "Input values except axis must either be float or int: "
             f"{list(input_variables.values())}"
         )
+        raise TypeError(msg)
     angle = (angle % 360) / 450 * 180 / math.pi
     if axis == "z":
         new_x = x * math.cos(angle) - y * math.sin(angle)

graphs/breadth_first_search_shortest_path.py

@@ -73,9 +73,10 @@ class Graph:
 
         target_vertex_parent = self.parent.get(target_vertex)
         if target_vertex_parent is None:
-            raise ValueError(
+            msg = (
                 f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}"
             )
+            raise ValueError(msg)
 
         return self.shortest_path(target_vertex_parent) + f"->{target_vertex}"
 

graphs/dijkstra_binary_grid.py

@@ -0,0 +1,89 @@
+"""
+This script implements the Dijkstra algorithm on a binary grid.
+The grid consists of 0s and 1s, where 1 represents
+a walkable node and 0 represents an obstacle.
+The algorithm finds the shortest path from a start node to a destination node.
+Diagonal movement can be allowed or disallowed.
+"""
+
+from heapq import heappop, heappush
+
+import numpy as np
+
+
+def dijkstra(
+    grid: np.ndarray,
+    source: tuple[int, int],
+    destination: tuple[int, int],
+    allow_diagonal: bool,
+) -> tuple[float | int, list[tuple[int, int]]]:
+    """
+    Implements Dijkstra's algorithm on a binary grid.
+
+    Args:
+        grid (np.ndarray): A 2D numpy array representing the grid.
+        1 represents a walkable node and 0 represents an obstacle.
+        source (Tuple[int, int]): A tuple representing the start node.
+        destination (Tuple[int, int]): A tuple representing the
+        destination node.
+        allow_diagonal (bool): A boolean determining whether
+        diagonal movements are allowed.
+
+    Returns:
+        Tuple[Union[float, int], List[Tuple[int, int]]]:
+        The shortest distance from the start node to the destination node
+        and the shortest path as a list of nodes.
+
+    >>> dijkstra(np.array([[1, 1, 1], [0, 1, 0], [0, 1, 1]]), (0, 0), (2, 2), False)
+    (4.0, [(0, 0), (0, 1), (1, 1), (2, 1), (2, 2)])
+
+    >>> dijkstra(np.array([[1, 1, 1], [0, 1, 0], [0, 1, 1]]), (0, 0), (2, 2), True)
+    (2.0, [(0, 0), (1, 1), (2, 2)])
+
+    >>> dijkstra(np.array([[1, 1, 1], [0, 0, 1], [0, 1, 1]]), (0, 0), (2, 2), False)
+    (4.0, [(0, 0), (0, 1), (0, 2), (1, 2), (2, 2)])
+    """
+    rows, cols = grid.shape
+    dx = [-1, 1, 0, 0]
+    dy = [0, 0, -1, 1]
+    if allow_diagonal:
+        dx += [-1, -1, 1, 1]
+        dy += [-1, 1, -1, 1]
+
+    queue, visited = [(0, source)], set()
+    matrix = np.full((rows, cols), np.inf)
+    matrix[source] = 0
+    predecessors = np.empty((rows, cols), dtype=object)
+    predecessors[source] = None
+
+    while queue:
+        (dist, (x, y)) = heappop(queue)
+        if (x, y) in visited:
+            continue
+        visited.add((x, y))
+
+        if (x, y) == destination:
+            path = []
+            while (x, y) != source:
+                path.append((x, y))
+                x, y = predecessors[x, y]
+            path.append(source)  # add the source manually
+            path.reverse()
+            return matrix[destination], path
+
+        for i in range(len(dx)):
+            nx, ny = x + dx[i], y + dy[i]
+            if 0 <= nx < rows and 0 <= ny < cols:
+                next_node = grid[nx][ny]
+                if next_node == 1 and matrix[nx, ny] > dist + 1:
+                    heappush(queue, (dist + 1, (nx, ny)))
+                    matrix[nx, ny] = dist + 1
+                    predecessors[nx, ny] = (x, y)
+
+    return np.inf, []
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

graphs/directed_and_undirected_(weighted)_graph.py

@@ -39,7 +39,7 @@ class DirectedGraph:
         stack = []
         visited = []
         if s == -2:
-            s = list(self.graph)[0]
+            s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         ss = s
@@ -87,7 +87,7 @@ class DirectedGraph:
         d = deque()
         visited = []
         if s == -2:
-            s = list(self.graph)[0]
+            s = next(iter(self.graph))
         d.append(s)
         visited.append(s)
         while d:
@@ -114,7 +114,7 @@ class DirectedGraph:
         stack = []
         visited = []
         if s == -2:
-            s = list(self.graph)[0]
+            s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         ss = s
@@ -146,7 +146,7 @@ class DirectedGraph:
     def cycle_nodes(self):
         stack = []
         visited = []
-        s = list(self.graph)[0]
+        s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         parent = -2
@@ -199,7 +199,7 @@ class DirectedGraph:
     def has_cycle(self):
         stack = []
         visited = []
-        s = list(self.graph)[0]
+        s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         parent = -2
@@ -305,7 +305,7 @@ class Graph:
         stack = []
         visited = []
         if s == -2:
-            s = list(self.graph)[0]
+            s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         ss = s
@@ -353,7 +353,7 @@ class Graph:
         d = deque()
         visited = []
         if s == -2:
-            s = list(self.graph)[0]
+            s = next(iter(self.graph))
         d.append(s)
         visited.append(s)
         while d:
@@ -371,7 +371,7 @@ class Graph:
     def cycle_nodes(self):
         stack = []
         visited = []
-        s = list(self.graph)[0]
+        s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         parent = -2
@@ -424,7 +424,7 @@ class Graph:
     def has_cycle(self):
         stack = []
         visited = []
-        s = list(self.graph)[0]
+        s = next(iter(self.graph))
         stack.append(s)
         visited.append(s)
         parent = -2

graphs/edmonds_karp_multiple_source_and_sink.py

@@ -113,7 +113,7 @@ class PushRelabelExecutor(MaximumFlowAlgorithmExecutor):
         vertices_list = [
             i
             for i in range(self.verticies_count)
-            if i != self.source_index and i != self.sink_index
+            if i not in {self.source_index, self.sink_index}
         ]
 
         # move through list

graphs/eulerian_path_and_circuit_for_undirected_graph.py

@@ -20,7 +20,7 @@ def check_circuit_or_path(graph, max_node):
     odd_degree_nodes = 0
     odd_node = -1
     for i in range(max_node):
-        if i not in graph.keys():
+        if i not in graph:
             continue
         if len(graph[i]) % 2 == 1:
             odd_degree_nodes += 1

