From a7bfa224554f277ed68be9e4ef3f6d1cd89008af Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 30 Sep 2024 22:16:17 +0200
Subject: [PATCH 1/9] [pre-commit.ci] pre-commit autoupdate (#11594)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

updates:
- [github.com/astral-sh/ruff-pre-commit: v0.6.7 → v0.6.8](https://github.com/astral-sh/ruff-pre-commit/compare/v0.6.7...v0.6.8)
- [github.com/abravalheri/validate-pyproject: v0.19 → v0.20.2](https://github.com/abravalheri/validate-pyproject/compare/v0.19...v0.20.2)

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 .pre-commit-config.yaml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 7b219597f..8a8e5c1f6 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -16,7 +16,7 @@ repos:
       - id: auto-walrus
 
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.6.7
+    rev: v0.6.8
     hooks:
       - id: ruff
       - id: ruff-format
@@ -42,7 +42,7 @@ repos:
         pass_filenames: false
 
   - repo: https://github.com/abravalheri/validate-pyproject
-    rev: v0.19
+    rev: v0.20.2
     hooks:
       - id: validate-pyproject
 

From 0177ae1cd596f4f3c0ee7490666d74504deb0298 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Mon, 30 Sep 2024 23:01:15 +0200
Subject: [PATCH 2/9] Upgrade to Python 3.13 (#11588)

---
 .github/workflows/build.yml                   |  6 ++-
 DIRECTORY.md                                  |  1 -
 computer_vision/haralick_descriptors.py       |  8 ++--
 data_structures/heap/binomial_heap.py         |  6 +--
 electronics/circular_convolution.py           |  6 +--
 fractals/julia_sets.py                        | 18 ++++-----
 graphics/bezier_curve.py                      |  8 ++--
 graphs/dijkstra_binary_grid.py                |  2 +-
 linear_algebra/src/power_iteration.py         |  2 +-
 linear_programming/simplex.py                 | 32 +++++++--------
 machine_learning/decision_tree.py             |  8 ++--
 machine_learning/forecasting/run.py           |  8 ++--
 machine_learning/k_nearest_neighbours.py      |  2 +-
 machine_learning/logistic_regression.py       |  4 +-
 machine_learning/loss_functions.py            | 40 +++++++++----------
 machine_learning/mfcc.py                      | 13 +++---
 .../multilayer_perceptron_classifier.py       |  2 +-
 machine_learning/scoring_functions.py         | 22 +++++-----
 machine_learning/similarity_search.py         |  2 +-
 machine_learning/support_vector_machines.py   |  6 +--
 maths/euclidean_distance.py                   |  8 ++--
 maths/euler_method.py                         |  2 +-
 maths/euler_modified.py                       |  4 +-
 maths/gaussian.py                             | 16 ++++----
 maths/minkowski_distance.py                   |  2 +-
 maths/numerical_analysis/adams_bashforth.py   |  8 ++--
 maths/numerical_analysis/runge_kutta.py       |  2 +-
 .../runge_kutta_fehlberg_45.py                |  4 +-
 maths/numerical_analysis/runge_kutta_gills.py |  2 +-
 maths/softmax.py                              |  2 +-
 .../two_hidden_layers_neural_network.py       |  6 +--
 other/bankers_algorithm.py                    |  8 ++--
 physics/in_static_equilibrium.py              |  2 +-
 requirements.txt                              |  4 +-
 ..._tweets.py => get_user_tweets.py.DISABLED} |  0
 35 files changed, 135 insertions(+), 131 deletions(-)
 rename web_programming/{get_user_tweets.py => get_user_tweets.py.DISABLED} (100%)

diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index a113b4608..dad2b2fac 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -12,7 +12,7 @@ jobs:
       - uses: actions/checkout@v4
       - uses: actions/setup-python@v5
         with:
-          python-version: 3.12
+          python-version: 3.13
           allow-prereleases: true
       - uses: actions/cache@v4
         with:
@@ -26,6 +26,10 @@ jobs:
         # TODO: #8818 Re-enable quantum tests
         run: pytest
           --ignore=quantum/q_fourier_transform.py
+          --ignore=computer_vision/cnn_classification.py
+          --ignore=dynamic_programming/k_means_clustering_tensorflow.py
+          --ignore=machine_learning/lstm/lstm_prediction.py
+          --ignore=neural_network/input_data.py
           --ignore=project_euler/
           --ignore=scripts/validate_solutions.py
           --cov-report=term-missing:skip-covered
diff --git a/DIRECTORY.md b/DIRECTORY.md
index 955001e2a..56ab8377f 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -1343,7 +1343,6 @@
   * [Get Ip Geolocation](web_programming/get_ip_geolocation.py)
   * [Get Top Billionaires](web_programming/get_top_billionaires.py)
   * [Get Top Hn Posts](web_programming/get_top_hn_posts.py)
-  * [Get User Tweets](web_programming/get_user_tweets.py)
   * [Giphy](web_programming/giphy.py)
   * [Instagram Crawler](web_programming/instagram_crawler.py)
   * [Instagram Pic](web_programming/instagram_pic.py)
diff --git a/computer_vision/haralick_descriptors.py b/computer_vision/haralick_descriptors.py
index 634f04957..54632160d 100644
--- a/computer_vision/haralick_descriptors.py
+++ b/computer_vision/haralick_descriptors.py
@@ -19,7 +19,7 @@ def root_mean_square_error(original: np.ndarray, reference: np.ndarray) -> float
         >>> root_mean_square_error(np.array([1, 2, 3]), np.array([6, 4, 2]))
         3.1622776601683795
     """
-    return np.sqrt(((original - reference) ** 2).mean())
+    return float(np.sqrt(((original - reference) ** 2).mean()))
 
 
 def normalize_image(
@@ -273,7 +273,7 @@ def haralick_descriptors(matrix: np.ndarray) -> list[float]:
         >>> morphological = opening_filter(binary)
         >>> mask_1 = binary_mask(gray, morphological)[0]
         >>> concurrency = matrix_concurrency(mask_1, (0, 1))
-        >>> haralick_descriptors(concurrency)
+        >>> [float(f) for f in haralick_descriptors(concurrency)]
         [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
     """
     # Function np.indices could be used for bigger input types,
@@ -335,7 +335,7 @@ def get_descriptors(
     return np.concatenate(descriptors, axis=None)
 
 
-def euclidean(point_1: np.ndarray, point_2: np.ndarray) -> np.float32:
+def euclidean(point_1: np.ndarray, point_2: np.ndarray) -> float:
     """
     Simple method for calculating the euclidean distance between two points,
     with type np.ndarray.
@@ -346,7 +346,7 @@ def euclidean(point_1: np.ndarray, point_2: np.ndarray) -> np.float32:
         >>> euclidean(a, b)
         3.3166247903554
     """
-    return np.sqrt(np.sum(np.square(point_1 - point_2)))
+    return float(np.sqrt(np.sum(np.square(point_1 - point_2))))
 
 
 def get_distances(descriptors: np.ndarray, base: int) -> list[tuple[int, float]]:
diff --git a/data_structures/heap/binomial_heap.py b/data_structures/heap/binomial_heap.py
index 099bd2871..9cfdf0c12 100644
--- a/data_structures/heap/binomial_heap.py
+++ b/data_structures/heap/binomial_heap.py
@@ -73,7 +73,7 @@ class BinomialHeap:
     30
 
     Deleting - delete() test
-    >>> [first_heap.delete_min() for _ in range(20)]
+    >>> [int(first_heap.delete_min()) for _ in range(20)]
     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
 
     Create a new Heap
@@ -118,7 +118,7 @@ class BinomialHeap:
     values in merged heap; (merge is inplace)
     >>> results = []
     >>> while not first_heap.is_empty():
-    ...     results.append(first_heap.delete_min())
+    ...     results.append(int(first_heap.delete_min()))
     >>> results
     [17, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 34]
     """
@@ -354,7 +354,7 @@ class BinomialHeap:
         # Merge heaps
         self.merge_heaps(new_heap)
 
-        return min_value
+        return int(min_value)
 
     def pre_order(self):
         """
diff --git a/electronics/circular_convolution.py b/electronics/circular_convolution.py
index 768f2ad94..d06e76be7 100644
--- a/electronics/circular_convolution.py
+++ b/electronics/circular_convolution.py
@@ -39,7 +39,7 @@ class CircularConvolution:
         Usage:
         >>> convolution = CircularConvolution()
         >>> convolution.circular_convolution()
-        [10, 10, 6, 14]
+        [10.0, 10.0, 6.0, 14.0]
 
         >>> convolution.first_signal = [0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6]
         >>> convolution.second_signal = [0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5]
@@ -54,7 +54,7 @@ class CircularConvolution:
         >>> convolution.first_signal = [1, -1, 2, 3, -1]
         >>> convolution.second_signal = [1, 2, 3]
         >>> convolution.circular_convolution()
-        [8, -2, 3, 4, 11]
+        [8.0, -2.0, 3.0, 4.0, 11.0]
 
         """
 
@@ -91,7 +91,7 @@ class CircularConvolution:
         final_signal = np.matmul(np.transpose(matrix), np.transpose(self.first_signal))
 
