Merge c84aca23a8 into fcf82a1eda

* Implemented Exponential Search with binary search for improved performance on large sorted arrays.

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

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* Added type hints and doctests for binary_search and exponential_search functions. Improved code documentation and ensured testability.

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

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* Update and rename Exponential_Search.py to exponential_search.py

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---------

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

CONTRIBUTING.md

@@ -96,7 +96,7 @@ We want your work to be readable by others; therefore, we encourage you to note
 
   ```bash
   python3 -m pip install ruff  # only required the first time
-  ruff .
+  ruff check
   ```
 
 - Original code submission require docstrings or comments to describe your work.

data_structures/stacks/lexicographical_numbers.py

@@ -0,0 +1,38 @@
+from collections.abc import Iterator
+
+
+def lexical_order(max_number: int) -> Iterator[int]:
+    """
+    Generate numbers in lexical order from 1 to max_number.
+
+    >>> " ".join(map(str, lexical_order(13)))
+    '1 10 11 12 13 2 3 4 5 6 7 8 9'
+    >>> list(lexical_order(1))
+    [1]
+    >>> " ".join(map(str, lexical_order(20)))
+    '1 10 11 12 13 14 15 16 17 18 19 2 20 3 4 5 6 7 8 9'
+    >>> " ".join(map(str, lexical_order(25)))
+    '1 10 11 12 13 14 15 16 17 18 19 2 20 21 22 23 24 25 3 4 5 6 7 8 9'
+    >>> list(lexical_order(12))
+    [1, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9]
+    """
+
+    stack = [1]
+
+    while stack:
+        num = stack.pop()
+        if num > max_number:
+            continue
+
+        yield num
+        if (num % 10) != 9:
+            stack.append(num + 1)
+
+        stack.append(num * 10)
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    print(f"Numbers from 1 to 25 in lexical order: {list(lexical_order(26))}")

dynamic_programming/longest_common_subsequence.py

@@ -28,6 +28,24 @@ def longest_common_subsequence(x: str, y: str):
     (2, 'ph')
     >>> longest_common_subsequence("computer", "food")
     (1, 'o')
+    >>> longest_common_subsequence("", "abc")  # One string is empty
+    (0, '')
+    >>> longest_common_subsequence("abc", "")  # Other string is empty
+    (0, '')
+    >>> longest_common_subsequence("", "")  # Both strings are empty
+    (0, '')
+    >>> longest_common_subsequence("abc", "def")  # No common subsequence
+    (0, '')
+    >>> longest_common_subsequence("abc", "abc")  # Identical strings
+    (3, 'abc')
+    >>> longest_common_subsequence("a", "a")  # Single character match
+    (1, 'a')
+    >>> longest_common_subsequence("a", "b")  # Single character no match
+    (0, '')
+    >>> longest_common_subsequence("abcdef", "ace")  # Interleaved subsequence
+    (3, 'ace')
+    >>> longest_common_subsequence("ABCD", "ACBD")  # No repeated characters
+    (3, 'ABD')
     """
     # find the length of strings
 

graphs/directed_and_undirected_weighted_graph.py

@@ -14,6 +14,18 @@ class DirectedGraph:
     # adding the weight is optional
     # handles repetition
     def add_pair(self, u, v, w=1):
+        """
+        Adds a directed edge u->v with weight w.
+        >>> dg = DirectedGraph()
+        >>> dg.add_pair(-1,2)
+        >>> dg.add_pair(1,3,5)
+        >>> dg.add_pair(1,3,5)
+        >>> dg.add_pair(1,3,6)
+        >>> dg.all_nodes()
+        [-1, 2, 1, 3]
+        >>> dg.graph[1]
+        [[5, 3], [6, 3]]
+        """
         if self.graph.get(u):
             if self.graph[u].count([w, v]) == 0:
                 self.graph[u].append([w, v])
@@ -23,10 +35,36 @@ class DirectedGraph:
             self.graph[v] = []
 
     def all_nodes(self):
+        """
+        Returns list of all nodes in the graph.
+        >>> dg = DirectedGraph()
+        >>> dg.all_nodes()
+        []
+        >>> dg.add_pair(1,1)
+        >>> dg.all_nodes()
+        [1]
+        >>> dg.add_pair(2,3,3)
+        >>> dg.all_nodes()
+        [1, 2, 3]
+        """
         return list(self.graph)
 