graphs/graph_adjacency_list.py

@@ -0,0 +1,589 @@
+#!/usr/bin/env python3
+"""
+Author: Vikram Nithyanandam
+
+Description:
+The following implementation is a robust unweighted Graph data structure
+implemented using an adjacency list. This vertices and edges of this graph can be
+effectively initialized and modified while storing your chosen generic
+value in each vertex.
+
+Adjacency List: https://en.wikipedia.org/wiki/Adjacency_list
+
+Potential Future Ideas:
+- Add a flag to set edge weights on and set edge weights
+- Make edge weights and vertex values customizable to store whatever the client wants
+- Support multigraph functionality if the client wants it
+"""
+from __future__ import annotations
+
+import random
+import unittest
+from pprint import pformat
+from typing import Generic, TypeVar
+
+T = TypeVar("T")
+
+
+class GraphAdjacencyList(Generic[T]):
+    def __init__(
+        self, vertices: list[T], edges: list[list[T]], directed: bool = True
+    ) -> None:
+        """
+        Parameters:
+         - vertices: (list[T]) The list of vertex names the client wants to
+        pass in. Default is empty.
+        - edges: (list[list[T]]) The list of edges the client wants to
+        pass in. Each edge is a 2-element list. Default is empty.
+        - directed: (bool) Indicates if graph is directed or undirected.
+        Default is True.
+        """
+        self.adj_list: dict[T, list[T]] = {}  # dictionary of lists of T
+        self.directed = directed
+
+        # Falsey checks
+        edges = edges or []
+        vertices = vertices or []
+
+        for vertex in vertices:
+            self.add_vertex(vertex)
+
+        for edge in edges:
+            if len(edge) != 2:
+                msg = f"Invalid input: {edge} is the wrong length."
+                raise ValueError(msg)
+            self.add_edge(edge[0], edge[1])
+
+    def add_vertex(self, vertex: T) -> None:
+        """
+        Adds a vertex to the graph. If the given vertex already exists,
+        a ValueError will be thrown.
+        """
+        if self.contains_vertex(vertex):
+            msg = f"Incorrect input: {vertex} is already in the graph."
+            raise ValueError(msg)
+        self.adj_list[vertex] = []
+
+    def add_edge(self, source_vertex: T, destination_vertex: T) -> None:
+        """
+        Creates an edge from source vertex to destination vertex. If any
+        given vertex doesn't exist or the edge already exists, a ValueError
+        will be thrown.
+        """
+        if not (
+            self.contains_vertex(source_vertex)
+            and self.contains_vertex(destination_vertex)
+        ):
+            msg = (
+                f"Incorrect input: Either {source_vertex} or "
+                f"{destination_vertex} does not exist"
+            )
+            raise ValueError(msg)
+        if self.contains_edge(source_vertex, destination_vertex):
+            msg = (
+                "Incorrect input: The edge already exists between "
+                f"{source_vertex} and {destination_vertex}"
+            )
+            raise ValueError(msg)
+
+        # add the destination vertex to the list associated with the source vertex
+        # and vice versa if not directed
+        self.adj_list[source_vertex].append(destination_vertex)
+        if not self.directed:
+            self.adj_list[destination_vertex].append(source_vertex)
+
+    def remove_vertex(self, vertex: T) -> None:
+        """
+        Removes the given vertex from the graph and deletes all incoming and
+        outgoing edges from the given vertex as well. If the given vertex
+        does not exist, a ValueError will be thrown.
+        """
+        if not self.contains_vertex(vertex):
+            msg = f"Incorrect input: {vertex} does not exist in this graph."
+            raise ValueError(msg)
+
+        if not self.directed:
+            # If not directed, find all neighboring vertices and delete all references
+            # of edges connecting to the given vertex
+            for neighbor in self.adj_list[vertex]:
+                self.adj_list[neighbor].remove(vertex)
+        else:
+            # If directed, search all neighbors of all vertices and delete all
+            # references of edges connecting to the given vertex
+            for edge_list in self.adj_list.values():
+                if vertex in edge_list:
+                    edge_list.remove(vertex)
+
+        # Finally, delete the given vertex and all of its outgoing edge references
+        self.adj_list.pop(vertex)
+
+    def remove_edge(self, source_vertex: T, destination_vertex: T) -> None:
+        """
+        Removes the edge between the two vertices. If any given vertex
+        doesn't exist or the edge does not exist, a ValueError will be thrown.
+        """
+        if not (
+            self.contains_vertex(source_vertex)
+            and self.contains_vertex(destination_vertex)
+        ):
+            msg = (
+                f"Incorrect input: Either {source_vertex} or "
+                f"{destination_vertex} does not exist"
+            )
+            raise ValueError(msg)
+        if not self.contains_edge(source_vertex, destination_vertex):
+            msg = (
+                "Incorrect input: The edge does NOT exist between "
+                f"{source_vertex} and {destination_vertex}"
+            )
+            raise ValueError(msg)
+
+        # remove the destination vertex from the list associated with the source
+        # vertex and vice versa if not directed
+        self.adj_list[source_vertex].remove(destination_vertex)
+        if not self.directed:
+            self.adj_list[destination_vertex].remove(source_vertex)
+
+    def contains_vertex(self, vertex: T) -> bool:
+        """
+        Returns True if the graph contains the vertex, False otherwise.
+        """
+        return vertex in self.adj_list
+
+    def contains_edge(self, source_vertex: T, destination_vertex: T) -> bool:
+        """
+        Returns True if the graph contains the edge from the source_vertex to the
+        destination_vertex, False otherwise. If any given vertex doesn't exist, a
+        ValueError will be thrown.
+        """
+        if not (
+            self.contains_vertex(source_vertex)
+            and self.contains_vertex(destination_vertex)
+        ):
+            msg = (
+                f"Incorrect input: Either {source_vertex} "
+                f"or {destination_vertex} does not exist."
+            )
+            raise ValueError(msg)
+
+        return destination_vertex in self.adj_list[source_vertex]
+
+    def clear_graph(self) -> None:
+        """
+        Clears all vertices and edges.
+        """
+        self.adj_list = {}
+
+    def __repr__(self) -> str:
+        return pformat(self.adj_list)
+
+
+class TestGraphAdjacencyList(unittest.TestCase):
+    def __assert_graph_edge_exists_check(
+        self,
+        undirected_graph: GraphAdjacencyList,
+        directed_graph: GraphAdjacencyList,
+        edge: list[int],
+    ) -> None:
+        self.assertTrue(undirected_graph.contains_edge(edge[0], edge[1]))
+        self.assertTrue(undirected_graph.contains_edge(edge[1], edge[0]))
+        self.assertTrue(directed_graph.contains_edge(edge[0], edge[1]))
+
+    def __assert_graph_edge_does_not_exist_check(
+        self,
+        undirected_graph: GraphAdjacencyList,
+        directed_graph: GraphAdjacencyList,
+        edge: list[int],
+    ) -> None:
+        self.assertFalse(undirected_graph.contains_edge(edge[0], edge[1]))
+        self.assertFalse(undirected_graph.contains_edge(edge[1], edge[0]))
+        self.assertFalse(directed_graph.contains_edge(edge[0], edge[1]))
+
+    def __assert_graph_vertex_exists_check(
+        self,
+        undirected_graph: GraphAdjacencyList,
+        directed_graph: GraphAdjacencyList,
+        vertex: int,
+    ) -> None:
+        self.assertTrue(undirected_graph.contains_vertex(vertex))
+        self.assertTrue(directed_graph.contains_vertex(vertex))
+
+    def __assert_graph_vertex_does_not_exist_check(
+        self,
+        undirected_graph: GraphAdjacencyList,
+        directed_graph: GraphAdjacencyList,
+        vertex: int,
+    ) -> None:
+        self.assertFalse(undirected_graph.contains_vertex(vertex))
+        self.assertFalse(directed_graph.contains_vertex(vertex))
+
+    def __generate_random_edges(
+        self, vertices: list[int], edge_pick_count: int
+    ) -> list[list[int]]:
+        self.assertTrue(edge_pick_count <= len(vertices))
+
+        random_source_vertices: list[int] = random.sample(
+            vertices[0 : int(len(vertices) / 2)], edge_pick_count
+        )
+        random_destination_vertices: list[int] = random.sample(
+            vertices[int(len(vertices) / 2) :], edge_pick_count
+        )
+        random_edges: list[list[int]] = []
+
+        for source in random_source_vertices:
+            for dest in random_destination_vertices:
+                random_edges.append([source, dest])
+
+        return random_edges
+
+    def __generate_graphs(
+        self, vertex_count: int, min_val: int, max_val: int, edge_pick_count: int
+    ) -> tuple[GraphAdjacencyList, GraphAdjacencyList, list[int], list[list[int]]]:
+        if max_val - min_val + 1 < vertex_count:
+            raise ValueError(
+                "Will result in duplicate vertices. Either increase range "
+                "between min_val and max_val or decrease vertex count."
+            )
+
+        # generate graph input
+        random_vertices: list[int] = random.sample(
+            range(min_val, max_val + 1), vertex_count
+        )
+        random_edges: list[list[int]] = self.__generate_random_edges(
+            random_vertices, edge_pick_count
+        )
+
+        # build graphs
+        undirected_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=random_edges, directed=False
+        )
+        directed_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=random_edges, directed=True
+        )
+
+        return undirected_graph, directed_graph, random_vertices, random_edges
+
+    def test_init_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        # test graph initialization with vertices and edges
+        for num in random_vertices:
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, num
+            )
+
+        for edge in random_edges:
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, edge
+            )
+        self.assertFalse(undirected_graph.directed)
+        self.assertTrue(directed_graph.directed)
+
+    def test_contains_vertex(self) -> None:
+        random_vertices: list[int] = random.sample(range(101), 20)
+
+        # Build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=[], directed=True
+        )
+
+        # Test contains_vertex
+        for num in range(101):
+            self.assertEqual(
+                num in random_vertices, undirected_graph.contains_vertex(num)
+            )
+            self.assertEqual(
+                num in random_vertices, directed_graph.contains_vertex(num)
+            )
+
+    def test_add_vertices(self) -> None:
+        random_vertices: list[int] = random.sample(range(101), 20)
+
+        # build empty graphs
+        undirected_graph: GraphAdjacencyList = GraphAdjacencyList(
+            vertices=[], edges=[], directed=False
+        )
+        directed_graph: GraphAdjacencyList = GraphAdjacencyList(
+            vertices=[], edges=[], directed=True
+        )
+
+        # run add_vertex
+        for num in random_vertices:
+            undirected_graph.add_vertex(num)
+
+        for num in random_vertices:
+            directed_graph.add_vertex(num)
+
+        # test add_vertex worked
+        for num in random_vertices:
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, num
+            )
+
+    def test_remove_vertices(self) -> None:
+        random_vertices: list[int] = random.sample(range(101), 20)
+
+        # build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=[], directed=True
+        )
+
+        # test remove_vertex worked
+        for num in random_vertices:
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, num
+            )
+
+            undirected_graph.remove_vertex(num)
+            directed_graph.remove_vertex(num)
+
+            self.__assert_graph_vertex_does_not_exist_check(
+                undirected_graph, directed_graph, num
+            )
+
+    def test_add_and_remove_vertices_repeatedly(self) -> None:
+        random_vertices1: list[int] = random.sample(range(51), 20)
+        random_vertices2: list[int] = random.sample(range(51, 101), 20)
+
+        # build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyList(
+            vertices=random_vertices1, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyList(
+            vertices=random_vertices1, edges=[], directed=True
+        )
+
+        # test adding and removing vertices
+        for i, _ in enumerate(random_vertices1):
+            undirected_graph.add_vertex(random_vertices2[i])
+            directed_graph.add_vertex(random_vertices2[i])
+
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, random_vertices2[i]
+            )
+
+            undirected_graph.remove_vertex(random_vertices1[i])
+            directed_graph.remove_vertex(random_vertices1[i])
+
+            self.__assert_graph_vertex_does_not_exist_check(
+                undirected_graph, directed_graph, random_vertices1[i]
+            )
+
+        # remove all vertices
+        for i, _ in enumerate(random_vertices1):
+            undirected_graph.remove_vertex(random_vertices2[i])
+            directed_graph.remove_vertex(random_vertices2[i])
+
+            self.__assert_graph_vertex_does_not_exist_check(
+                undirected_graph, directed_graph, random_vertices2[i]
+            )
+
+    def test_contains_edge(self) -> None:
+        # generate graphs and graph input
+        vertex_count = 20
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(vertex_count, 0, 100, 4)
+
+        # generate all possible edges for testing
+        all_possible_edges: list[list[int]] = []
+        for i in range(vertex_count - 1):
+            for j in range(i + 1, vertex_count):
+                all_possible_edges.append([random_vertices[i], random_vertices[j]])
+                all_possible_edges.append([random_vertices[j], random_vertices[i]])
+
+        # test contains_edge function
+        for edge in all_possible_edges:
+            if edge in random_edges:
+                self.__assert_graph_edge_exists_check(
+                    undirected_graph, directed_graph, edge
+                )
+            elif [edge[1], edge[0]] in random_edges:
+                # since this edge exists for undirected but the reverse
+                # may not exist for directed
+                self.__assert_graph_edge_exists_check(
+                    undirected_graph, directed_graph, [edge[1], edge[0]]
+                )
+            else:
+                self.__assert_graph_edge_does_not_exist_check(
+                    undirected_graph, directed_graph, edge
+                )
+
+    def test_add_edge(self) -> None:
+        # generate graph input
+        random_vertices: list[int] = random.sample(range(101), 15)
+        random_edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
+
+        # build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyList(
+            vertices=random_vertices, edges=[], directed=True
+        )
+
+        # run and test add_edge
+        for edge in random_edges:
+            undirected_graph.add_edge(edge[0], edge[1])
+            directed_graph.add_edge(edge[0], edge[1])
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, edge
+            )
+
+    def test_remove_edge(self) -> None:
+        # generate graph input and graphs
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        # run and test remove_edge
+        for edge in random_edges:
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, edge
+            )
+            undirected_graph.remove_edge(edge[0], edge[1])
+            directed_graph.remove_edge(edge[0], edge[1])
+            self.__assert_graph_edge_does_not_exist_check(
+                undirected_graph, directed_graph, edge
+            )
+
+    def test_add_and_remove_edges_repeatedly(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        # make some more edge options!
+        more_random_edges: list[list[int]] = []
+
+        while len(more_random_edges) != len(random_edges):
+            edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
+            for edge in edges:
+                if len(more_random_edges) == len(random_edges):
+                    break
+                elif edge not in more_random_edges and edge not in random_edges:
+                    more_random_edges.append(edge)
+
+        for i, _ in enumerate(random_edges):
+            undirected_graph.add_edge(more_random_edges[i][0], more_random_edges[i][1])
+            directed_graph.add_edge(more_random_edges[i][0], more_random_edges[i][1])
+
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, more_random_edges[i]
+            )
+
+            undirected_graph.remove_edge(random_edges[i][0], random_edges[i][1])
+            directed_graph.remove_edge(random_edges[i][0], random_edges[i][1])
+
+            self.__assert_graph_edge_does_not_exist_check(
+                undirected_graph, directed_graph, random_edges[i]
+            )
+
+    def test_add_vertex_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for vertex in random_vertices:
+            with self.assertRaises(ValueError):
+                undirected_graph.add_vertex(vertex)
+            with self.assertRaises(ValueError):
+                directed_graph.add_vertex(vertex)
+
+    def test_remove_vertex_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for i in range(101):
+            if i not in random_vertices:
+                with self.assertRaises(ValueError):
+                    undirected_graph.remove_vertex(i)
+                with self.assertRaises(ValueError):
+                    directed_graph.remove_vertex(i)
+
+    def test_add_edge_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for edge in random_edges:
+            with self.assertRaises(ValueError):
+                undirected_graph.add_edge(edge[0], edge[1])
+            with self.assertRaises(ValueError):
+                directed_graph.add_edge(edge[0], edge[1])
+
+    def test_remove_edge_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        more_random_edges: list[list[int]] = []
+
+        while len(more_random_edges) != len(random_edges):
+            edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
+            for edge in edges:
+                if len(more_random_edges) == len(random_edges):
+                    break
+                elif edge not in more_random_edges and edge not in random_edges:
+                    more_random_edges.append(edge)
+
+        for edge in more_random_edges:
+            with self.assertRaises(ValueError):
+                undirected_graph.remove_edge(edge[0], edge[1])
+            with self.assertRaises(ValueError):
+                directed_graph.remove_edge(edge[0], edge[1])
+
+    def test_contains_edge_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for vertex in random_vertices:
+            with self.assertRaises(ValueError):
+                undirected_graph.contains_edge(vertex, 102)
+            with self.assertRaises(ValueError):
+                directed_graph.contains_edge(vertex, 102)
+
+        with self.assertRaises(ValueError):
+            undirected_graph.contains_edge(103, 102)
+        with self.assertRaises(ValueError):
+            directed_graph.contains_edge(103, 102)
+
+
+if __name__ == "__main__":
+    unittest.main()