         # rounding-off to two decimal places
-        return [round(i, 2) for i in final_signal]
+        return [float(round(i, 2)) for i in final_signal]
 
 
 if __name__ == "__main__":
diff --git a/fractals/julia_sets.py b/fractals/julia_sets.py
index 1eef4573b..bea599d44 100644
--- a/fractals/julia_sets.py
+++ b/fractals/julia_sets.py
@@ -40,11 +40,11 @@ nb_pixels = 666
 def eval_exponential(c_parameter: complex, z_values: np.ndarray) -> np.ndarray:
     """
     Evaluate $e^z + c$.
-    >>> eval_exponential(0, 0)
+    >>> float(eval_exponential(0, 0))
     1.0
-    >>> abs(eval_exponential(1, np.pi*1.j)) < 1e-15
+    >>> bool(abs(eval_exponential(1, np.pi*1.j)) < 1e-15)
     True
-    >>> abs(eval_exponential(1.j, 0)-1-1.j) < 1e-15
+    >>> bool(abs(eval_exponential(1.j, 0)-1-1.j) < 1e-15)
     True
     """
     return np.exp(z_values) + c_parameter
@@ -98,20 +98,20 @@ def iterate_function(
 
     >>> iterate_function(eval_quadratic_polynomial, 0, 3, np.array([0,1,2])).shape
     (3,)
-    >>> np.round(iterate_function(eval_quadratic_polynomial,
+    >>> complex(np.round(iterate_function(eval_quadratic_polynomial,
     ... 0,
     ... 3,
-    ... np.array([0,1,2]))[0])
+    ... np.array([0,1,2]))[0]))
     0j
-    >>> np.round(iterate_function(eval_quadratic_polynomial,
+    >>> complex(np.round(iterate_function(eval_quadratic_polynomial,
     ... 0,
     ... 3,
-    ... np.array([0,1,2]))[1])
+    ... np.array([0,1,2]))[1]))
     (1+0j)
-    >>> np.round(iterate_function(eval_quadratic_polynomial,
+    >>> complex(np.round(iterate_function(eval_quadratic_polynomial,
     ... 0,
     ... 3,
-    ... np.array([0,1,2]))[2])
+    ... np.array([0,1,2]))[2]))
     (256+0j)
     """
 
diff --git a/graphics/bezier_curve.py b/graphics/bezier_curve.py
index 9d906f179..6c7dcd4f0 100644
--- a/graphics/bezier_curve.py
+++ b/graphics/bezier_curve.py
@@ -30,9 +30,9 @@ class BezierCurve:
         returns the x, y values of basis function at time t
 
         >>> curve = BezierCurve([(1,1), (1,2)])
-        >>> curve.basis_function(0)
+        >>> [float(x) for x in curve.basis_function(0)]
         [1.0, 0.0]
-        >>> curve.basis_function(1)
+        >>> [float(x) for x in curve.basis_function(1)]
         [0.0, 1.0]
         """
         assert 0 <= t <= 1, "Time t must be between 0 and 1."
@@ -55,9 +55,9 @@ class BezierCurve:
             The last point in the curve is when t = 1.
 
         >>> curve = BezierCurve([(1,1), (1,2)])
-        >>> curve.bezier_curve_function(0)
+        >>> tuple(float(x) for x in curve.bezier_curve_function(0))
         (1.0, 1.0)
-        >>> curve.bezier_curve_function(1)
+        >>> tuple(float(x) for x in curve.bezier_curve_function(1))
         (1.0, 2.0)
         """
 
diff --git a/graphs/dijkstra_binary_grid.py b/graphs/dijkstra_binary_grid.py
index c23d82343..06293a87d 100644
--- a/graphs/dijkstra_binary_grid.py
+++ b/graphs/dijkstra_binary_grid.py
@@ -69,7 +69,7 @@ def dijkstra(
                 x, y = predecessors[x, y]
             path.append(source)  # add the source manually
             path.reverse()
-            return matrix[destination], path
+            return float(matrix[destination]), path
 
         for i in range(len(dx)):
             nx, ny = x + dx[i], y + dy[i]
diff --git a/linear_algebra/src/power_iteration.py b/linear_algebra/src/power_iteration.py
index 24fbd9a5e..83c2ce48c 100644
--- a/linear_algebra/src/power_iteration.py
+++ b/linear_algebra/src/power_iteration.py
@@ -78,7 +78,7 @@ def power_iteration(
     if is_complex:
         lambda_ = np.real(lambda_)
 
-    return lambda_, vector
+    return float(lambda_), vector
 
 
 def test_power_iteration() -> None:
diff --git a/linear_programming/simplex.py b/linear_programming/simplex.py
index dc171bacd..a8affe1b7 100644
--- a/linear_programming/simplex.py
+++ b/linear_programming/simplex.py
@@ -107,8 +107,8 @@ class Tableau:
 
     def find_pivot(self) -> tuple[Any, Any]:
         """Finds the pivot row and column.
-        >>> Tableau(np.array([[-2,1,0,0,0], [3,1,1,0,6], [1,2,0,1,7.]]),
-        ... 2, 0).find_pivot()
+        >>> tuple(int(x) for x in Tableau(np.array([[-2,1,0,0,0], [3,1,1,0,6],
+        ... [1,2,0,1,7.]]), 2, 0).find_pivot())
         (1, 0)
         """
         objective = self.objectives[-1]
@@ -215,8 +215,8 @@ class Tableau:
         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, 0).run_simplex()
+        >>> {key: float(value) for key, value in Tableau(np.array([[-1,-1,0,0,0],
+        ... [1,3,1,0,4],[3,1,0,1,4.]]), 2, 0).run_simplex().items()}
         {'P': 2.0, 'x1': 1.0, 'x2': 1.0}
 
         # Standard linear program with 3 variables:
@@ -224,21 +224,21 @@ class Tableau:
         ST:  2x1 +  x2 +  x3 ≤ 2
               x1 + 2x2 + 3x3 ≤ 5
              2x1 + 2x2 +  x3 ≤ 6
-        >>> Tableau(np.array([
+        >>> {key: float(value) for key, value in Tableau(np.array([
         ... [-3,-1,-3,0,0,0,0],
         ... [2,1,1,1,0,0,2],
         ... [1,2,3,0,1,0,5],
         ... [2,2,1,0,0,1,6.]
-        ... ]),3,0).run_simplex() # doctest: +ELLIPSIS
+        ... ]),3,0).run_simplex().items()} # doctest: +ELLIPSIS
         {'P': 5.4, 'x1': 0.199..., 'x3': 1.6}
 
 
         # Optimal tableau input:
-        >>> Tableau(np.array([
+        >>> {key: float(value) for key, value in 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, 0).run_simplex()
+        ... ]), 2, 0).run_simplex().items()}
         {'P': 2.0, 'x1': 1.0, 'x2': 1.0}
 
         # Non-standard: >= constraints
@@ -246,25 +246,25 @@ class Tableau:
         ST:   x1 +  x2 +  x3 <= 40
              2x1 +  x2 -  x3 >= 10
                  -  x2 +  x3 >= 10
-        >>> Tableau(np.array([
+        >>> {key: float(value) for key, value in 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, 2).run_simplex()
+        ... ]), 3, 2).run_simplex().items()}
         {'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([
+        >>> {key: float(value) for key, value in Tableau(np.array([
         ... [8, 6, 0, 0, 52],
         ... [1, 1, 0, 0, 0],
         ... [2, 1, 1, 0, 12],
         ... [6, 5, 0, 1, 40.],
-        ... ]), 2, 2).run_simplex()
+        ... ]), 2, 2).run_simplex().items()}
         {'P': 7.0, 'x1': 5.0, 'x2': 2.0}
 
 
@@ -275,7 +275,7 @@ class Tableau:
              2x1 + 4x2 <= 48
               x1 +  x2 >= 10
              x1        >= 2
-        >>> Tableau(np.array([
+        >>> {key: float(value) for key, value in Tableau(np.array([
         ... [2, 1, 0, 0, 0, -1, -1, 0, 0, 12.0],
         ... [-8, -6, 0, 0, 0, 0, 0, 0, 0, 0.0],
         ... [1, 3, 1, 0, 0, 0, 0, 0, 0, 33.0],
@@ -283,7 +283,7 @@ class Tableau:
         ... [2, 4, 0, 0, 1, 0, 0, 0, 0, 48.0],
         ... [1, 1, 0, 0, 0, -1, 0, 1, 0, 10.0],
         ... [1, 0, 0, 0, 0, 0, -1, 0, 1, 2.0]
-        ... ]), 2, 2).run_simplex() # doctest: +ELLIPSIS
+        ... ]), 2, 2).run_simplex().items()} # doctest: +ELLIPSIS
         {'P': 132.0, 'x1': 12.000... 'x2': 5.999...}
         """
         # Stop simplex algorithm from cycling.
@@ -307,11 +307,11 @@ class Tableau:
     def interpret_tableau(self) -> dict[str, float]:
         """Given the final tableau, add the corresponding values of the basic
         decision variables to the `output_dict`
-        >>> Tableau(np.array([
+        >>> {key: float(value) for key, value in Tableau(np.array([
         ... [0,0,0.875,0.375,5],
         ... [0,1,0.375,-0.125,1],
         ... [1,0,-0.125,0.375,1]
-        ... ]),2, 0).interpret_tableau()
+        ... ]),2, 0).interpret_tableau().items()}
         {'P': 5.0, 'x1': 1.0, 'x2': 1.0}
         """
         # P = RHS of final tableau
diff --git a/machine_learning/decision_tree.py b/machine_learning/decision_tree.py
index d0bd6ab0b..72970431c 100644
--- a/machine_learning/decision_tree.py
+++ b/machine_learning/decision_tree.py
@@ -26,15 +26,15 @@ class DecisionTree:
         >>> tester = DecisionTree()
         >>> test_labels = np.array([1,2,3,4,5,6,7,8,9,10])
         >>> test_prediction = float(6)
-        >>> tester.mean_squared_error(test_labels, test_prediction) == (
+        >>> bool(tester.mean_squared_error(test_labels, test_prediction) == (
         ...     TestDecisionTree.helper_mean_squared_error_test(test_labels,
-        ...         test_prediction))
+        ...         test_prediction)))
         True
         >>> test_labels = np.array([1,2,3])
         >>> test_prediction = float(2)
-        >>> tester.mean_squared_error(test_labels, test_prediction) == (
+        >>> bool(tester.mean_squared_error(test_labels, test_prediction) == (
         ...     TestDecisionTree.helper_mean_squared_error_test(test_labels,
-        ...         test_prediction))
+        ...         test_prediction)))
         True
         """
         if labels.ndim != 1:
diff --git a/machine_learning/forecasting/run.py b/machine_learning/forecasting/run.py
index dbb86caf8..9d81b03cd 100644
--- a/machine_learning/forecasting/run.py
+++ b/machine_learning/forecasting/run.py
@@ -28,7 +28,7 @@ def linear_regression_prediction(
     input : training data (date, total_user, total_event) in list of float
     output : list of total user prediction in float
     >>> n = linear_regression_prediction([2,3,4,5], [5,3,4,6], [3,1,2,4], [2,1], [2,2])
-    >>> abs(n - 5.0) < 1e-6  # Checking precision because of floating point errors
+    >>> bool(abs(n - 5.0) < 1e-6)  # Checking precision because of floating point errors
     True
     """
     x = np.array([[1, item, train_mtch[i]] for i, item in enumerate(train_dt)])
@@ -56,7 +56,7 @@ def sarimax_predictor(train_user: list, train_match: list, test_match: list) ->
     )
     model_fit = model.fit(disp=False, maxiter=600, method="nm")
     result = model_fit.predict(1, len(test_match), exog=[test_match])
-    return result[0]
+    return float(result[0])
 
 
 def support_vector_regressor(x_train: list, x_test: list, train_user: list) -> float:
@@ -75,7 +75,7 @@ def support_vector_regressor(x_train: list, x_test: list, train_user: list) -> f
     regressor = SVR(kernel="rbf", C=1, gamma=0.1, epsilon=0.1)
     regressor.fit(x_train, train_user)
     y_pred = regressor.predict(x_test)
-    return y_pred[0]
+    return float(y_pred[0])
 
 
 def interquartile_range_checker(train_user: list) -> float:
@@ -92,7 +92,7 @@ def interquartile_range_checker(train_user: list) -> float:
     q3 = np.percentile(train_user, 75)
     iqr = q3 - q1
     low_lim = q1 - (iqr * 0.1)
-    return low_lim
+    return float(low_lim)
 
 
 def data_safety_checker(list_vote: list, actual_result: float) -> bool:
diff --git a/machine_learning/k_nearest_neighbours.py b/machine_learning/k_nearest_neighbours.py
index a43757c5c..fbc1b8bd2 100644
--- a/machine_learning/k_nearest_neighbours.py
+++ b/machine_learning/k_nearest_neighbours.py
@@ -42,7 +42,7 @@ class KNN:
         >>> KNN._euclidean_distance(np.array([1, 2, 3]), np.array([1, 8, 11]))
         10.0
         """
-        return np.linalg.norm(a - b)
+        return float(np.linalg.norm(a - b))
 
     def classify(self, pred_point: np.ndarray[float], k: int = 5) -> str:
         """
diff --git a/machine_learning/logistic_regression.py b/machine_learning/logistic_regression.py
index 090af5382..496026631 100644
--- a/machine_learning/logistic_regression.py
+++ b/machine_learning/logistic_regression.py
@@ -45,7 +45,7 @@ def sigmoid_function(z: float | np.ndarray) -> float | np.ndarray:
     @returns: returns value in the range 0 to 1
 
     Examples:
-    >>> sigmoid_function(4)
+    >>> float(sigmoid_function(4))
     0.9820137900379085
     >>> sigmoid_function(np.array([-3, 3]))
     array([0.04742587, 0.95257413])
@@ -100,7 +100,7 @@ def cost_function(h: np.ndarray, y: np.ndarray) -> float:
     References:
        - https://en.wikipedia.org/wiki/Logistic_regression
     """
-    return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()
+    return float((-y * np.log(h) - (1 - y) * np.log(1 - h)).mean())
 
 
 def log_likelihood(x, y, weights):
diff --git a/machine_learning/loss_functions.py b/machine_learning/loss_functions.py
index 150035661..0bd9aa8b5 100644
--- a/machine_learning/loss_functions.py
+++ b/machine_learning/loss_functions.py
@@ -22,7 +22,7 @@ def binary_cross_entropy(
 
     >>> true_labels = np.array([0, 1, 1, 0, 1])
     >>> predicted_probs = np.array([0.2, 0.7, 0.9, 0.3, 0.8])
-    >>> binary_cross_entropy(true_labels, predicted_probs)
+    >>> float(binary_cross_entropy(true_labels, predicted_probs))
     0.2529995012327421
     >>> true_labels = np.array([0, 1, 1, 0, 1])
     >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
@@ -68,7 +68,7 @@ def binary_focal_cross_entropy(
 
     >>> true_labels = np.array([0, 1, 1, 0, 1])
     >>> predicted_probs = np.array([0.2, 0.7, 0.9, 0.3, 0.8])
-    >>> binary_focal_cross_entropy(true_labels, predicted_probs)
+    >>> float(binary_focal_cross_entropy(true_labels, predicted_probs))
     0.008257977659239775
     >>> true_labels = np.array([0, 1, 1, 0, 1])
     >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
@@ -108,7 +108,7 @@ def categorical_cross_entropy(
 
     >>> true_labels = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
     >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1], [0.0, 0.1, 0.9]])
-    >>> categorical_cross_entropy(true_labels, pred_probs)
+    >>> float(categorical_cross_entropy(true_labels, pred_probs))
     0.567395975254385
     >>> true_labels = np.array([[1, 0], [0, 1]])
     >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
@@ -179,13 +179,13 @@ def categorical_focal_cross_entropy(
     >>> true_labels = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
     >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1], [0.0, 0.1, 0.9]])
     >>> alpha = np.array([0.6, 0.2, 0.7])
-    >>> categorical_focal_cross_entropy(true_labels, pred_probs, alpha)
+    >>> float(categorical_focal_cross_entropy(true_labels, pred_probs, alpha))
     0.0025966118981496423
 
     >>> true_labels = np.array([[0, 1, 0], [0, 0, 1]])
     >>> pred_probs = np.array([[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
     >>> alpha = np.array([0.25, 0.25, 0.25])
-    >>> categorical_focal_cross_entropy(true_labels, pred_probs, alpha)
+    >>> float(categorical_focal_cross_entropy(true_labels, pred_probs, alpha))
     0.23315276982014324
 
     >>> true_labels = np.array([[1, 0], [0, 1]])
@@ -265,7 +265,7 @@ def hinge_loss(y_true: np.ndarray, y_pred: np.ndarray) -> float:
 
     >>> true_labels = np.array([-1, 1, 1, -1, 1])
     >>> pred = np.array([-4, -0.3, 0.7, 5, 10])
-    >>> hinge_loss(true_labels, pred)
+    >>> float(hinge_loss(true_labels, pred))
     1.52
     >>> true_labels = np.array([-1, 1, 1, -1, 1, 1])
     >>> pred = np.array([-4, -0.3, 0.7, 5, 10])
@@ -309,11 +309,11 @@ def huber_loss(y_true: np.ndarray, y_pred: np.ndarray, delta: float) -> float:
 
     >>> true_values = np.array([0.9, 10.0, 2.0, 1.0, 5.2])
     >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
-    >>> np.isclose(huber_loss(true_values, predicted_values, 1.0), 2.102)
+    >>> bool(np.isclose(huber_loss(true_values, predicted_values, 1.0), 2.102))
     True
     >>> true_labels = np.array([11.0, 21.0, 3.32, 4.0, 5.0])
     >>> predicted_probs = np.array([8.3, 20.8, 2.9, 11.2, 5.0])
-    >>> np.isclose(huber_loss(true_labels, predicted_probs, 1.0), 1.80164)
+    >>> bool(np.isclose(huber_loss(true_labels, predicted_probs, 1.0), 1.80164))
     True
     >>> true_labels = np.array([11.0, 21.0, 3.32, 4.0])
     >>> predicted_probs = np.array([8.3, 20.8, 2.9, 11.2, 5.0])
@@ -347,7 +347,7 @@ def mean_squared_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
 