graphs/graph_adjacency_matrix.py

@@ -0,0 +1,608 @@
+#!/usr/bin/env python3
+"""
+Author: Vikram Nithyanandam
+
+Description:
+The following implementation is a robust unweighted Graph data structure
+implemented using an adjacency matrix. This vertices and edges of this graph can be
+effectively initialized and modified while storing your chosen generic
+value in each vertex.
+
+Adjacency Matrix: https://mathworld.wolfram.com/AdjacencyMatrix.html
+
+Potential Future Ideas:
+- Add a flag to set edge weights on and set edge weights
+- Make edge weights and vertex values customizable to store whatever the client wants
+- Support multigraph functionality if the client wants it
+"""
+from __future__ import annotations
+
+import random
+import unittest
+from pprint import pformat
+from typing import Generic, TypeVar
+
+T = TypeVar("T")
+
+
+class GraphAdjacencyMatrix(Generic[T]):
+    def __init__(
+        self, vertices: list[T], edges: list[list[T]], directed: bool = True
+    ) -> None:
+        """
+        Parameters:
+        - vertices: (list[T]) The list of vertex names the client wants to
+        pass in. Default is empty.
+        - edges: (list[list[T]]) The list of edges the client wants to
+        pass in. Each edge is a 2-element list. Default is empty.
+        - directed: (bool) Indicates if graph is directed or undirected.
+        Default is True.
+        """
+        self.directed = directed
+        self.vertex_to_index: dict[T, int] = {}
+        self.adj_matrix: list[list[int]] = []
+
+        # Falsey checks
+        edges = edges or []
+        vertices = vertices or []
+
+        for vertex in vertices:
+            self.add_vertex(vertex)
+
+        for edge in edges:
+            if len(edge) != 2:
+                msg = f"Invalid input: {edge} must have length 2."
+                raise ValueError(msg)
+            self.add_edge(edge[0], edge[1])
+
+    def add_edge(self, source_vertex: T, destination_vertex: T) -> None:
+        """
+        Creates an edge from source vertex to destination vertex. If any
+        given vertex doesn't exist or the edge already exists, a ValueError
+        will be thrown.
+        """
+        if not (
+            self.contains_vertex(source_vertex)
+            and self.contains_vertex(destination_vertex)
+        ):
+            msg = (
+                f"Incorrect input: Either {source_vertex} or "
+                f"{destination_vertex} does not exist"
+            )
+            raise ValueError(msg)
+        if self.contains_edge(source_vertex, destination_vertex):
+            msg = (
+                "Incorrect input: The edge already exists between "
+                f"{source_vertex} and {destination_vertex}"
+            )
+            raise ValueError(msg)
+
+        # Get the indices of the corresponding vertices and set their edge value to 1.
+        u: int = self.vertex_to_index[source_vertex]
+        v: int = self.vertex_to_index[destination_vertex]
+        self.adj_matrix[u][v] = 1
+        if not self.directed:
+            self.adj_matrix[v][u] = 1
+
+    def remove_edge(self, source_vertex: T, destination_vertex: T) -> None:
+        """
+        Removes the edge between the two vertices. If any given vertex
+        doesn't exist or the edge does not exist, a ValueError will be thrown.
+        """
+        if not (
+            self.contains_vertex(source_vertex)
+            and self.contains_vertex(destination_vertex)
+        ):
+            msg = (
+                f"Incorrect input: Either {source_vertex} or "
+                f"{destination_vertex} does not exist"
+            )
+            raise ValueError(msg)
+        if not self.contains_edge(source_vertex, destination_vertex):
+            msg = (
+                "Incorrect input: The edge does NOT exist between "
+                f"{source_vertex} and {destination_vertex}"
+            )
+            raise ValueError(msg)
+
+        # Get the indices of the corresponding vertices and set their edge value to 0.
+        u: int = self.vertex_to_index[source_vertex]
+        v: int = self.vertex_to_index[destination_vertex]
+        self.adj_matrix[u][v] = 0
+        if not self.directed:
+            self.adj_matrix[v][u] = 0
+
+    def add_vertex(self, vertex: T) -> None:
+        """
+        Adds a vertex to the graph. If the given vertex already exists,
+        a ValueError will be thrown.
+        """
+        if self.contains_vertex(vertex):
+            msg = f"Incorrect input: {vertex} already exists in this graph."
+            raise ValueError(msg)
+
+        # build column for vertex
+        for row in self.adj_matrix:
+            row.append(0)
+
+        # build row for vertex and update other data structures
+        self.adj_matrix.append([0] * (len(self.adj_matrix) + 1))
+        self.vertex_to_index[vertex] = len(self.adj_matrix) - 1
+
+    def remove_vertex(self, vertex: T) -> None:
+        """
+        Removes the given vertex from the graph and deletes all incoming and
+        outgoing edges from the given vertex as well. If the given vertex
+        does not exist, a ValueError will be thrown.
+        """
+        if not self.contains_vertex(vertex):
+            msg = f"Incorrect input: {vertex} does not exist in this graph."
+            raise ValueError(msg)
+
+        # first slide up the rows by deleting the row corresponding to
+        # the vertex being deleted.
+        start_index = self.vertex_to_index[vertex]
+        self.adj_matrix.pop(start_index)
+
+        # next, slide the columns to the left by deleting the values in
+        # the column corresponding to the vertex being deleted
+        for lst in self.adj_matrix:
+            lst.pop(start_index)
+
+        # final clean up
+        self.vertex_to_index.pop(vertex)
+
+        # decrement indices for vertices shifted by the deleted vertex in the adj matrix
+        for vertex in self.vertex_to_index:
+            if self.vertex_to_index[vertex] >= start_index:
+                self.vertex_to_index[vertex] = self.vertex_to_index[vertex] - 1
+
+    def contains_vertex(self, vertex: T) -> bool:
+        """
+        Returns True if the graph contains the vertex, False otherwise.
+        """
+        return vertex in self.vertex_to_index
+
+    def contains_edge(self, source_vertex: T, destination_vertex: T) -> bool:
+        """
+        Returns True if the graph contains the edge from the source_vertex to the
+        destination_vertex, False otherwise. If any given vertex doesn't exist, a
+        ValueError will be thrown.
+        """
+        if not (
+            self.contains_vertex(source_vertex)
+            and self.contains_vertex(destination_vertex)
+        ):
+            msg = (
+                f"Incorrect input: Either {source_vertex} "
+                f"or {destination_vertex} does not exist."
+            )
+            raise ValueError(msg)
+
+        u = self.vertex_to_index[source_vertex]
+        v = self.vertex_to_index[destination_vertex]
+        return self.adj_matrix[u][v] == 1
+
+    def clear_graph(self) -> None:
+        """
+        Clears all vertices and edges.
+        """
+        self.vertex_to_index = {}
+        self.adj_matrix = []
+
+    def __repr__(self) -> str:
+        first = "Adj Matrix:\n" + pformat(self.adj_matrix)
+        second = "\nVertex to index mapping:\n" + pformat(self.vertex_to_index)
+        return first + second
+
+
+class TestGraphMatrix(unittest.TestCase):
+    def __assert_graph_edge_exists_check(
+        self,
+        undirected_graph: GraphAdjacencyMatrix,
+        directed_graph: GraphAdjacencyMatrix,
+        edge: list[int],
+    ) -> None:
+        self.assertTrue(undirected_graph.contains_edge(edge[0], edge[1]))
+        self.assertTrue(undirected_graph.contains_edge(edge[1], edge[0]))
+        self.assertTrue(directed_graph.contains_edge(edge[0], edge[1]))
+
+    def __assert_graph_edge_does_not_exist_check(
+        self,
+        undirected_graph: GraphAdjacencyMatrix,
+        directed_graph: GraphAdjacencyMatrix,
+        edge: list[int],
+    ) -> None:
+        self.assertFalse(undirected_graph.contains_edge(edge[0], edge[1]))
+        self.assertFalse(undirected_graph.contains_edge(edge[1], edge[0]))
+        self.assertFalse(directed_graph.contains_edge(edge[0], edge[1]))
+
+    def __assert_graph_vertex_exists_check(
+        self,
+        undirected_graph: GraphAdjacencyMatrix,
+        directed_graph: GraphAdjacencyMatrix,
+        vertex: int,
+    ) -> None:
+        self.assertTrue(undirected_graph.contains_vertex(vertex))
+        self.assertTrue(directed_graph.contains_vertex(vertex))
+
+    def __assert_graph_vertex_does_not_exist_check(
+        self,
+        undirected_graph: GraphAdjacencyMatrix,
+        directed_graph: GraphAdjacencyMatrix,
+        vertex: int,
+    ) -> None:
+        self.assertFalse(undirected_graph.contains_vertex(vertex))
+        self.assertFalse(directed_graph.contains_vertex(vertex))
+
+    def __generate_random_edges(
+        self, vertices: list[int], edge_pick_count: int
+    ) -> list[list[int]]:
+        self.assertTrue(edge_pick_count <= len(vertices))
+
+        random_source_vertices: list[int] = random.sample(
+            vertices[0 : int(len(vertices) / 2)], edge_pick_count
+        )
+        random_destination_vertices: list[int] = random.sample(
+            vertices[int(len(vertices) / 2) :], edge_pick_count
+        )
+        random_edges: list[list[int]] = []
+
+        for source in random_source_vertices:
+            for dest in random_destination_vertices:
+                random_edges.append([source, dest])
+
+        return random_edges
+
+    def __generate_graphs(
+        self, vertex_count: int, min_val: int, max_val: int, edge_pick_count: int
+    ) -> tuple[GraphAdjacencyMatrix, GraphAdjacencyMatrix, list[int], list[list[int]]]:
+        if max_val - min_val + 1 < vertex_count:
+            raise ValueError(
+                "Will result in duplicate vertices. Either increase "
+                "range between min_val and max_val or decrease vertex count"
+            )
+
+        # generate graph input
+        random_vertices: list[int] = random.sample(
+            range(min_val, max_val + 1), vertex_count
+        )
+        random_edges: list[list[int]] = self.__generate_random_edges(
+            random_vertices, edge_pick_count
+        )
+
+        # build graphs
+        undirected_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=random_edges, directed=False
+        )
+        directed_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=random_edges, directed=True
+        )
+
+        return undirected_graph, directed_graph, random_vertices, random_edges
+
+    def test_init_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        # test graph initialization with vertices and edges
+        for num in random_vertices:
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, num
+            )
+
+        for edge in random_edges:
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, edge
+            )
+
+        self.assertFalse(undirected_graph.directed)
+        self.assertTrue(directed_graph.directed)
+
+    def test_contains_vertex(self) -> None:
+        random_vertices: list[int] = random.sample(range(101), 20)
+
+        # Build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=[], directed=True
+        )
+
+        # Test contains_vertex
+        for num in range(101):
+            self.assertEqual(
+                num in random_vertices, undirected_graph.contains_vertex(num)
+            )
+            self.assertEqual(
+                num in random_vertices, directed_graph.contains_vertex(num)
+            )
+
+    def test_add_vertices(self) -> None:
+        random_vertices: list[int] = random.sample(range(101), 20)
+
+        # build empty graphs
+        undirected_graph: GraphAdjacencyMatrix = GraphAdjacencyMatrix(
+            vertices=[], edges=[], directed=False
+        )
+        directed_graph: GraphAdjacencyMatrix = GraphAdjacencyMatrix(
+            vertices=[], edges=[], directed=True
+        )
+
+        # run add_vertex
+        for num in random_vertices:
+            undirected_graph.add_vertex(num)
+
+        for num in random_vertices:
+            directed_graph.add_vertex(num)
+
+        # test add_vertex worked
+        for num in random_vertices:
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, num
+            )
+
+    def test_remove_vertices(self) -> None:
+        random_vertices: list[int] = random.sample(range(101), 20)
+
+        # build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=[], directed=True
+        )
+
+        # test remove_vertex worked
+        for num in random_vertices:
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, num
+            )
+
+            undirected_graph.remove_vertex(num)
+            directed_graph.remove_vertex(num)
+
+            self.__assert_graph_vertex_does_not_exist_check(
+                undirected_graph, directed_graph, num
+            )
+
+    def test_add_and_remove_vertices_repeatedly(self) -> None:
+        random_vertices1: list[int] = random.sample(range(51), 20)
+        random_vertices2: list[int] = random.sample(range(51, 101), 20)
+
+        # build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices1, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices1, edges=[], directed=True
+        )
+
+        # test adding and removing vertices
+        for i, _ in enumerate(random_vertices1):
+            undirected_graph.add_vertex(random_vertices2[i])
+            directed_graph.add_vertex(random_vertices2[i])
+
+            self.__assert_graph_vertex_exists_check(
+                undirected_graph, directed_graph, random_vertices2[i]
+            )
+
+            undirected_graph.remove_vertex(random_vertices1[i])
+            directed_graph.remove_vertex(random_vertices1[i])
+
+            self.__assert_graph_vertex_does_not_exist_check(
+                undirected_graph, directed_graph, random_vertices1[i]
+            )
+
+        # remove all vertices
+        for i, _ in enumerate(random_vertices1):
+            undirected_graph.remove_vertex(random_vertices2[i])
+            directed_graph.remove_vertex(random_vertices2[i])
+
+            self.__assert_graph_vertex_does_not_exist_check(
+                undirected_graph, directed_graph, random_vertices2[i]
+            )
+
+    def test_contains_edge(self) -> None:
+        # generate graphs and graph input
+        vertex_count = 20
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(vertex_count, 0, 100, 4)
+
+        # generate all possible edges for testing
+        all_possible_edges: list[list[int]] = []
+        for i in range(vertex_count - 1):
+            for j in range(i + 1, vertex_count):
+                all_possible_edges.append([random_vertices[i], random_vertices[j]])
+                all_possible_edges.append([random_vertices[j], random_vertices[i]])
+
+        # test contains_edge function
+        for edge in all_possible_edges:
+            if edge in random_edges:
+                self.__assert_graph_edge_exists_check(
+                    undirected_graph, directed_graph, edge
+                )
+            elif [edge[1], edge[0]] in random_edges:
+                # since this edge exists for undirected but the reverse may
+                # not exist for directed
+                self.__assert_graph_edge_exists_check(
+                    undirected_graph, directed_graph, [edge[1], edge[0]]
+                )
+            else:
+                self.__assert_graph_edge_does_not_exist_check(
+                    undirected_graph, directed_graph, edge
+                )
+
+    def test_add_edge(self) -> None:
+        # generate graph input
+        random_vertices: list[int] = random.sample(range(101), 15)
+        random_edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
+
+        # build graphs WITHOUT edges
+        undirected_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=[], directed=False
+        )
+        directed_graph = GraphAdjacencyMatrix(
+            vertices=random_vertices, edges=[], directed=True
+        )
+
+        # run and test add_edge
+        for edge in random_edges:
+            undirected_graph.add_edge(edge[0], edge[1])
+            directed_graph.add_edge(edge[0], edge[1])
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, edge
+            )
+
+    def test_remove_edge(self) -> None:
+        # generate graph input and graphs
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        # run and test remove_edge
+        for edge in random_edges:
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, edge
+            )
+            undirected_graph.remove_edge(edge[0], edge[1])
+            directed_graph.remove_edge(edge[0], edge[1])
+            self.__assert_graph_edge_does_not_exist_check(
+                undirected_graph, directed_graph, edge
+            )
+
+    def test_add_and_remove_edges_repeatedly(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        # make some more edge options!
+        more_random_edges: list[list[int]] = []
+
+        while len(more_random_edges) != len(random_edges):
+            edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
+            for edge in edges:
+                if len(more_random_edges) == len(random_edges):
+                    break
+                elif edge not in more_random_edges and edge not in random_edges:
+                    more_random_edges.append(edge)
+
+        for i, _ in enumerate(random_edges):
+            undirected_graph.add_edge(more_random_edges[i][0], more_random_edges[i][1])
+            directed_graph.add_edge(more_random_edges[i][0], more_random_edges[i][1])
+
+            self.__assert_graph_edge_exists_check(
+                undirected_graph, directed_graph, more_random_edges[i]
+            )
+
+            undirected_graph.remove_edge(random_edges[i][0], random_edges[i][1])
+            directed_graph.remove_edge(random_edges[i][0], random_edges[i][1])
+
+            self.__assert_graph_edge_does_not_exist_check(
+                undirected_graph, directed_graph, random_edges[i]
+            )
+
+    def test_add_vertex_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for vertex in random_vertices:
+            with self.assertRaises(ValueError):
+                undirected_graph.add_vertex(vertex)
+            with self.assertRaises(ValueError):
+                directed_graph.add_vertex(vertex)
+
+    def test_remove_vertex_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for i in range(101):
+            if i not in random_vertices:
+                with self.assertRaises(ValueError):
+                    undirected_graph.remove_vertex(i)
+                with self.assertRaises(ValueError):
+                    directed_graph.remove_vertex(i)
+
+    def test_add_edge_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for edge in random_edges:
+            with self.assertRaises(ValueError):
+                undirected_graph.add_edge(edge[0], edge[1])
+            with self.assertRaises(ValueError):
+                directed_graph.add_edge(edge[0], edge[1])
+
+    def test_remove_edge_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        more_random_edges: list[list[int]] = []
+
+        while len(more_random_edges) != len(random_edges):
+            edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
+            for edge in edges:
+                if len(more_random_edges) == len(random_edges):
+                    break
+                elif edge not in more_random_edges and edge not in random_edges:
+                    more_random_edges.append(edge)
+
+        for edge in more_random_edges:
+            with self.assertRaises(ValueError):
+                undirected_graph.remove_edge(edge[0], edge[1])
+            with self.assertRaises(ValueError):
+                directed_graph.remove_edge(edge[0], edge[1])
+
+    def test_contains_edge_exception_check(self) -> None:
+        (
+            undirected_graph,
+            directed_graph,
+            random_vertices,
+            random_edges,
+        ) = self.__generate_graphs(20, 0, 100, 4)
+
+        for vertex in random_vertices:
+            with self.assertRaises(ValueError):
+                undirected_graph.contains_edge(vertex, 102)
+            with self.assertRaises(ValueError):
+                directed_graph.contains_edge(vertex, 102)
+
+        with self.assertRaises(ValueError):
+            undirected_graph.contains_edge(103, 102)
+        with self.assertRaises(ValueError):
+            directed_graph.contains_edge(103, 102)
+
+
+if __name__ == "__main__":
+    unittest.main()