     >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
-    >>> np.isclose(mean_squared_error(true_values, predicted_values), 0.028)
+    >>> bool(np.isclose(mean_squared_error(true_values, predicted_values), 0.028))
     True
     >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
@@ -381,11 +381,11 @@ def mean_absolute_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
 
     >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
-    >>> np.isclose(mean_absolute_error(true_values, predicted_values), 0.16)
+    >>> bool(np.isclose(mean_absolute_error(true_values, predicted_values), 0.16))
     True
     >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
-    >>> np.isclose(mean_absolute_error(true_values, predicted_values), 2.16)
+    >>> bool(np.isclose(mean_absolute_error(true_values, predicted_values), 2.16))
     False
     >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_probs = np.array([0.3, 0.8, 0.9, 5.2])
@@ -420,7 +420,7 @@ def mean_squared_logarithmic_error(y_true: np.ndarray, y_pred: np.ndarray) -> fl
 
     >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
-    >>> mean_squared_logarithmic_error(true_values, predicted_values)
+    >>> float(mean_squared_logarithmic_error(true_values, predicted_values))
     0.0030860877925181344
     >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
     >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
@@ -459,17 +459,17 @@ def mean_absolute_percentage_error(
     Examples:
     >>> y_true = np.array([10, 20, 30, 40])
     >>> y_pred = np.array([12, 18, 33, 45])
-    >>> mean_absolute_percentage_error(y_true, y_pred)
+    >>> float(mean_absolute_percentage_error(y_true, y_pred))
     0.13125
 
     >>> y_true = np.array([1, 2, 3, 4])
     >>> y_pred = np.array([2, 3, 4, 5])
-    >>> mean_absolute_percentage_error(y_true, y_pred)
+    >>> float(mean_absolute_percentage_error(y_true, y_pred))
     0.5208333333333333
 
     >>> y_true = np.array([34, 37, 44, 47, 48, 48, 46, 43, 32, 27, 26, 24])
     >>> y_pred = np.array([37, 40, 46, 44, 46, 50, 45, 44, 34, 30, 22, 23])
-    >>> mean_absolute_percentage_error(y_true, y_pred)
+    >>> float(mean_absolute_percentage_error(y_true, y_pred))
     0.064671076436071
     """
     if len(y_true) != len(y_pred):
@@ -511,7 +511,7 @@ def perplexity_loss(
     ...      [[0.03, 0.26, 0.21, 0.18, 0.30],
     ...       [0.28, 0.10, 0.33, 0.15, 0.12]]]
     ... )
-    >>> perplexity_loss(y_true, y_pred)
+    >>> float(perplexity_loss(y_true, y_pred))
     5.0247347775367945
     >>> y_true = np.array([[1, 4], [2, 3]])
     >>> y_pred = np.array(
@@ -600,17 +600,17 @@ def smooth_l1_loss(y_true: np.ndarray, y_pred: np.ndarray, beta: float = 1.0) ->
 
     >>> y_true = np.array([3, 5, 2, 7])
     >>> y_pred = np.array([2.9, 4.8, 2.1, 7.2])
-    >>> smooth_l1_loss(y_true, y_pred, 1.0)
+    >>> float(smooth_l1_loss(y_true, y_pred, 1.0))
     0.012500000000000022
 
     >>> y_true = np.array([2, 4, 6])
     >>> y_pred = np.array([1, 5, 7])
-    >>> smooth_l1_loss(y_true, y_pred, 1.0)
+    >>> float(smooth_l1_loss(y_true, y_pred, 1.0))
     0.5
 
     >>> y_true = np.array([1, 3, 5, 7])
     >>> y_pred = np.array([1, 3, 5, 7])
-    >>> smooth_l1_loss(y_true, y_pred, 1.0)
+    >>> float(smooth_l1_loss(y_true, y_pred, 1.0))
     0.0
 
     >>> y_true = np.array([1, 3, 5])
@@ -647,7 +647,7 @@ def kullback_leibler_divergence(y_true: np.ndarray, y_pred: np.ndarray) -> float
 
     >>> true_labels = np.array([0.2, 0.3, 0.5])
     >>> predicted_probs = np.array([0.3, 0.3, 0.4])
-    >>> kullback_leibler_divergence(true_labels, predicted_probs)
+    >>> float(kullback_leibler_divergence(true_labels, predicted_probs))
     0.030478754035472025
     >>> true_labels = np.array([0.2, 0.3, 0.5])
     >>> predicted_probs = np.array([0.3, 0.3, 0.4, 0.5])
diff --git a/machine_learning/mfcc.py b/machine_learning/mfcc.py
index a1e99ce4a..dcc3151d5 100644
--- a/machine_learning/mfcc.py
+++ b/machine_learning/mfcc.py
@@ -162,9 +162,9 @@ def normalize(audio: np.ndarray) -> np.ndarray:
     Examples:
     >>> audio = np.array([1, 2, 3, 4, 5])
     >>> normalized_audio = normalize(audio)
-    >>> np.max(normalized_audio)
+    >>> float(np.max(normalized_audio))
     1.0
-    >>> np.min(normalized_audio)
+    >>> float(np.min(normalized_audio))
     0.2
     """
     # Divide the entire audio signal by the maximum absolute value
@@ -229,7 +229,8 @@ def calculate_fft(audio_windowed: np.ndarray, ftt_size: int = 1024) -> np.ndarra
     Examples:
     >>> audio_windowed = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
     >>> audio_fft = calculate_fft(audio_windowed, ftt_size=4)
-    >>> np.allclose(audio_fft[0], np.array([6.0+0.j, -1.5+0.8660254j, -1.5-0.8660254j]))
+    >>> bool(np.allclose(audio_fft[0], np.array([6.0+0.j, -1.5+0.8660254j,
+    ...     -1.5-0.8660254j])))
     True
     """
     # Transpose the audio data to have time in rows and channels in columns
@@ -281,7 +282,7 @@ def freq_to_mel(freq: float) -> float:
         The frequency in mel scale.
 
     Examples:
-    >>> round(freq_to_mel(1000), 2)
+    >>> float(round(freq_to_mel(1000), 2))
     999.99
     """
     # Use the formula to convert frequency to the mel scale
@@ -321,7 +322,7 @@ def mel_spaced_filterbank(
         Mel-spaced filter bank.
 
     Examples:
-    >>> round(mel_spaced_filterbank(8000, 10, 1024)[0][1], 10)
+    >>> float(round(mel_spaced_filterbank(8000, 10, 1024)[0][1], 10))
     0.0004603981
     """
     freq_min = 0
@@ -438,7 +439,7 @@ def discrete_cosine_transform(dct_filter_num: int, filter_num: int) -> np.ndarra
         The DCT basis matrix.
 
     Examples:
-    >>> round(discrete_cosine_transform(3, 5)[0][0], 5)
+    >>> float(round(discrete_cosine_transform(3, 5)[0][0], 5))
     0.44721
     """
     basis = np.empty((dct_filter_num, filter_num))
diff --git a/machine_learning/multilayer_perceptron_classifier.py b/machine_learning/multilayer_perceptron_classifier.py
index e99a4131e..40f998c7d 100644
--- a/machine_learning/multilayer_perceptron_classifier.py
+++ b/machine_learning/multilayer_perceptron_classifier.py
@@ -17,7 +17,7 @@ Y = clf.predict(test)
 
 def wrapper(y):
     """
-    >>> wrapper(Y)
+    >>> [int(x) for x in wrapper(Y)]
     [0, 0, 1]
     """
     return list(y)
diff --git a/machine_learning/scoring_functions.py b/machine_learning/scoring_functions.py
index 08b969a95..f6b685f4f 100644
--- a/machine_learning/scoring_functions.py
+++ b/machine_learning/scoring_functions.py
@@ -20,11 +20,11 @@ def mae(predict, actual):
     """
     Examples(rounded for precision):
     >>> actual = [1,2,3];predict = [1,4,3]
-    >>> np.around(mae(predict,actual),decimals = 2)
+    >>> float(np.around(mae(predict,actual),decimals = 2))
     0.67
 
     >>> actual = [1,1,1];predict = [1,1,1]
-    >>> mae(predict,actual)
+    >>> float(mae(predict,actual))
     0.0
     """
     predict = np.array(predict)
@@ -41,11 +41,11 @@ def mse(predict, actual):
     """
     Examples(rounded for precision):
     >>> actual = [1,2,3];predict = [1,4,3]
-    >>> np.around(mse(predict,actual),decimals = 2)
+    >>> float(np.around(mse(predict,actual),decimals = 2))
     1.33
 
     >>> actual = [1,1,1];predict = [1,1,1]
-    >>> mse(predict,actual)
+    >>> float(mse(predict,actual))
     0.0
     """
     predict = np.array(predict)
@@ -63,11 +63,11 @@ def rmse(predict, actual):
     """
     Examples(rounded for precision):
     >>> actual = [1,2,3];predict = [1,4,3]
-    >>> np.around(rmse(predict,actual),decimals = 2)
+    >>> float(np.around(rmse(predict,actual),decimals = 2))
     1.15
 