graphs/graph_matrix.py

@@ -1,24 +0,0 @@
-class Graph:
-    def __init__(self, vertex):
-        self.vertex = vertex
-        self.graph = [[0] * vertex for i in range(vertex)]
-
-    def add_edge(self, u, v):
-        self.graph[u - 1][v - 1] = 1
-        self.graph[v - 1][u - 1] = 1
-
-    def show(self):
-        for i in self.graph:
-            for j in i:
-                print(j, end=" ")
-            print(" ")
-
-
-g = Graph(100)
-
-g.add_edge(1, 4)
-g.add_edge(4, 2)
-g.add_edge(4, 5)
-g.add_edge(2, 5)
-g.add_edge(5, 3)
-g.show()

graphs/greedy_best_first.py

@@ -58,8 +58,8 @@ class Node:
         The heuristic here is the Manhattan Distance
         Could elaborate to offer more than one choice
         """
-        dy = abs(self.pos_x - self.goal_x)
-        dx = abs(self.pos_y - self.goal_y)
+        dx = abs(self.pos_x - self.goal_x)
+        dy = abs(self.pos_y - self.goal_y)
         return dx + dy
 
     def __lt__(self, other) -> bool:

greedy_methods/minimum_waiting_time.py

@@ -0,0 +1,48 @@
+"""
+Calculate the minimum waiting time using a greedy algorithm.
+reference: https://www.youtube.com/watch?v=Sf3eiO12eJs
+
+For doctests run following command:
+python -m doctest -v minimum_waiting_time.py
+
+The minimum_waiting_time function uses a greedy algorithm to calculate the minimum
+time for queries to complete. It sorts the list in non-decreasing order, calculates
+the waiting time for each query by multiplying its position in the list with the
+sum of all remaining query times, and returns the total waiting time. A doctest
+ensures that the function produces the correct output.
+"""
+
+
+def minimum_waiting_time(queries: list[int]) -> int:
+    """
+    This function takes a list of query times and returns the minimum waiting time
+    for all queries to be completed.
+
+    Args:
+        queries: A list of queries measured in picoseconds
+
+    Returns:
+        total_waiting_time: Minimum waiting time measured in picoseconds
+
+    Examples:
+    >>> minimum_waiting_time([3, 2, 1, 2, 6])
+    17
+    >>> minimum_waiting_time([3, 2, 1])
+    4
+    >>> minimum_waiting_time([1, 2, 3, 4])
+    10
+    >>> minimum_waiting_time([5, 5, 5, 5])
+    30
+    >>> minimum_waiting_time([])
+    0
+    """
+    n = len(queries)
+    if n in (0, 1):
+        return 0
+    return sum(query * (n - i - 1) for i, query in enumerate(sorted(queries)))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

linear_algebra/src/rank_of_matrix.py

@@ -0,0 +1,89 @@
+"""
+Calculate the rank of a matrix.
+
+See: https://en.wikipedia.org/wiki/Rank_(linear_algebra)
+"""
+
+
+def rank_of_matrix(matrix: list[list[int | float]]) -> int:
+    """
+    Finds the rank of a matrix.
+    Args:
+        matrix: The matrix as a list of lists.
+    Returns:
+        The rank of the matrix.
+    Example:
+    >>> matrix1 = [[1, 2, 3],
+    ...            [4, 5, 6],
+    ...            [7, 8, 9]]
+    >>> rank_of_matrix(matrix1)
+    2
+    >>> matrix2 = [[1, 0, 0],
+    ...            [0, 1, 0],
+    ...            [0, 0, 0]]
+    >>> rank_of_matrix(matrix2)
+    2
+    >>> matrix3 = [[1, 2, 3, 4],
+    ...            [5, 6, 7, 8],
+    ...            [9, 10, 11, 12]]
+    >>> rank_of_matrix(matrix3)
+    2
+    >>> rank_of_matrix([[2,3,-1,-1],
+    ...                [1,-1,-2,4],
+    ...                [3,1,3,-2],
+    ...                [6,3,0,-7]])
+    4
+    >>> rank_of_matrix([[2,1,-3,-6],
+    ...                [3,-3,1,2],
+    ...                [1,1,1,2]])
+    3
+    >>> rank_of_matrix([[2,-1,0],
+    ...                [1,3,4],
+    ...                [4,1,-3]])
+    3
+    >>> rank_of_matrix([[3,2,1],
+    ...                [-6,-4,-2]])
+    1
+    >>> rank_of_matrix([[],[]])
+    0
+    >>> rank_of_matrix([[1]])
+    1
+    >>> rank_of_matrix([[]])
+    0
+    """
+
+    rows = len(matrix)
+    columns = len(matrix[0])
+    rank = min(rows, columns)
+
+    for row in range(rank):
+        # Check if diagonal element is not zero
+        if matrix[row][row] != 0:
+            # Eliminate all the elements below the diagonal
+            for col in range(row + 1, rows):
+                multiplier = matrix[col][row] / matrix[row][row]
+                for i in range(row, columns):
+                    matrix[col][i] -= multiplier * matrix[row][i]
+        else:
+            # Find a non-zero diagonal element to swap rows
+            reduce = True
+            for i in range(row + 1, rows):
+                if matrix[i][row] != 0:
+                    matrix[row], matrix[i] = matrix[i], matrix[row]
+                    reduce = False
+                    break
+            if reduce:
+                rank -= 1
+                for i in range(rows):
+                    matrix[i][row] = matrix[i][rank]
+
+            # Reduce the row pointer by one to stay on the same row
+            row -= 1
+
+    return rank
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

linear_algebra/src/schur_complement.py

@@ -31,16 +31,18 @@ def schur_complement(
     shape_c = np.shape(mat_c)
 
     if shape_a[0] != shape_b[0]:
-        raise ValueError(
-            f"Expected the same number of rows for A and B. \
-            Instead found A of size {shape_a} and B of size {shape_b}"
+        msg = (
+            "Expected the same number of rows for A and B. "
+            f"Instead found A of size {shape_a} and B of size {shape_b}"
         )
+        raise ValueError(msg)
 