     >>> actual = [1,1,1];predict = [1,1,1]
-    >>> rmse(predict,actual)
+    >>> float(rmse(predict,actual))
     0.0
     """
     predict = np.array(predict)
@@ -84,12 +84,10 @@ def rmse(predict, actual):
 def rmsle(predict, actual):
     """
     Examples(rounded for precision):
-    >>> actual = [10,10,30];predict = [10,2,30]
-    >>> np.around(rmsle(predict,actual),decimals = 2)
+    >>> float(np.around(rmsle(predict=[10, 2, 30], actual=[10, 10, 30]), decimals=2))
     0.75
 
-    >>> actual = [1,1,1];predict = [1,1,1]
-    >>> rmsle(predict,actual)
+    >>> float(rmsle(predict=[1, 1, 1], actual=[1, 1, 1]))
     0.0
     """
     predict = np.array(predict)
@@ -117,12 +115,12 @@ def mbd(predict, actual):
 
     Here the model overpredicts
     >>> actual = [1,2,3];predict = [2,3,4]
-    >>> np.around(mbd(predict,actual),decimals = 2)
+    >>> float(np.around(mbd(predict,actual),decimals = 2))
     50.0
 
     Here the model underpredicts
     >>> actual = [1,2,3];predict = [0,1,1]
-    >>> np.around(mbd(predict,actual),decimals = 2)
+    >>> float(np.around(mbd(predict,actual),decimals = 2))
     -66.67
     """
     predict = np.array(predict)
diff --git a/machine_learning/similarity_search.py b/machine_learning/similarity_search.py
index 0bc3b17d7..c8a573796 100644
--- a/machine_learning/similarity_search.py
+++ b/machine_learning/similarity_search.py
@@ -153,7 +153,7 @@ def cosine_similarity(input_a: np.ndarray, input_b: np.ndarray) -> float:
     >>> cosine_similarity(np.array([1, 2]), np.array([6, 32]))
     0.9615239476408232
     """
-    return np.dot(input_a, input_b) / (norm(input_a) * norm(input_b))
+    return float(np.dot(input_a, input_b) / (norm(input_a) * norm(input_b)))
 
 
 if __name__ == "__main__":
diff --git a/machine_learning/support_vector_machines.py b/machine_learning/support_vector_machines.py
index 24046115e..d17c9044a 100644
--- a/machine_learning/support_vector_machines.py
+++ b/machine_learning/support_vector_machines.py
@@ -14,11 +14,11 @@ def norm_squared(vector: ndarray) -> float:
     Returns:
         float: squared second norm of vector
 
-    >>> norm_squared([1, 2])
+    >>> int(norm_squared([1, 2]))
     5
-    >>> norm_squared(np.asarray([1, 2]))
+    >>> int(norm_squared(np.asarray([1, 2])))
     5
-    >>> norm_squared([0, 0])
+    >>> int(norm_squared([0, 0]))
     0
     """
     return np.dot(vector, vector)
diff --git a/maths/euclidean_distance.py b/maths/euclidean_distance.py
index 9b29b37b0..aa7f3efc7 100644
--- a/maths/euclidean_distance.py
+++ b/maths/euclidean_distance.py
@@ -13,13 +13,13 @@ def euclidean_distance(vector_1: Vector, vector_2: Vector) -> VectorOut:
     """
     Calculate the distance between the two endpoints of two vectors.
     A vector is defined as a list, tuple, or numpy 1D array.
-    >>> euclidean_distance((0, 0), (2, 2))
+    >>> float(euclidean_distance((0, 0), (2, 2)))
     2.8284271247461903
-    >>> euclidean_distance(np.array([0, 0, 0]), np.array([2, 2, 2]))
+    >>> float(euclidean_distance(np.array([0, 0, 0]), np.array([2, 2, 2])))
     3.4641016151377544
-    >>> euclidean_distance(np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8]))
+    >>> float(euclidean_distance(np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8])))
     8.0
-    >>> euclidean_distance([1, 2, 3, 4], [5, 6, 7, 8])
+    >>> float(euclidean_distance([1, 2, 3, 4], [5, 6, 7, 8]))
     8.0
     """
     return np.sqrt(np.sum((np.asarray(vector_1) - np.asarray(vector_2)) ** 2))
diff --git a/maths/euler_method.py b/maths/euler_method.py
index 30f193e6d..c6adb07e2 100644
--- a/maths/euler_method.py
+++ b/maths/euler_method.py
@@ -26,7 +26,7 @@ def explicit_euler(
     ...     return y
     >>> y0 = 1
     >>> y = explicit_euler(f, y0, 0.0, 0.01, 5)
-    >>> y[-1]
+    >>> float(y[-1])
     144.77277243257308
     """
     n = int(np.ceil((x_end - x0) / step_size))
diff --git a/maths/euler_modified.py b/maths/euler_modified.py
index d02123e1e..bb282e9f0 100644
--- a/maths/euler_modified.py
+++ b/maths/euler_modified.py
@@ -24,13 +24,13 @@ def euler_modified(
     >>> def f1(x, y):
     ...     return -2*x*(y**2)
     >>> y = euler_modified(f1, 1.0, 0.0, 0.2, 1.0)
-    >>> y[-1]
+    >>> float(y[-1])
     0.503338255442106
     >>> import math
     >>> def f2(x, y):
     ...     return -2*y + (x**3)*math.exp(-2*x)
     >>> y = euler_modified(f2, 1.0, 0.0, 0.1, 0.3)
-    >>> y[-1]
+    >>> float(y[-1])
     0.5525976431951775
     """
     n = int(np.ceil((x_end - x0) / step_size))
diff --git a/maths/gaussian.py b/maths/gaussian.py
index 0e02010a9..b1e62ea77 100644
--- a/maths/gaussian.py
+++ b/maths/gaussian.py
@@ -5,18 +5,18 @@ Reference: https://en.wikipedia.org/wiki/Gaussian_function
 from numpy import exp, pi, sqrt
 
 
-def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int:
+def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> float:
     """
-    >>> gaussian(1)
+    >>> float(gaussian(1))
     0.24197072451914337
 
-    >>> gaussian(24)
+    >>> float(gaussian(24))
     3.342714441794458e-126
 
-    >>> gaussian(1, 4, 2)
+    >>> float(gaussian(1, 4, 2))
     0.06475879783294587
 
-    >>> gaussian(1, 5, 3)
+    >>> float(gaussian(1, 5, 3))
     0.05467002489199788
 
     Supports NumPy Arrays
@@ -29,7 +29,7 @@ def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int:
            5.05227108e-15, 1.02797736e-18, 7.69459863e-23, 2.11881925e-27,
            2.14638374e-32, 7.99882776e-38, 1.09660656e-43])
 
-    >>> gaussian(15)
+    >>> float(gaussian(15))
     5.530709549844416e-50
 
     >>> gaussian([1,2, 'string'])
@@ -47,10 +47,10 @@ def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int:
         ...
     OverflowError: (34, 'Result too large')
 
-    >>> gaussian(10**-326)
+    >>> float(gaussian(10**-326))
     0.3989422804014327
 
-    >>> gaussian(2523, mu=234234, sigma=3425)
+    >>> float(gaussian(2523, mu=234234, sigma=3425))
     0.0
     """
     return 1 / sqrt(2 * pi * sigma**2) * exp(-((x - mu) ** 2) / (2 * sigma**2))
diff --git a/maths/minkowski_distance.py b/maths/minkowski_distance.py
index 3237124e8..99f02e31e 100644
--- a/maths/minkowski_distance.py
+++ b/maths/minkowski_distance.py
@@ -19,7 +19,7 @@ def minkowski_distance(
     >>> minkowski_distance([1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], 2)
     8.0
     >>> import numpy as np
-    >>> np.isclose(5.0, minkowski_distance([5.0], [0.0], 3))
+    >>> bool(np.isclose(5.0, minkowski_distance([5.0], [0.0], 3)))
     True
     >>> minkowski_distance([1.0], [2.0], -1)
     Traceback (most recent call last):
diff --git a/maths/numerical_analysis/adams_bashforth.py b/maths/numerical_analysis/adams_bashforth.py
index fb4061710..26244a585 100644
--- a/maths/numerical_analysis/adams_bashforth.py
+++ b/maths/numerical_analysis/adams_bashforth.py
@@ -102,7 +102,7 @@ class AdamsBashforth:
         >>> def f(x, y):
         ...     return x + y
         >>> y = AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_3()
-        >>> y[3]
+        >>> float(y[3])
         0.15533333333333332
 
         >>> AdamsBashforth(f, [0, 0.2], [0, 0], 0.2, 1).step_3()
@@ -140,9 +140,9 @@ class AdamsBashforth:
         ...     return x + y
         >>> y = AdamsBashforth(
         ...    f, [0, 0.2, 0.4, 0.6], [0, 0, 0.04, 0.128], 0.2, 1).step_4()
-        >>> y[4]
+        >>> float(y[4])
         0.30699999999999994
-        >>> y[5]
+        >>> float(y[5])
         0.5771083333333333
 
         >>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_4()
@@ -185,7 +185,7 @@ class AdamsBashforth:
         >>> y = AdamsBashforth(
         ...     f, [0, 0.2, 0.4, 0.6, 0.8], [0, 0.02140, 0.02140, 0.22211, 0.42536],
         ...     0.2, 1).step_5()
-        >>> y[-1]
+        >>> float(y[-1])
         0.05436839444444452
 
         >>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_5()
diff --git a/maths/numerical_analysis/runge_kutta.py b/maths/numerical_analysis/runge_kutta.py
index 4cac017ee..3a25b0fb0 100644
--- a/maths/numerical_analysis/runge_kutta.py
+++ b/maths/numerical_analysis/runge_kutta.py
@@ -19,7 +19,7 @@ def runge_kutta(f, y0, x0, h, x_end):
     ...     return y
     >>> y0 = 1
     >>> y = runge_kutta(f, y0, 0.0, 0.01, 5)
-    >>> y[-1]
+    >>> float(y[-1])
     148.41315904125113
     """
     n = int(np.ceil((x_end - x0) / h))
diff --git a/maths/numerical_analysis/runge_kutta_fehlberg_45.py b/maths/numerical_analysis/runge_kutta_fehlberg_45.py
index 8181fe301..0fbd60a35 100644
--- a/maths/numerical_analysis/runge_kutta_fehlberg_45.py
+++ b/maths/numerical_analysis/runge_kutta_fehlberg_45.py
@@ -34,12 +34,12 @@ def runge_kutta_fehlberg_45(
     >>> def f(x, y):
     ...     return 1 + y**2
     >>> y = runge_kutta_fehlberg_45(f, 0, 0, 0.2, 1)
-    >>> y[1]
+    >>> float(y[1])
     0.2027100937470787
     >>> def f(x,y):
     ...     return x
     >>> y = runge_kutta_fehlberg_45(f, -1, 0, 0.2, 0)
-    >>> y[1]
+    >>> float(y[1])
     -0.18000000000000002
     >>> y = runge_kutta_fehlberg_45(5, 0, 0, 0.1, 1)
     Traceback (most recent call last):
diff --git a/maths/numerical_analysis/runge_kutta_gills.py b/maths/numerical_analysis/runge_kutta_gills.py
index 451cde4cb..5d9672679 100644
--- a/maths/numerical_analysis/runge_kutta_gills.py
+++ b/maths/numerical_analysis/runge_kutta_gills.py
@@ -34,7 +34,7 @@ def runge_kutta_gills(
     >>> def f(x, y):
     ...     return (x-y)/2
     >>> y = runge_kutta_gills(f, 0, 3, 0.2, 5)
-    >>> y[-1]
+    >>> float(y[-1])
     3.4104259225717537
 
     >>> def f(x,y):
diff --git a/maths/softmax.py b/maths/softmax.py
index 04cf77525..95c95e66f 100644
--- a/maths/softmax.py
+++ b/maths/softmax.py
@@ -28,7 +28,7 @@ def softmax(vector):
 
     The softmax vector adds up to one. We need to ceil to mitigate for
     precision
-    >>> np.ceil(np.sum(softmax([1,2,3,4])))
+    >>> float(np.ceil(np.sum(softmax([1,2,3,4]))))
     1.0
 
     >>> vec = np.array([5,5])
diff --git a/neural_network/two_hidden_layers_neural_network.py b/neural_network/two_hidden_layers_neural_network.py
index d488de590..1b7c0beed 100644
--- a/neural_network/two_hidden_layers_neural_network.py
+++ b/neural_network/two_hidden_layers_neural_network.py
@@ -64,7 +64,7 @@ class TwoHiddenLayerNeuralNetwork:
         >>> nn = TwoHiddenLayerNeuralNetwork(input_val, output_val)
         >>> res = nn.feedforward()
         >>> array_sum = np.sum(res)
-        >>> np.isnan(array_sum)
+        >>> bool(np.isnan(array_sum))
         False
         """
         # Layer_between_input_and_first_hidden_layer is the layer connecting the
@@ -105,7 +105,7 @@ class TwoHiddenLayerNeuralNetwork:
         >>> res = nn.feedforward()
         >>> nn.back_propagation()
         >>> updated_weights = nn.second_hidden_layer_and_output_layer_weights
-        >>> (res == updated_weights).all()
+        >>> bool((res == updated_weights).all())
         False
         """
 
@@ -171,7 +171,7 @@ class TwoHiddenLayerNeuralNetwork:
         >>> first_iteration_weights = nn.feedforward()
         >>> nn.back_propagation()
         >>> updated_weights = nn.second_hidden_layer_and_output_layer_weights
-        >>> (first_iteration_weights == updated_weights).all()
+        >>> bool((first_iteration_weights == updated_weights).all())
         False
         """
         for iteration in range(1, iterations + 1):
diff --git a/other/bankers_algorithm.py b/other/bankers_algorithm.py
index 858eb0b2c..d4254f479 100644
--- a/other/bankers_algorithm.py
+++ b/other/bankers_algorithm.py
@@ -87,9 +87,11 @@ class BankersAlgorithm:
         This function builds an index control dictionary to track original ids/indices
         of processes when altered during execution of method "main"
             Return: {0: [a: int, b: int], 1: [c: int, d: int]}
-        >>> (BankersAlgorithm(test_claim_vector, test_allocated_res_table,
-        ...     test_maximum_claim_table)._BankersAlgorithm__need_index_manager()
-        ...     )  # doctest: +NORMALIZE_WHITESPACE
+        >>> index_control = BankersAlgorithm(
+        ...     test_claim_vector, test_allocated_res_table, test_maximum_claim_table
+        ... )._BankersAlgorithm__need_index_manager()
+        >>> {key: [int(x) for x in value] for key, value
+        ...     in index_control.items()}  # doctest: +NORMALIZE_WHITESPACE
         {0: [1, 2, 0, 3], 1: [0, 1, 3, 1], 2: [1, 1, 0, 2], 3: [1, 3, 2, 0],
          4: [2, 0, 0, 3]}
         """
diff --git a/physics/in_static_equilibrium.py b/physics/in_static_equilibrium.py
index e3c2f9d07..fb5a9b5ff 100644
--- a/physics/in_static_equilibrium.py
+++ b/physics/in_static_equilibrium.py
@@ -53,7 +53,7 @@ def in_static_equilibrium(
     # summation of moments is zero
     moments: NDArray[float64] = cross(location, forces)
     sum_moments: float = sum(moments)
-    return abs(sum_moments) < eps
+    return bool(abs(sum_moments) < eps)
 
 
 if __name__ == "__main__":
diff --git a/requirements.txt b/requirements.txt
index bb3d67139..afbf25ba6 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,7 +1,7 @@
 beautifulsoup4
 fake_useragent
 imageio
-keras ; python_version < '3.12'
+keras
 lxml
 matplotlib
 numpy
@@ -17,7 +17,7 @@ rich
 scikit-learn
 statsmodels
 sympy
-tensorflow
+tensorflow ; python_version < '3.13'
 tweepy
 # yulewalker  # uncomment once audio_filters/equal_loudness_filter.py is fixed
 typing_extensions
diff --git a/web_programming/get_user_tweets.py b/web_programming/get_user_tweets.py.DISABLED
similarity index 100%
rename from web_programming/get_user_tweets.py
rename to web_programming/get_user_tweets.py.DISABLED

From 0abeeab39f4a612968a10b0541f630239b78f34f Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Tue, 1 Oct 2024 17:32:31 +0200
Subject: [PATCH 3/9] Drop six from our GitHub Actions (#11621)

Drop https://six.readthedocs.io
---
 .github/workflows/build.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index dad2b2fac..f54cc982d 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -20,7 +20,7 @@ jobs:
           key: ${{ runner.os }}-pip-${{ hashFiles('requirements.txt') }}
       - name: Install dependencies
         run: |
-          python -m pip install --upgrade pip setuptools six wheel
+          python -m pip install --upgrade pip setuptools wheel
           python -m pip install pytest-cov -r requirements.txt
       - name: Run tests
         # TODO: #8818 Re-enable quantum tests

From 43a47e01eb2c2b681fa377b02150edba5cc76e32 Mon Sep 17 00:00:00 2001
From: Hardik Pawar <97388607+Hardvan@users.noreply.github.com>
Date: Wed, 2 Oct 2024 08:18:17 +0530
Subject: [PATCH 4/9] Add word ladder algorithm in backtracking (#11590)

* Add word ladder algorithm in backtracking

* Improve comments and implement ruff checks

* updating DIRECTORY.md

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Change BFS to Backtracking

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Incorporate PR Changes

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Add type hints for backtrack function

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: Hardvan <Hardvan@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 DIRECTORY.md                |   1 +
 backtracking/word_ladder.py | 100 ++++++++++++++++++++++++++++++++++++
 2 files changed, 101 insertions(+)
 create mode 100644 backtracking/word_ladder.py

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 56ab8377f..cdbbac684 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -22,6 +22,7 @@
   * [Rat In Maze](backtracking/rat_in_maze.py)
   * [Sudoku](backtracking/sudoku.py)
   * [Sum Of Subsets](backtracking/sum_of_subsets.py)
+  * [Word Ladder](backtracking/word_ladder.py)
   * [Word Search](backtracking/word_search.py)
 