     if shape_b[1] != shape_c[1]:
-        raise ValueError(
-            f"Expected the same number of columns for B and C. \
-            Instead found B of size {shape_b} and C of size {shape_c}"
+        msg = (
+            "Expected the same number of columns for B and C. "
+            f"Instead found B of size {shape_b} and C of size {shape_c}"
         )
+        raise ValueError(msg)
 
     a_inv = pseudo_inv
     if a_inv is None:

linear_programming/simplex.py

@@ -0,0 +1,311 @@
+"""
+Python implementation of the simplex algorithm for solving linear programs in
+tabular form with
+- `>=`, `<=`, and `=` constraints and
+- each variable `x1, x2, ...>= 0`.
+
+See https://gist.github.com/imengus/f9619a568f7da5bc74eaf20169a24d98 for how to
+convert linear programs to simplex tableaus, and the steps taken in the simplex
+algorithm.
+
+Resources:
+https://en.wikipedia.org/wiki/Simplex_algorithm
+https://tinyurl.com/simplex4beginners
+"""
+from typing import Any
+
+import numpy as np
+
+
+class Tableau:
+    """Operate on simplex tableaus
+
+    >>> t = Tableau(np.array([[-1,-1,0,0,-1],[1,3,1,0,4],[3,1,0,1,4.]]), 2)
+    Traceback (most recent call last):
+    ...
+    ValueError: RHS must be > 0
+    """
+
+    def __init__(self, tableau: np.ndarray, n_vars: int) -> None:
+        # Check if RHS is negative
+        if np.any(tableau[:, -1], where=tableau[:, -1] < 0):
+            raise ValueError("RHS must be > 0")
+
+        self.tableau = tableau
+        self.n_rows, _ = tableau.shape
+
+        # Number of decision variables x1, x2, x3...
+        self.n_vars = n_vars
+
+        # Number of artificial variables to be minimised
+        self.n_art_vars = len(np.where(tableau[self.n_vars : -1] == -1)[0])
+
+        # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
+        self.n_stages = (self.n_art_vars > 0) + 1
+
+        # Number of slack variables added to make inequalities into equalities
+        self.n_slack = self.n_rows - self.n_stages
+
+        # Objectives for each stage
+        self.objectives = ["max"]
+
+        # In two stage simplex, first minimise then maximise
+        if self.n_art_vars:
+            self.objectives.append("min")
+
+        self.col_titles = [""]
+
+        # Index of current pivot row and column
+        self.row_idx = None
+        self.col_idx = None
+
+        # Does objective row only contain (non)-negative values?
+        self.stop_iter = False
+
+    @staticmethod
+    def generate_col_titles(*args: int) -> list[str]:
+        """Generate column titles for tableau of specific dimensions
+
+        >>> Tableau.generate_col_titles(2, 3, 1)
+        ['x1', 'x2', 's1', 's2', 's3', 'a1', 'RHS']
+
+        >>> Tableau.generate_col_titles()
+        Traceback (most recent call last):
+        ...
+        ValueError: Must provide n_vars, n_slack, and n_art_vars
+        >>> Tableau.generate_col_titles(-2, 3, 1)
+        Traceback (most recent call last):
+        ...
+        ValueError: All arguments must be non-negative integers
+        """
+        if len(args) != 3:
+            raise ValueError("Must provide n_vars, n_slack, and n_art_vars")
+
+        if not all(x >= 0 and isinstance(x, int) for x in args):
+            raise ValueError("All arguments must be non-negative integers")
+
+        # decision | slack | artificial
+        string_starts = ["x", "s", "a"]
+        titles = []
+        for i in range(3):
+            for j in range(args[i]):
+                titles.append(string_starts[i] + str(j + 1))
+        titles.append("RHS")
+        return titles
+
+    def find_pivot(self, tableau: np.ndarray) -> tuple[Any, Any]:
+        """Finds the pivot row and column.
+        >>> t = Tableau(np.array([[-2,1,0,0,0], [3,1,1,0,6], [1,2,0,1,7.]]), 2)
+        >>> t.find_pivot(t.tableau)
+        (1, 0)
+        """
+        objective = self.objectives[-1]
+
+        # Find entries of highest magnitude in objective rows
+        sign = (objective == "min") - (objective == "max")
+        col_idx = np.argmax(sign * tableau[0, : self.n_vars])
+
+        # Choice is only valid if below 0 for maximise, and above for minimise
+        if sign * self.tableau[0, col_idx] <= 0:
+            self.stop_iter = True
+            return 0, 0
+
+        # Pivot row is chosen as having the lowest quotient when elements of
+        # the pivot column divide the right-hand side
+
+        # Slice excluding the objective rows
+        s = slice(self.n_stages, self.n_rows)
+
+        # RHS
+        dividend = tableau[s, -1]
+
+        # Elements of pivot column within slice
+        divisor = tableau[s, col_idx]
+
+        # Array filled with nans
+        nans = np.full(self.n_rows - self.n_stages, np.nan)
+
+        # If element in pivot column is greater than zeron_stages, return
+        # quotient or nan otherwise
+        quotients = np.divide(dividend, divisor, out=nans, where=divisor > 0)
+
+        # Arg of minimum quotient excluding the nan values. n_stages is added
+        # to compensate for earlier exclusion of objective columns
+        row_idx = np.nanargmin(quotients) + self.n_stages
+        return row_idx, col_idx
+
+    def pivot(self, tableau: np.ndarray, row_idx: int, col_idx: int) -> np.ndarray:
+        """Pivots on value on the intersection of pivot row and column.
+
+        >>> t = Tableau(np.array([[-2,-3,0,0,0],[1,3,1,0,4],[3,1,0,1,4.]]), 2)
+        >>> t.pivot(t.tableau, 1, 0).tolist()
+        ... # doctest: +NORMALIZE_WHITESPACE
+        [[0.0, 3.0, 2.0, 0.0, 8.0],
+        [1.0, 3.0, 1.0, 0.0, 4.0],
+        [0.0, -8.0, -3.0, 1.0, -8.0]]
+        """
+        # Avoid changes to original tableau
+        piv_row = tableau[row_idx].copy()
+
+        piv_val = piv_row[col_idx]
+
+        # Entry becomes 1
+        piv_row *= 1 / piv_val
+
+        # Variable in pivot column becomes basic, ie the only non-zero entry
+        for idx, coeff in enumerate(tableau[:, col_idx]):
+            tableau[idx] += -coeff * piv_row
+        tableau[row_idx] = piv_row
+        return tableau
+
+    def change_stage(self, tableau: np.ndarray) -> np.ndarray:
+        """Exits first phase of the two-stage method by deleting artificial
+        rows and columns, or completes the algorithm if exiting the standard
+        case.
+
+        >>> t = Tableau(np.array([
+        ... [3, 3, -1, -1, 0, 0, 4],
+        ... [2, 1, 0, 0, 0, 0, 0.],
+        ... [1, 2, -1, 0, 1, 0, 2],
+        ... [2, 1, 0, -1, 0, 1, 2]
+        ... ]), 2)
+        >>> t.change_stage(t.tableau).tolist()
+        ... # doctest: +NORMALIZE_WHITESPACE
+        [[2.0, 1.0, 0.0, 0.0, 0.0, 0.0],
+        [1.0, 2.0, -1.0, 0.0, 1.0, 2.0],
+        [2.0, 1.0, 0.0, -1.0, 0.0, 2.0]]
+        """
+        # Objective of original objective row remains
+        self.objectives.pop()
+
+        if not self.objectives:
+            return tableau
+
+        # Slice containing ids for artificial columns
+        s = slice(-self.n_art_vars - 1, -1)
+
+        # Delete the artificial variable columns
+        tableau = np.delete(tableau, s, axis=1)
+
+        # Delete the objective row of the first stage
+        tableau = np.delete(tableau, 0, axis=0)
+
+        self.n_stages = 1
+        self.n_rows -= 1
+        self.n_art_vars = 0
+        self.stop_iter = False
+        return tableau
+
+    def run_simplex(self) -> dict[Any, Any]:
+        """Operate on tableau until objective function cannot be
+        improved further.
+
+        # Standard linear program:
+        Max:  x1 +  x2
+        ST:   x1 + 3x2 <= 4
+             3x1 +  x2 <= 4
+        >>> Tableau(np.array([[-1,-1,0,0,0],[1,3,1,0,4],[3,1,0,1,4.]]),
+        ... 2).run_simplex()
+        {'P': 2.0, 'x1': 1.0, 'x2': 1.0}
+
+        # Optimal tableau input:
+        >>> Tableau(np.array([
+        ... [0, 0, 0.25, 0.25, 2],
+        ... [0, 1, 0.375, -0.125, 1],
+        ... [1, 0, -0.125, 0.375, 1]
+        ... ]), 2).run_simplex()
+        {'P': 2.0, 'x1': 1.0, 'x2': 1.0}
+
+        # Non-standard: >= constraints
+        Max: 2x1 + 3x2 +  x3
+        ST:   x1 +  x2 +  x3 <= 40
+             2x1 +  x2 -  x3 >= 10
+                 -  x2 +  x3 >= 10
+        >>> Tableau(np.array([
+        ... [2, 0, 0, 0, -1, -1, 0, 0, 20],
+        ... [-2, -3, -1, 0, 0, 0, 0, 0, 0],
+        ... [1, 1, 1, 1, 0, 0, 0, 0, 40],
+        ... [2, 1, -1, 0, -1, 0, 1, 0, 10],
+        ... [0, -1, 1, 0, 0, -1, 0, 1, 10.]
+        ... ]), 3).run_simplex()
+        {'P': 70.0, 'x1': 10.0, 'x2': 10.0, 'x3': 20.0}
+
+        # Non standard: minimisation and equalities
+        Min: x1 +  x2
+        ST: 2x1 +  x2 = 12
+            6x1 + 5x2 = 40
+        >>> Tableau(np.array([
+        ... [8, 6, 0, -1, 0, -1, 0, 0, 52],
+        ... [1, 1, 0, 0, 0, 0, 0, 0, 0],
+        ... [2, 1, 1, 0, 0, 0, 0, 0, 12],
+        ... [2, 1, 0, -1, 0, 0, 1, 0, 12],
+        ... [6, 5, 0, 0, 1, 0, 0, 0, 40],
+        ... [6, 5, 0, 0, 0, -1, 0, 1, 40.]
+        ... ]), 2).run_simplex()
+        {'P': 7.0, 'x1': 5.0, 'x2': 2.0}
+        """
+        # Stop simplex algorithm from cycling.
+        for _ in range(100):
+            # Completion of each stage removes an objective. If both stages
+            # are complete, then no objectives are left
+            if not self.objectives:
+                self.col_titles = self.generate_col_titles(
+                    self.n_vars, self.n_slack, self.n_art_vars
+                )
+
+                # Find the values of each variable at optimal solution
+                return self.interpret_tableau(self.tableau, self.col_titles)
+
+            row_idx, col_idx = self.find_pivot(self.tableau)
+
+            # If there are no more negative values in objective row
+            if self.stop_iter:
+                # Delete artificial variable columns and rows. Update attributes
+                self.tableau = self.change_stage(self.tableau)
+            else:
+                self.tableau = self.pivot(self.tableau, row_idx, col_idx)
+        return {}
+
+    def interpret_tableau(
+        self, tableau: np.ndarray, col_titles: list[str]
+    ) -> dict[str, float]:
+        """Given the final tableau, add the corresponding values of the basic
+        decision variables to the `output_dict`
+        >>> tableau = np.array([
+        ... [0,0,0.875,0.375,5],
+        ... [0,1,0.375,-0.125,1],
+        ... [1,0,-0.125,0.375,1]
+        ... ])
+        >>> t = Tableau(tableau, 2)
+        >>> t.interpret_tableau(tableau, ["x1", "x2", "s1", "s2", "RHS"])
+        {'P': 5.0, 'x1': 1.0, 'x2': 1.0}
+        """
+        # P = RHS of final tableau
+        output_dict = {"P": abs(tableau[0, -1])}
+
+        for i in range(self.n_vars):
+            # Gives ids of nonzero entries in the ith column
+            nonzero = np.nonzero(tableau[:, i])
+            n_nonzero = len(nonzero[0])
+
+            # First entry in the nonzero ids
+            nonzero_rowidx = nonzero[0][0]
+            nonzero_val = tableau[nonzero_rowidx, i]
+
+            # If there is only one nonzero value in column, which is one
+            if n_nonzero == nonzero_val == 1:
+                rhs_val = tableau[nonzero_rowidx, -1]
+                output_dict[col_titles[i]] = rhs_val
+
+        # Check for basic variables
+        for title in col_titles:
+            # Don't add RHS or slack variables to output dict
+            if title[0] not in "R-s-a":
+                output_dict.setdefault(title, 0)
+        return output_dict
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