 ## Bit Manipulation
diff --git a/backtracking/word_ladder.py b/backtracking/word_ladder.py
new file mode 100644
index 000000000..7d9fd00f6
--- /dev/null
+++ b/backtracking/word_ladder.py
@@ -0,0 +1,100 @@
+"""
+Word Ladder is a classic problem in computer science.
+The problem is to transform a start word into an end word
+by changing one letter at a time.
+Each intermediate word must be a valid word from a given list of words.
+The goal is to find a transformation sequence
+from the start word to the end word.
+
+Wikipedia: https://en.wikipedia.org/wiki/Word_ladder
+"""
+
+import string
+
+
+def backtrack(
+    current_word: str, path: list[str], end_word: str, word_set: set[str]
+) -> list[str]:
+    """
+    Helper function to perform backtracking to find the transformation
+    from the current_word to the end_word.
+
+    Parameters:
+    current_word (str): The current word in the transformation sequence.
+    path (list[str]): The list of transformations from begin_word to current_word.
+    end_word (str): The target word for transformation.
+    word_set (set[str]): The set of valid words for transformation.
+
+    Returns:
+    list[str]: The list of transformations from begin_word to end_word.
+               Returns an empty list if there is no valid
+                transformation from current_word to end_word.
+
+    Example:
+    >>> backtrack("hit", ["hit"], "cog", {"hot", "dot", "dog", "lot", "log", "cog"})
+    ['hit', 'hot', 'dot', 'lot', 'log', 'cog']
+
+    >>> backtrack("hit", ["hit"], "cog", {"hot", "dot", "dog", "lot", "log"})
+    []
+
+    >>> backtrack("lead", ["lead"], "gold", {"load", "goad", "gold", "lead", "lord"})
+    ['lead', 'lead', 'load', 'goad', 'gold']
+
+    >>> backtrack("game", ["game"], "code", {"came", "cage", "code", "cade", "gave"})
+    ['game', 'came', 'cade', 'code']
+    """
+
+    # Base case: If the current word is the end word, return the path
+    if current_word == end_word:
+        return path
+
+    # Try all possible single-letter transformations
+    for i in range(len(current_word)):
+        for c in string.ascii_lowercase:  # Try changing each letter
+            transformed_word = current_word[:i] + c + current_word[i + 1 :]
+            if transformed_word in word_set:
+                word_set.remove(transformed_word)
+                # Recur with the new word added to the path
+                result = backtrack(
+                    transformed_word, [*path, transformed_word], end_word, word_set
+                )
+                if result:  # valid transformation found
+                    return result
+                word_set.add(transformed_word)  # backtrack
+
+    return []  # No valid transformation found
+
+
+def word_ladder(begin_word: str, end_word: str, word_set: set[str]) -> list[str]:
+    """
+    Solve the Word Ladder problem using Backtracking and return
+    the list of transformations from begin_word to end_word.
+
+    Parameters:
+    begin_word (str): The word from which the transformation starts.
+    end_word (str): The target word for transformation.
+    word_list (list[str]): The list of valid words for transformation.
+
+    Returns:
+    list[str]: The list of transformations from begin_word to end_word.
+               Returns an empty list if there is no valid transformation.
+
+    Example:
+    >>> word_ladder("hit", "cog", ["hot", "dot", "dog", "lot", "log", "cog"])
+    ['hit', 'hot', 'dot', 'lot', 'log', 'cog']
+
+    >>> word_ladder("hit", "cog", ["hot", "dot", "dog", "lot", "log"])
+    []
+
+    >>> word_ladder("lead", "gold", ["load", "goad", "gold", "lead", "lord"])
+    ['lead', 'lead', 'load', 'goad', 'gold']
+
+    >>> word_ladder("game", "code", ["came", "cage", "code", "cade", "gave"])
+    ['game', 'came', 'cade', 'code']
+    """
+
+    if end_word not in word_set:  # no valid transformation possible
+        return []
+
+    # Perform backtracking starting from the begin_word
+    return backtrack(begin_word, [begin_word], end_word, word_set)

From 00e9d862248a27281d4de24c8c7eb2d7b018531c Mon Sep 17 00:00:00 2001
From: Hardik Pawar <97388607+Hardvan@users.noreply.github.com>
Date: Wed, 2 Oct 2024 08:24:12 +0530
Subject: [PATCH 5/9] Improve comments, add doctests in symmetric_tree.py
 (#11619)

---
 data_structures/binary_tree/symmetric_tree.py | 67 +++++++++++++++++--
 1 file changed, 62 insertions(+), 5 deletions(-)

diff --git a/data_structures/binary_tree/symmetric_tree.py b/data_structures/binary_tree/symmetric_tree.py
index 98a766cab..2bfeac98b 100644
--- a/data_structures/binary_tree/symmetric_tree.py
+++ b/data_structures/binary_tree/symmetric_tree.py
@@ -13,7 +13,21 @@ from dataclasses import dataclass
 @dataclass
 class Node:
     """
-    A Node has data variable and pointers to Nodes to its left and right.
+    A Node represents an element of a binary tree, which contains:
+
+    Attributes:
+    data: The value stored in the node (int).
+    left: Pointer to the left child node (Node or None).
+    right: Pointer to the right child node (Node or None).
+
+    Example:
+    >>> node = Node(1, Node(2), Node(3))
+    >>> node.data
+    1
+    >>> node.left.data
+    2
+    >>> node.right.data
+    3
     """
 
     data: int
@@ -24,12 +38,25 @@ class Node:
 def make_symmetric_tree() -> Node:
     r"""
     Create a symmetric tree for testing.
+
     The tree looks like this:
            1
          /   \
         2     2
       / \    / \
      3   4   4  3
+
+    Returns:
+    Node: Root node of a symmetric tree.
+
+    Example:
+    >>> tree = make_symmetric_tree()
+    >>> tree.data
+    1
+    >>> tree.left.data == tree.right.data
+    True
+    >>> tree.left.left.data == tree.right.right.data
+    True
     """
     root = Node(1)
     root.left = Node(2)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
     r"""
-    Create a asymmetric tree for testing.
+    Create an asymmetric tree for testing.
+
     The tree looks like this:
            1
          /   \
         2     2
       / \    / \
      3   4   3  4
+
+    Returns:
+    Node: Root node of an asymmetric tree.
+
+    Example:
+    >>> tree = make_asymmetric_tree()
+    >>> tree.data
+    1
+    >>> tree.left.data == tree.right.data
+    True
+    >>> tree.left.left.data == tree.right.right.data
+    False
     """
     root = Node(1)
     root.left = Node(2)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
     """
-    Test cases for is_symmetric_tree function
+    Check if a binary tree is symmetric (i.e., a mirror of itself).
+
+    Parameters:
+    tree: The root node of the binary tree.
+
+    Returns:
+    bool: True if the tree is symmetric, False otherwise.
+
+    Example:
     >>> is_symmetric_tree(make_symmetric_tree())
     True
     >>> is_symmetric_tree(make_asymmetric_tree())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 def is_mirror(left: Node | None, right: Node | None) -> bool:
     """
+    Check if two subtrees are mirror images of each other.
+
+    Parameters:
+    left: The root node of the left subtree.
+    right: The root node of the right subtree.
+
+    Returns:
+    bool: True if the two subtrees are mirrors of each other, False otherwise.
+
+    Example:
     >>> tree1 = make_symmetric_tree()
-    >>> tree1.right.right = Node(3)
     >>> is_mirror(tree1.left, tree1.right)
     True
     >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
         # One side is empty while the other is not, which is not symmetric.
         return False
     if left.data == right.data:
-        # The values match, so check the subtree
+        # The values match, so check the subtrees recursively.
         return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
     return False
 

From 918fa8bb8ae1f052921fffd188d229d4713c73c9 Mon Sep 17 00:00:00 2001
From: 1227haran <68032825+1227haran@users.noreply.github.com>
Date: Wed, 2 Oct 2024 23:37:07 +0530
Subject: [PATCH 6/9] Optimized O(n) to O(1) (#11669)

---
 data_structures/linked_list/has_loop.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/data_structures/linked_list/has_loop.py b/data_structures/linked_list/has_loop.py
index bc06ffe15..f49e01579 100644
--- a/data_structures/linked_list/has_loop.py
+++ b/data_structures/linked_list/has_loop.py
@@ -14,11 +14,11 @@ class Node:
 
     def __iter__(self):
         node = self
-        visited = []
+        visited = set()
         while node:
             if node in visited:
                 raise ContainsLoopError
-            visited.append(node)
+            visited.add(node)
             yield node.data
             node = node.next_node
 

From f4b4ac159a17e0621e7f37141b165d58ca655b81 Mon Sep 17 00:00:00 2001
From: Ali Rashid <110668489+alirashidAR@users.noreply.github.com>
Date: Thu, 3 Oct 2024 05:24:56 +0530
Subject: [PATCH 7/9] Adding Doctests to floyd_warshall.py (#11690)