machine_learning/linear_discriminant_analysis.py

@@ -399,7 +399,7 @@ def main():
         if input("Press any key to restart or 'q' for quit: ").strip().lower() == "q":
             print("\n" + "GoodBye!".center(100, "-") + "\n")
             break
-        system("clear" if name == "posix" else "cls")  # noqa: S605
+        system("cls" if name == "nt" else "clear")  # noqa: S605
 
 
 if __name__ == "__main__":

machine_learning/local_weighted_learning/local_weighted_learning.py

@@ -1,14 +1,55 @@
+"""
+Locally weighted linear regression, also called local regression, is a type of
+non-parametric linear regression that prioritizes data closest to a given
+prediction point. The algorithm estimates the vector of model coefficients β
+using weighted least squares regression:
+
+β = (XᵀWX)⁻¹(XᵀWy),
+
+where X is the design matrix, y is the response vector, and W is the diagonal
+weight matrix.
+
+This implementation calculates wᵢ, the weight of the ith training sample, using
+the Gaussian weight:
+
+wᵢ = exp(-‖xᵢ - x‖²/(2τ²)),
+
+where xᵢ is the ith training sample, x is the prediction point, τ is the
+"bandwidth", and ‖x‖ is the Euclidean norm (also called the 2-norm or the L²
+norm). The bandwidth τ controls how quickly the weight of a training sample
+decreases as its distance from the prediction point increases. One can think of
+the Gaussian weight as a bell curve centered around the prediction point: a
+training sample is weighted lower if it's farther from the center, and τ
+controls the spread of the bell curve.
+
+Other types of locally weighted regression such as locally estimated scatterplot
+smoothing (LOESS) typically use different weight functions.
+
+References:
+    - https://en.wikipedia.org/wiki/Local_regression
+    - https://en.wikipedia.org/wiki/Weighted_least_squares
+    - https://cs229.stanford.edu/notes2022fall/main_notes.pdf
+"""
+
 import matplotlib.pyplot as plt
 import numpy as np
 
 
-def weighted_matrix(
-    point: np.array, training_data_x: np.array, bandwidth: float
-) -> np.array:
+def weight_matrix(point: np.ndarray, x_train: np.ndarray, tau: float) -> np.ndarray:
     """
-    Calculate the weight for every point in the data set.
-    point --> the x value at which we want to make predictions
-    >>> weighted_matrix(
+    Calculate the weight of every point in the training data around a given
+    prediction point
+
+    Args:
+        point: x-value at which the prediction is being made
+        x_train: ndarray of x-values for training
+        tau: bandwidth value, controls how quickly the weight of training values
+            decreases as the distance from the prediction point increases
+
+    Returns:
+        m x m weight matrix around the prediction point, where m is the size of
+        the training set
+    >>> weight_matrix(
     ...     np.array([1., 1.]),
     ...     np.array([[16.99, 10.34], [21.01,23.68], [24.59,25.69]]),
     ...     0.6
@@ -17,25 +58,30 @@ def weighted_matrix(
            [0.00000000e+000, 0.00000000e+000, 0.00000000e+000],
            [0.00000000e+000, 0.00000000e+000, 0.00000000e+000]])
     """
-    m, _ = np.shape(training_data_x)  # m is the number of training samples
-    weights = np.eye(m)  # Initializing weights as identity matrix
-
-    # calculating weights for all training examples [x(i)'s]
+    m = len(x_train)  # Number of training samples
+    weights = np.eye(m)  # Initialize weights as identity matrix
     for j in range(m):
-        diff = point - training_data_x[j]
-        weights[j, j] = np.exp(diff @ diff.T / (-2.0 * bandwidth**2))
+        diff = point - x_train[j]
+        weights[j, j] = np.exp(diff @ diff.T / (-2.0 * tau**2))
+
     return weights
 
 
 def local_weight(
-    point: np.array,
-    training_data_x: np.array,
-    training_data_y: np.array,
-    bandwidth: float,
-) -> np.array:
+    point: np.ndarray, x_train: np.ndarray, y_train: np.ndarray, tau: float
+) -> np.ndarray:
     """
-    Calculate the local weights using the weight_matrix function on training data.
-    Return the weighted matrix.
+    Calculate the local weights at a given prediction point using the weight
+    matrix for that point
+
+    Args:
+        point: x-value at which the prediction is being made
+        x_train: ndarray of x-values for training
+        y_train: ndarray of y-values for training
+        tau: bandwidth value, controls how quickly the weight of training values
+            decreases as the distance from the prediction point increases
+    Returns:
+        ndarray of local weights
     >>> local_weight(
     ...     np.array([1., 1.]),
     ...     np.array([[16.99, 10.34], [21.01,23.68], [24.59,25.69]]),
@@ -45,19 +91,28 @@ def local_weight(
     array([[0.00873174],
            [0.08272556]])
     """
-    weight = weighted_matrix(point, training_data_x, bandwidth)
-    w = np.linalg.inv(training_data_x.T @ (weight @ training_data_x)) @ (
-        training_data_x.T @ weight @ training_data_y.T
+    weight_mat = weight_matrix(point, x_train, tau)
+    weight = np.linalg.inv(x_train.T @ weight_mat @ x_train) @ (
+        x_train.T @ weight_mat @ y_train.T
     )
 
-    return w
+    return weight
 
 
 def local_weight_regression(
-    training_data_x: np.array, training_data_y: np.array, bandwidth: float
-) -> np.array:
+    x_train: np.ndarray, y_train: np.ndarray, tau: float
+) -> np.ndarray:
     """
-    Calculate predictions for each data point on axis
+    Calculate predictions for each point in the training data
+
+    Args:
+        x_train: ndarray of x-values for training
+        y_train: ndarray of y-values for training
+        tau: bandwidth value, controls how quickly the weight of training values
+            decreases as the distance from the prediction point increases
+
+    Returns:
+        ndarray of predictions
     >>> local_weight_regression(
     ...     np.array([[16.99, 10.34], [21.01, 23.68], [24.59, 25.69]]),
     ...     np.array([[1.01, 1.66, 3.5]]),
@@ -65,77 +120,57 @@ def local_weight_regression(
     ... )
     array([1.07173261, 1.65970737, 3.50160179])
     """
-    m, _ = np.shape(training_data_x)
-    ypred = np.zeros(m)
+    y_pred = np.zeros(len(x_train))  # Initialize array of predictions
+    for i, item in enumerate(x_train):
+        y_pred[i] = item @ local_weight(item, x_train, y_train, tau)
 
-    for i, item in enumerate(training_data_x):
-        ypred[i] = item @ local_weight(
-            item, training_data_x, training_data_y, bandwidth
-        )
-
-    return ypred
+    return y_pred
 
 
 def load_data(
-    dataset_name: str, cola_name: str, colb_name: str
-) -> tuple[np.array, np.array, np.array, np.array]:
+    dataset_name: str, x_name: str, y_name: str
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """
     Load data from seaborn and split it into x and y points
+    >>> pass    # No doctests, function is for demo purposes only
     """
     import seaborn as sns
 
     data = sns.load_dataset(dataset_name)
-    col_a = np.array(data[cola_name])  # total_bill
-    col_b = np.array(data[colb_name])  # tip
+    x_data = np.array(data[x_name])
+    y_data = np.array(data[y_name])
 
-    mcol_a = col_a.copy()
-    mcol_b = col_b.copy()
+    one = np.ones(len(y_data))
 
-    one = np.ones(np.shape(mcol_b)[0], dtype=int)
+    # pairing elements of one and x_data
+    x_train = np.column_stack((one, x_data))
 
-    # pairing elements of one and mcol_a
-    training_data_x = np.column_stack((one, mcol_a))
-
-    return training_data_x, mcol_b, col_a, col_b
-
-
-def get_preds(training_data_x: np.array, mcol_b: np.array, tau: float) -> np.array:
-    """
-    Get predictions with minimum error for each training data
-    >>> get_preds(
-    ...     np.array([[16.99, 10.34], [21.01, 23.68], [24.59, 25.69]]),
-    ...     np.array([[1.01, 1.66, 3.5]]),
-    ...     0.6
-    ... )
-    array([1.07173261, 1.65970737, 3.50160179])
-    """
-    ypred = local_weight_regression(training_data_x, mcol_b, tau)
-    return ypred
+    return x_train, x_data, y_data
 
 
 def plot_preds(
-    training_data_x: np.array,
-    predictions: np.array,
-    col_x: np.array,
-    col_y: np.array,
-    cola_name: str,
-    colb_name: str,
-) -> plt.plot:
+    x_train: np.ndarray,
+    preds: np.ndarray,
+    x_data: np.ndarray,
+    y_data: np.ndarray,
+    x_name: str,
+    y_name: str,
+) -> None:
     """
     Plot predictions and display the graph
+    >>> pass    # No doctests, function is for demo purposes only
     """
-    xsort = training_data_x.copy()
-    xsort.sort(axis=0)
-    plt.scatter(col_x, col_y, color="blue")
+    x_train_sorted = np.sort(x_train, axis=0)
+    plt.scatter(x_data, y_data, color="blue")
     plt.plot(
-        xsort[:, 1],
-        predictions[training_data_x[:, 1].argsort(0)],
+        x_train_sorted[:, 1],
+        preds[x_train[:, 1].argsort(0)],
         color="yellow",
         linewidth=5,
     )
     plt.title("Local Weighted Regression")
-    plt.xlabel(cola_name)
-    plt.ylabel(colb_name)
+    plt.xlabel(x_name)
+    plt.ylabel(y_name)
     plt.show()
 
 
@@ -144,6 +179,7 @@ if __name__ == "__main__":
 
     doctest.testmod()
 