* Ruff test resolution

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 dynamic_programming/floyd_warshall.py | 47 +++++++++++++++++++++++++--
 1 file changed, 45 insertions(+), 2 deletions(-)

diff --git a/dynamic_programming/floyd_warshall.py b/dynamic_programming/floyd_warshall.py
index 2331f3e65..b92c6667f 100644
--- a/dynamic_programming/floyd_warshall.py
+++ b/dynamic_programming/floyd_warshall.py
@@ -12,19 +12,58 @@ class Graph:
         ]  # dp[i][j] stores minimum distance from i to j
 
     def add_edge(self, u, v, w):
+        """
+        Adds a directed edge from node u
+        to node v with weight w.
+
+        >>> g = Graph(3)
+        >>> g.add_edge(0, 1, 5)
+        >>> g.dp[0][1]
+        5
+        """
         self.dp[u][v] = w
 
     def floyd_warshall(self):
+        """
+        Computes the shortest paths between all pairs of
+        nodes using the Floyd-Warshall algorithm.
+
+        >>> g = Graph(3)
+        >>> g.add_edge(0, 1, 1)
+        >>> g.add_edge(1, 2, 2)
+        >>> g.floyd_warshall()
+        >>> g.show_min(0, 2)
+        3
+        >>> g.show_min(2, 0)
+        inf
+        """
         for k in range(self.n):
             for i in range(self.n):
                 for j in range(self.n):
                     self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j])
 
     def show_min(self, u, v):
+        """
+        Returns the minimum distance from node u to node v.
+
+        >>> g = Graph(3)
+        >>> g.add_edge(0, 1, 3)
+        >>> g.add_edge(1, 2, 4)
+        >>> g.floyd_warshall()
+        >>> g.show_min(0, 2)
+        7
+        >>> g.show_min(1, 0)
+        inf
+        """
         return self.dp[u][v]
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Example usage
     graph = Graph(5)
     graph.add_edge(0, 2, 9)
     graph.add_edge(0, 4, 10)
@@ -38,5 +77,9 @@ if __name__ == "__main__":
     graph.add_edge(4, 2, 4)
     graph.add_edge(4, 3, 9)
     graph.floyd_warshall()
-    graph.show_min(1, 4)
-    graph.show_min(0, 3)
+    print(
+        graph.show_min(1, 4)
+    )  # Should output the minimum distance from node 1 to node 4
+    print(
+        graph.show_min(0, 3)
+    )  # Should output the minimum distance from node 0 to node 3

From 080e7903a06765808c12c0c9c0b242f485cb9ce7 Mon Sep 17 00:00:00 2001
From: Aswin P Kumar <118362715+AswinPKumar01@users.noreply.github.com>
Date: Thu, 3 Oct 2024 05:33:48 +0530
Subject: [PATCH 8/9] Add Word Break algorithm (#11687)

* Add Word Break algorithm

* Add Word Break algorithm

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 backtracking/word_break.py | 71 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)
 create mode 100644 backtracking/word_break.py

diff --git a/backtracking/word_break.py b/backtracking/word_break.py
new file mode 100644
index 000000000..1f2ab073f
--- /dev/null
+++ b/backtracking/word_break.py
@@ -0,0 +1,71 @@
+"""
+Word Break Problem is a well-known problem in computer science.
+Given a string and a dictionary of words, the task is to determine if
+the string can be segmented into a sequence of one or more dictionary words.
+
+Wikipedia: https://en.wikipedia.org/wiki/Word_break_problem
+"""
+
+
+def backtrack(input_string: str, word_dict: set[str], start: int) -> bool:
+    """
+    Helper function that uses backtracking to determine if a valid
+    word segmentation is possible starting from index 'start'.
+
+    Parameters:
+    input_string (str): The input string to be segmented.
+    word_dict (set[str]): A set of valid dictionary words.
+    start (int): The starting index of the substring to be checked.
+
+    Returns:
+    bool: True if a valid segmentation is possible, otherwise False.
+
+    Example:
+    >>> backtrack("leetcode", {"leet", "code"}, 0)
+    True
+
+    >>> backtrack("applepenapple", {"apple", "pen"}, 0)
+    True
+
+    >>> backtrack("catsandog", {"cats", "dog", "sand", "and", "cat"}, 0)
+    False
+    """
+
+    # Base case: if the starting index has reached the end of the string
+    if start == len(input_string):
+        return True
+
+    # Try every possible substring from 'start' to 'end'
+    for end in range(start + 1, len(input_string) + 1):
+        if input_string[start:end] in word_dict and backtrack(
+            input_string, word_dict, end
+        ):
+            return True
+
+    return False
+
+
+def word_break(input_string: str, word_dict: set[str]) -> bool:
+    """
+    Determines if the input string can be segmented into a sequence of
+    valid dictionary words using backtracking.
+
+    Parameters:
+    input_string (str): The input string to segment.
+    word_dict (set[str]): The set of valid words.
+
+    Returns:
+    bool: True if the string can be segmented into valid words, otherwise False.
+
+    Example:
+    >>> word_break("leetcode", {"leet", "code"})
+    True
+
+    >>> word_break("applepenapple", {"apple", "pen"})
+    True
+
+    >>> word_break("catsandog", {"cats", "dog", "sand", "and", "cat"})
+    False
+    """
+
+    return backtrack(input_string, word_dict, 0)

From 40f65e8150045dc82a7a58fe7cff6bfb353999f2 Mon Sep 17 00:00:00 2001
From: JeevaRamanathan <64531160+JeevaRamanathan@users.noreply.github.com>
Date: Thu, 3 Oct 2024 05:48:01 +0530
Subject: [PATCH 9/9] Improve comments, docstrings in next_greatest_element.py
 (#11685)

* Improve comments in next_greatest_element.py

Signed-off-by: JeevaRamanathan <jeevaramanathan.m@infosys.com>

* few changes

Signed-off-by: JeevaRamanathan <jeevaramanathan.m@infosys.com>

* updated descriptions of the functions parameters

Signed-off-by: JeevaRamanathan <jeevaramanathan.m@infosys.com>

---------

Signed-off-by: JeevaRamanathan <jeevaramanathan.m@infosys.com>
---
 .../stacks/next_greater_element.py            | 58 ++++++++++++++-----
 1 file changed, 45 insertions(+), 13 deletions(-)

diff --git a/data_structures/stacks/next_greater_element.py b/data_structures/stacks/next_greater_element.py
index 7d76d1f47..216850b4b 100644
--- a/data_structures/stacks/next_greater_element.py
+++ b/data_structures/stacks/next_greater_element.py
@@ -6,9 +6,20 @@ expect = [-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]
 
 def next_greatest_element_slow(arr: list[float]) -> list[float]:
     """
-    Get the Next Greatest Element (NGE) for all elements in a list.
-    Maximum element present after the current one which is also greater than the
-    current one.
+    Get the Next Greatest Element (NGE) for each element in the array
+    by checking all subsequent elements to find the next greater one.
+
+    This is a brute-force implementation, and it has a time complexity
+    of O(n^2), where n is the size of the array.
+
+    Args:
+        arr: List of numbers for which the NGE is calculated.
+
+    Returns:
+        List containing the next greatest elements. If no
+        greater element is found, -1 is placed in the result.
+
+    Example:
     >>> next_greatest_element_slow(arr) == expect
     True
     """
@@ -28,9 +39,21 @@ def next_greatest_element_slow(arr: list[float]) -> list[float]:
 
 def next_greatest_element_fast(arr: list[float]) -> list[float]:
     """
-    Like next_greatest_element_slow() but changes the loops to use
-    enumerate() instead of range(len()) for the outer loop and
-    for in a slice of arr for the inner loop.
+    Find the Next Greatest Element (NGE) for each element in the array
+    using a more readable approach. This implementation utilizes
+    enumerate() for the outer loop and slicing for the inner loop.
+
+    While this improves readability over next_greatest_element_slow(),
+    it still has a time complexity of O(n^2).
+
+    Args:
+        arr: List of numbers for which the NGE is calculated.
+
+    Returns:
+        List containing the next greatest elements. If no
+        greater element is found, -1 is placed in the result.
+
+    Example:
     >>> next_greatest_element_fast(arr) == expect
     True
     """
@@ -47,14 +70,23 @@ def next_greatest_element_fast(arr: list[float]) -> list[float]:
 
 def next_greatest_element(arr: list[float]) -> list[float]:
     """
-    Get the Next Greatest Element (NGE) for all elements in a list.
-    Maximum element present after the current one which is also greater than the
-    current one.
+    Efficient solution to find the Next Greatest Element (NGE) for all elements
+    using a stack. The time complexity is reduced to O(n), making it suitable
+    for larger arrays.
 
-    A naive way to solve this is to take two loops and check for the next bigger
-    number but that will make the time complexity as O(n^2). The better way to solve
-    this would be to use a stack to keep track of maximum number giving a linear time
-    solution.
+    The stack keeps track of elements for which the next greater element hasn't
+    been found yet. By iterating through the array in reverse (from the last
+    element to the first), the stack is used to efficiently determine the next
+    greatest element for each element.
+
+    Args:
+        arr: List of numbers for which the NGE is calculated.
+
+    Returns:
+        List containing the next greatest elements. If no
+        greater element is found, -1 is placed in the result.
+
+    Example:
     >>> next_greatest_element(arr) == expect
     True
     """