-    training_data_x, mcol_b, col_a, col_b = load_data("tips", "total_bill", "tip")
-    predictions = get_preds(training_data_x, mcol_b, 0.5)
-    plot_preds(training_data_x, predictions, col_a, col_b, "total_bill", "tip")
+    # Demo with a dataset from the seaborn module
+    training_data_x, total_bill, tip = load_data("tips", "total_bill", "tip")
+    predictions = local_weight_regression(training_data_x, tip, 5)
+    plot_preds(training_data_x, predictions, total_bill, tip, "total_bill", "tip")

machine_learning/polymonial_regression.py

@@ -1,44 +0,0 @@
-import pandas as pd
-from matplotlib import pyplot as plt
-from sklearn.linear_model import LinearRegression
-
-# Splitting the dataset into the Training set and Test set
-from sklearn.model_selection import train_test_split
-
-# Fitting Polynomial Regression to the dataset
-from sklearn.preprocessing import PolynomialFeatures
-
-# Importing the dataset
-dataset = pd.read_csv(
-    "https://s3.us-west-2.amazonaws.com/public.gamelab.fun/dataset/"
-    "position_salaries.csv"
-)
-X = dataset.iloc[:, 1:2].values
-y = dataset.iloc[:, 2].values
-
-
-X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)
-
-
-poly_reg = PolynomialFeatures(degree=4)
-X_poly = poly_reg.fit_transform(X)
-pol_reg = LinearRegression()
-pol_reg.fit(X_poly, y)
-
-
-# Visualizing the Polymonial Regression results
-def viz_polymonial():
-    plt.scatter(X, y, color="red")
-    plt.plot(X, pol_reg.predict(poly_reg.fit_transform(X)), color="blue")
-    plt.title("Truth or Bluff (Linear Regression)")
-    plt.xlabel("Position level")
-    plt.ylabel("Salary")
-    plt.show()
-
-
-if __name__ == "__main__":
-    viz_polymonial()
-
-    # Predicting a new result with Polymonial Regression
-    pol_reg.predict(poly_reg.fit_transform([[5.5]]))
-    # output should be 132148.43750003

machine_learning/polynomial_regression.py

@@ -0,0 +1,213 @@
+"""
+Polynomial regression is a type of regression analysis that models the relationship
+between a predictor x and the response y as an mth-degree polynomial:
+
+y = β₀ + β₁x + β₂x² + ... + βₘxᵐ + ε
+
+By treating x, x², ..., xᵐ as distinct variables, we see that polynomial regression is a
+special case of multiple linear regression. Therefore, we can use ordinary least squares
+(OLS) estimation to estimate the vector of model parameters β = (β₀, β₁, β₂, ..., βₘ)
+for polynomial regression:
+
+β = (XᵀX)⁻¹Xᵀy = X⁺y
+
+where X is the design matrix, y is the response vector, and X⁺ denotes the Moore–Penrose
+pseudoinverse of X. In the case of polynomial regression, the design matrix is
+
+    |1  x₁  x₁² ⋯ x₁ᵐ|
+X = |1  x₂  x₂² ⋯ x₂ᵐ|
+    |⋮  ⋮   ⋮   ⋱ ⋮  |
+    |1  xₙ  xₙ² ⋯  xₙᵐ|
+
+In OLS estimation, inverting XᵀX to compute X⁺ can be very numerically unstable. This
+implementation sidesteps this need to invert XᵀX by computing X⁺ using singular value
+decomposition (SVD):
+
+β = VΣ⁺Uᵀy
+
+where UΣVᵀ is an SVD of X.
+
+References:
+    - https://en.wikipedia.org/wiki/Polynomial_regression
+    - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse
+    - https://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares
+    - https://en.wikipedia.org/wiki/Singular_value_decomposition
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+class PolynomialRegression:
+    __slots__ = "degree", "params"
+
+    def __init__(self, degree: int) -> None:
+        """
+        @raises ValueError: if the polynomial degree is negative
+        """
+        if degree < 0:
+            raise ValueError("Polynomial degree must be non-negative")
+
+        self.degree = degree
+        self.params = None
+
+    @staticmethod
+    def _design_matrix(data: np.ndarray, degree: int) -> np.ndarray:
+        """
+        Constructs a polynomial regression design matrix for the given input data. For
+        input data x = (x₁, x₂, ..., xₙ) and polynomial degree m, the design matrix is
+        the Vandermonde matrix
+
+            |1  x₁  x₁² ⋯ x₁ᵐ|
+        X = |1  x₂  x₂² ⋯ x₂ᵐ|
+            |⋮  ⋮   ⋮   ⋱ ⋮  |
+            |1  xₙ  xₙ² ⋯  xₙᵐ|
+
+        Reference: https://en.wikipedia.org/wiki/Vandermonde_matrix
+
+        @param data:    the input predictor values x, either for model fitting or for
+                        prediction
+        @param degree:  the polynomial degree m
+        @returns:       the Vandermonde matrix X (see above)
+        @raises ValueError: if input data is not N x 1
+
+        >>> x = np.array([0, 1, 2])
+        >>> PolynomialRegression._design_matrix(x, degree=0)
+        array([[1],
+               [1],
+               [1]])
+        >>> PolynomialRegression._design_matrix(x, degree=1)
+        array([[1, 0],
+               [1, 1],
+               [1, 2]])
+        >>> PolynomialRegression._design_matrix(x, degree=2)
+        array([[1, 0, 0],
+               [1, 1, 1],
+               [1, 2, 4]])
+        >>> PolynomialRegression._design_matrix(x, degree=3)
+        array([[1, 0, 0, 0],
+               [1, 1, 1, 1],
+               [1, 2, 4, 8]])
+        >>> PolynomialRegression._design_matrix(np.array([[0, 0], [0 , 0]]), degree=3)
+        Traceback (most recent call last):
+        ...
+        ValueError: Data must have dimensions N x 1
+        """
+        rows, *remaining = data.shape
+        if remaining:
+            raise ValueError("Data must have dimensions N x 1")
+
+        return np.vander(data, N=degree + 1, increasing=True)
+
+    def fit(self, x_train: np.ndarray, y_train: np.ndarray) -> None:
+        """
+        Computes the polynomial regression model parameters using ordinary least squares
+        (OLS) estimation:
+
+        β = (XᵀX)⁻¹Xᵀy = X⁺y
+
+        where X⁺ denotes the Moore–Penrose pseudoinverse of the design matrix X. This
+        function computes X⁺ using singular value decomposition (SVD).
+
+        References:
+            - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse
+            - https://en.wikipedia.org/wiki/Singular_value_decomposition
+            - https://en.wikipedia.org/wiki/Multicollinearity
+
+        @param x_train: the predictor values x for model fitting
+        @param y_train: the response values y for model fitting
+        @raises ArithmeticError:    if X isn't full rank, then XᵀX is singular and β
+                                    doesn't exist
+
+        >>> x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
+        >>> y = x**3 - 2 * x**2 + 3 * x - 5
+        >>> poly_reg = PolynomialRegression(degree=3)
+        >>> poly_reg.fit(x, y)
+        >>> poly_reg.params
+        array([-5.,  3., -2.,  1.])
+        >>> poly_reg = PolynomialRegression(degree=20)
+        >>> poly_reg.fit(x, y)
+        Traceback (most recent call last):
+        ...
+        ArithmeticError: Design matrix is not full rank, can't compute coefficients
+
+        Make sure errors don't grow too large:
+        >>> coefs = np.array([-250, 50, -2, 36, 20, -12, 10, 2, -1, -15, 1])
+        >>> y = PolynomialRegression._design_matrix(x, len(coefs) - 1) @ coefs
+        >>> poly_reg = PolynomialRegression(degree=len(coefs) - 1)
+        >>> poly_reg.fit(x, y)
+        >>> np.allclose(poly_reg.params, coefs, atol=10e-3)
+        True
+        """
+        X = PolynomialRegression._design_matrix(x_train, self.degree)  # noqa: N806
+        _, cols = X.shape
+        if np.linalg.matrix_rank(X) < cols:
+            raise ArithmeticError(
+                "Design matrix is not full rank, can't compute coefficients"
+            )
+
+        # np.linalg.pinv() computes the Moore–Penrose pseudoinverse using SVD
+        self.params = np.linalg.pinv(X) @ y_train
+
+    def predict(self, data: np.ndarray) -> np.ndarray:
+        """
+        Computes the predicted response values y for the given input data by
+        constructing the design matrix X and evaluating y = Xβ.
+
+        @param data:    the predictor values x for prediction
+        @returns:       the predicted response values y = Xβ
+        @raises ArithmeticError:    if this function is called before the model
+                                    parameters are fit
+
+        >>> x = np.array([0, 1, 2, 3, 4])
+        >>> y = x**3 - 2 * x**2 + 3 * x - 5
+        >>> poly_reg = PolynomialRegression(degree=3)
+        >>> poly_reg.fit(x, y)
+        >>> poly_reg.predict(np.array([-1]))
+        array([-11.])
+        >>> poly_reg.predict(np.array([-2]))
+        array([-27.])
+        >>> poly_reg.predict(np.array([6]))
+        array([157.])
+        >>> PolynomialRegression(degree=3).predict(x)
+        Traceback (most recent call last):
+        ...
+        ArithmeticError: Predictor hasn't been fit yet
+        """
+        if self.params is None:
+            raise ArithmeticError("Predictor hasn't been fit yet")
+
+        return PolynomialRegression._design_matrix(data, self.degree) @ self.params
+
+
+def main() -> None:
+    """
+    Fit a polynomial regression model to predict fuel efficiency using seaborn's mpg
+    dataset
+
+    >>> pass    # Placeholder, function is only for demo purposes
+    """
+    import seaborn as sns
+
+    mpg_data = sns.load_dataset("mpg")
+
+    poly_reg = PolynomialRegression(degree=2)
+    poly_reg.fit(mpg_data.weight, mpg_data.mpg)
+
+    weight_sorted = np.sort(mpg_data.weight)
+    predictions = poly_reg.predict(weight_sorted)
+
+    plt.scatter(mpg_data.weight, mpg_data.mpg, color="gray", alpha=0.5)
+    plt.plot(weight_sorted, predictions, color="red", linewidth=3)
+    plt.title("Predicting Fuel Efficiency Using Polynomial Regression")
+    plt.xlabel("Weight (lbs)")
+    plt.ylabel("Fuel Efficiency (mpg)")
+    plt.show()
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    main()

machine_learning/similarity_search.py

@@ -97,26 +97,29 @@ def similarity_search(
     """
 
     if dataset.ndim != value_array.ndim:
-        raise ValueError(
-            f"Wrong input data's dimensions... dataset : {dataset.ndim}, "
-            f"value_array : {value_array.ndim}"
+        msg = (
+            "Wrong input data's dimensions... "
+            f"dataset : {dataset.ndim}, value_array : {value_array.ndim}"
         )
+        raise ValueError(msg)
 
     try:
         if dataset.shape[1] != value_array.shape[1]:
-            raise ValueError(
-                f"Wrong input data's shape... dataset : {dataset.shape[1]}, "
-                f"value_array : {value_array.shape[1]}"
+            msg = (
+                "Wrong input data's shape... "
+                f"dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}"
             )
+            raise ValueError(msg)
     except IndexError:
         if dataset.ndim != value_array.ndim:
             raise TypeError("Wrong shape")
 
     if dataset.dtype != value_array.dtype:
-        raise TypeError(
-            f"Input data have different datatype... dataset : {dataset.dtype}, "
-            f"value_array : {value_array.dtype}"
+        msg = (
+            "Input data have different datatype... "
+            f"dataset : {dataset.dtype}, value_array : {value_array.dtype}"
         )
+        raise TypeError(msg)
 
     answer = []
 

machine_learning/support_vector_machines.py

@@ -74,7 +74,8 @@ class SVC:
             # sklear: def_gamma = 1/(n_features * X.var()) (wiki)
             # previously it was 1/(n_features)
         else:
-            raise ValueError(f"Unknown kernel: {kernel}")
+            msg = f"Unknown kernel: {kernel}"
+            raise ValueError(msg)
 
     # kernels
     def __linear(self, vector1: ndarray, vector2: ndarray) -> float:

maths/3n_plus_1.py

@@ -1,149 +0,0 @@
-from __future__ import annotations
-
-
-def n31(a: int) -> tuple[list[int], int]:
-    """
-    Returns the Collatz sequence and its length of any positive integer.
-    >>> n31(4)
-    ([4, 2, 1], 3)
-    """
-
-    if not isinstance(a, int):
-        raise TypeError(f"Must be int, not {type(a).__name__}")
-    if a < 1:
-        raise ValueError(f"Given integer must be positive, not {a}")
-
-    path = [a]
-    while a != 1:
-        if a % 2 == 0:
-            a //= 2
-        else:
-            a = 3 * a + 1
-        path.append(a)
-    return path, len(path)
-
-
-def test_n31():
-    """
-    >>> test_n31()
-    """
-    assert n31(4) == ([4, 2, 1], 3)
-    assert n31(11) == ([11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1], 15)
-    assert n31(31) == (
-        [
-            31,
-            94,
-            47,
-            142,
-            71,
-            214,
-            107,
-            322,
-            161,
-            484,
-            242,
-            121,
-            364,
-            182,
-            91,
-            274,
-            137,
-            412,
-            206,
-            103,
-            310,
-            155,
-            466,
-            233,
-            700,
-            350,
-            175,
-            526,
-            263,
-            790,
-            395,
-            1186,
-            593,
-            1780,
-            890,
-            445,
-            1336,
-            668,
-            334,
-            167,
-            502,
-            251,
-            754,
-            377,
-            1132,
-            566,
-            283,
-            850,
-            425,
-            1276,
-            638,
-            319,
-            958,
-            479,
-            1438,
-            719,
-            2158,
-            1079,
-            3238,
-            1619,
-            4858,
-            2429,
-            7288,
-            3644,
-            1822,
-            911,
-            2734,
-            1367,
-            4102,
-            2051,
-            6154,
-            3077,
-            9232,
-            4616,
-            2308,
-            1154,
-            577,
-            1732,
-            866,
-            433,
-            1300,
-            650,
-            325,
-            976,
-            488,
-            244,
-            122,
-            61,
-            184,
-            92,
-            46,
-            23,
-            70,
-            35,
-            106,
-            53,
-            160,
-            80,
-            40,
-            20,
-            10,
-            5,
-            16,
-            8,
-            4,
-            2,
-            1,
-        ],
-        107,
-    )
-
-
-if __name__ == "__main__":
-    num = 4
-    path, length = n31(num)
-    print(f"The Collatz sequence of {num} took {length} steps. \nPath: {path}")

maths/automorphic_number.py

@@ -40,7 +40,8 @@ def is_automorphic_number(number: int) -> bool:
     TypeError: Input value of [number=5.0] must be an integer
     """
     if not isinstance(number, int):
-        raise TypeError(f"Input value of [number={number}] must be an integer")
+        msg = f"Input value of [number={number}] must be an integer"
+        raise TypeError(msg)
     if number < 0:
         return False
     number_square = number * number

maths/catalan_number.py

@@ -31,10 +31,12 @@ def catalan(number: int) -> int:
     """
 
     if not isinstance(number, int):
-        raise TypeError(f"Input value of [number={number}] must be an integer")
+        msg = f"Input value of [number={number}] must be an integer"
+        raise TypeError(msg)
 
     if number < 1:
-        raise ValueError(f"Input value of [number={number}] must be > 0")
+        msg = f"Input value of [number={number}] must be > 0"
+        raise ValueError(msg)
 
     current_number = 1
 

maths/collatz_sequence.py

@@ -1,43 +1,66 @@
+"""
+The Collatz conjecture is a famous unsolved problem in mathematics. Given a starting
+positive integer, define the following sequence:
+- If the current term n is even, then the next term is n/2.
+- If the current term n is odd, then the next term is 3n + 1.
+The conjecture claims that this sequence will always reach 1 for any starting number.
+
+Other names for this problem include the 3n + 1 problem, the Ulam conjecture, Kakutani's
+problem, the Thwaites conjecture, Hasse's algorithm, the Syracuse problem, and the
+hailstone sequence.
+
+Reference: https://en.wikipedia.org/wiki/Collatz_conjecture
+"""
+
 from __future__ import annotations
 
+from collections.abc import Generator
 
-def collatz_sequence(n: int) -> list[int]:
+
+def collatz_sequence(n: int) -> Generator[int, None, None]:
     """
-    Collatz conjecture: start with any positive integer n. The next term is
-    obtained as follows:
-        If n term is even, the next term is: n / 2 .
-        If n is odd, the next term is: 3 * n + 1.
-
-    The conjecture states the sequence will always reach 1 for any starting value n.
-    Example:
-    >>> collatz_sequence(2.1)
+    Generate the Collatz sequence starting at n.
+    >>> tuple(collatz_sequence(2.1))
     Traceback (most recent call last):
         ...
-    Exception: Sequence only defined for natural numbers
-    >>> collatz_sequence(0)
+    Exception: Sequence only defined for positive integers
+    >>> tuple(collatz_sequence(0))
     Traceback (most recent call last):
         ...
-    Exception: Sequence only defined for natural numbers
-    >>> collatz_sequence(43)  # doctest: +NORMALIZE_WHITESPACE
-    [43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7,
-     22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
+    Exception: Sequence only defined for positive integers
+    >>> tuple(collatz_sequence(4))
+    (4, 2, 1)
+    >>> tuple(collatz_sequence(11))
+    (11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1)
+    >>> tuple(collatz_sequence(31))     # doctest: +NORMALIZE_WHITESPACE
+    (31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137,
+    412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593,
+    1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425,
+    1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644,
+    1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732,
+    866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53,
+    160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1)
+    >>> tuple(collatz_sequence(43))     # doctest: +NORMALIZE_WHITESPACE
+    (43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26,
+    13, 40, 20, 10, 5, 16, 8, 4, 2, 1)
     """
-
     if not isinstance(n, int) or n < 1:
-        raise Exception("Sequence only defined for natural numbers")
+        raise Exception("Sequence only defined for positive integers")
 
-    sequence = [n]
+    yield n
     while n != 1:
-        n = 3 * n + 1 if n & 1 else n // 2
-        sequence.append(n)
-    return sequence
+        if n % 2 == 0:
+            n //= 2
+        else:
+            n = 3 * n + 1
+        yield n
 
 
 def main():
-    n = 43
-    sequence = collatz_sequence(n)
+    n = int(input("Your number: "))
+    sequence = tuple(collatz_sequence(n))
     print(sequence)
-    print(f"collatz sequence from {n} took {len(sequence)} steps.")
+    print(f"Collatz sequence from {n} took {len(sequence)} steps.")
 
 
 if __name__ == "__main__":

maths/dual_number_automatic_differentiation.py

@@ -0,0 +1,141 @@
+from math import factorial
+
+"""
+https://en.wikipedia.org/wiki/Automatic_differentiation#Automatic_differentiation_using_dual_numbers
+https://blog.jliszka.org/2013/10/24/exact-numeric-nth-derivatives.html
+
+Note this only works for basic functions, f(x) where the power of x is positive.
+"""
+
+
+class Dual:
+    def __init__(self, real, rank):
+        self.real = real
+        if isinstance(rank, int):
+            self.duals = [1] * rank
+        else:
+            self.duals = rank
+
+    def __repr__(self):
+        return (
+            f"{self.real}+"
+            f"{'+'.join(str(dual)+'E'+str(n+1)for n,dual in enumerate(self.duals))}"
+        )
+
+    def reduce(self):
+        cur = self.duals.copy()
+        while cur[-1] == 0:
+            cur.pop(-1)
+        return Dual(self.real, cur)
+
+    def __add__(self, other):
+        if not isinstance(other, Dual):
+            return Dual(self.real + other, self.duals)
+        s_dual = self.duals.copy()
+        o_dual = other.duals.copy()
+        if len(s_dual) > len(o_dual):
+            o_dual.extend([1] * (len(s_dual) - len(o_dual)))
+        elif len(s_dual) < len(o_dual):
+            s_dual.extend([1] * (len(o_dual) - len(s_dual)))
+        new_duals = []
+        for i in range(len(s_dual)):
+            new_duals.append(s_dual[i] + o_dual[i])
+        return Dual(self.real + other.real, new_duals)
+
+    __radd__ = __add__
+
+    def __sub__(self, other):
+        return self + other * -1
+
+    def __mul__(self, other):
+        if not isinstance(other, Dual):
+            new_duals = []
+            for i in self.duals:
+                new_duals.append(i * other)
+            return Dual(self.real * other, new_duals)
+        new_duals = [0] * (len(self.duals) + len(other.duals) + 1)
+        for i, item in enumerate(self.duals):
+            for j, jtem in enumerate(other.duals):
+                new_duals[i + j + 1] += item * jtem
+        for k in range(len(self.duals)):
+            new_duals[k] += self.duals[k] * other.real
+        for index in range(len(other.duals)):
+            new_duals[index] += other.duals[index] * self.real
+        return Dual(self.real * other.real, new_duals)
+
+    __rmul__ = __mul__
+
+    def __truediv__(self, other):
+        if not isinstance(other, Dual):
+            new_duals = []
+            for i in self.duals:
+                new_duals.append(i / other)
+            return Dual(self.real / other, new_duals)
+        raise ValueError
+
+    def __floordiv__(self, other):
+        if not isinstance(other, Dual):
+            new_duals = []
+            for i in self.duals:
+                new_duals.append(i // other)
+            return Dual(self.real // other, new_duals)
+        raise ValueError
+
+    def __pow__(self, n):
+        if n < 0 or isinstance(n, float):
+            raise ValueError("power must be a positive integer")
+        if n == 0:
+            return 1
+        if n == 1:
+            return self
+        x = self
+        for _ in range(n - 1):
+            x *= self
+        return x
+
+
+def differentiate(func, position, order):
+    """
+    >>> differentiate(lambda x: x**2, 2, 2)
+    2
+    >>> differentiate(lambda x: x**2 * x**4, 9, 2)
+    196830
+    >>> differentiate(lambda y: 0.5 * (y + 3) ** 6, 3.5, 4)
+    7605.0
+    >>> differentiate(lambda y: y ** 2, 4, 3)
+    0
+    >>> differentiate(8, 8, 8)
+    Traceback (most recent call last):
+        ...
+    ValueError: differentiate() requires a function as input for func
+    >>> differentiate(lambda x: x **2, "", 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: differentiate() requires a float as input for position
+    >>> differentiate(lambda x: x**2, 3, "")
+    Traceback (most recent call last):
+        ...
+    ValueError: differentiate() requires an int as input for order
+    """
+    if not callable(func):
+        raise ValueError("differentiate() requires a function as input for func")
+    if not isinstance(position, (float, int)):
+        raise ValueError("differentiate() requires a float as input for position")
+    if not isinstance(order, int):
+        raise ValueError("differentiate() requires an int as input for order")
+    d = Dual(position, 1)
+    result = func(d)
+    if order == 0:
+        return result.real
+    return result.duals[order - 1] * factorial(order)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    def f(y):
+        return y**2 * y**4
+
+    print(differentiate(f, 9, 2))

maths/euclidean_distance.py

@@ -1,12 +1,12 @@
 from __future__ import annotations
 
+import typing
 from collections.abc import Iterable
-from typing import Union
 
 import numpy as np
 
-Vector = Union[Iterable[float], Iterable[int], np.ndarray]
-VectorOut = Union[np.float64, int, float]
+Vector = typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
+VectorOut = typing.Union[np.float64, int, float]  # noqa: UP007
 
 
 def euclidean_distance(vector_1: Vector, vector_2: Vector) -> VectorOut:

maths/factorial.py

@@ -55,7 +55,7 @@ def factorial_recursive(n: int) -> int:
         raise ValueError("factorial() only accepts integral values")
     if n < 0:
         raise ValueError("factorial() not defined for negative values")
-    return 1 if n == 0 or n == 1 else n * factorial(n - 1)
+    return 1 if n in {0, 1} else n * factorial(n - 1)
 
 
 if __name__ == "__main__":

maths/hexagonal_number.py

@@ -36,7 +36,8 @@ def hexagonal(number: int) -> int:
     TypeError: Input value of [number=11.0] must be an integer
     """
     if not isinstance(number, int):
-        raise TypeError(f"Input value of [number={number}] must be an integer")
+        msg = f"Input value of [number={number}] must be an integer"
+        raise TypeError(msg)
     if number < 1:
         raise ValueError("Input must be a positive integer")
     return number * (2 * number - 1)

maths/is_int_palindrome.py

@@ -0,0 +1,34 @@
+def is_int_palindrome(num: int) -> bool:
+    """
+    Returns whether `num` is a palindrome or not
+    (see for reference https://en.wikipedia.org/wiki/Palindromic_number).
+
+    >>> is_int_palindrome(-121)
+    False
+    >>> is_int_palindrome(0)
+    True
+    >>> is_int_palindrome(10)
+    False
+    >>> is_int_palindrome(11)
+    True
+    >>> is_int_palindrome(101)
+    True
+    >>> is_int_palindrome(120)
+    False
+    """
+    if num < 0:
+        return False
+
+    num_copy: int = num
+    rev_num: int = 0
+    while num > 0:
+        rev_num = rev_num * 10 + (num % 10)
+        num //= 10
+
+    return num_copy == rev_num
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()