     # handles if the input does not exist
     def remove_pair(self, u, v):
+        """
+        Removes all edges u->v if it exists.
+        >>> dg = DirectedGraph()
+        >>> dg.remove_pair(1,2) # silently exits
+        >>> dg.add_pair(0,5,2)
+        >>> dg.graph[0]
+        [[2, 5]]
+        >>> dg.remove_pair(5,0)
+        >>> dg.graph[0]
+        [[2, 5]]
+        >>> dg.remove_pair(0,5)
+        >>> dg.graph[0]
+        []
+        """
         if self.graph.get(u):
             for _ in self.graph[u]:
                 if _[1] == v:
@@ -34,41 +72,56 @@ class DirectedGraph:
 
     # if no destination is meant the default value is -1
     def dfs(self, s=-2, d=-1):
-        if s == d:
-            return []
+        """
+        Performs depth first search from s to find d.
+        Returns the path s->d as a list.
+        Returns dfs from s if d is not found
+        >>> dg = DirectedGraph()
+        >>> dg.dfs()
+        []
+        >>> dg.add_pair(1,1)
+        >>> dg.dfs(1,1)
+        [1]
+        >>> dg = DirectedGraph()
+        >>> dg.add_pair(0,1)
+        >>> dg.add_pair(0,2)
+        >>> dg.add_pair(1,3)
+        >>> dg.add_pair(1,4)
+        >>> dg.add_pair(1,5)
+        >>> dg.add_pair(2,5)
+        >>> dg.add_pair(5,6)
+        >>> dg.dfs(0,6)
+        [0, 2, 5, 6]
+        >>> dg.dfs(1,6)
+        [1, 5, 6]
+        >>> dg.dfs()
+        [0, 2, 5, 6, 1, 4, 3]
+        >>> dg.dfs(1,0)
+        [1, 5, 6, 4, 3]
+        """
         stack = []
         visited = []
         if s == -2:
+            if self.graph.get(s, None):
+                pass  # -2 is a node
+            elif len(self.graph) > 0:
                 s = next(iter(self.graph))
-        stack.append(s)
-        visited.append(s)
-        ss = s
-
-        while True:
-            # check if there is any non isolated nodes
-            if len(self.graph[s]) != 0:
-                ss = s
-                for node in self.graph[s]:
-                    if visited.count(node[1]) < 1:
-                        if node[1] == d:
-                            visited.append(d)
-                            return visited
             else:
-                            stack.append(node[1])
-                            visited.append(node[1])
-                            ss = node[1]
+                return []  # Graph empty
+        stack.append(s)
+
+        # Run dfs
+        while len(stack) > 0:
+            s = stack.pop()
+            visited.append(s)
+            # If reached d, return
+            if s == d:
                 break
 
-            # check if all the children are visited
-            if s == ss:
-                stack.pop()
-                if len(stack) != 0:
-                    s = stack[len(stack) - 1]
-            else:
-                s = ss
-
-            # check if se have reached the starting point
-            if len(stack) == 0:
+            # add not visited child nodes to stack
+            for _, ss in self.graph[s]:
+                if visited.count(ss) < 1:
+                    stack.append(ss)
         return visited
 
     # c is the count of nodes you want and if you leave it or pass -1 to the function
@@ -84,12 +137,42 @@ class DirectedGraph:
                     self.add_pair(i, n, 1)
 
     def bfs(self, s=-2):
+        """
+        Performs breadth first search from s
+        Returns list.
+        >>> dg = DirectedGraph()
+        >>> dg.bfs()
+        []
+        >>> dg.add_pair(1,1)
+        >>> dg.bfs(1)
+        [1]
+        >>> dg = DirectedGraph()
+        >>> dg.add_pair(0,1)
+        >>> dg.add_pair(0,2)
+        >>> dg.add_pair(1,3)
+        >>> dg.add_pair(1,4)
+        >>> dg.add_pair(1,5)
+        >>> dg.add_pair(2,5)
+        >>> dg.add_pair(5,6)
+        >>> dg.bfs(0)
+        [0, 1, 2, 3, 4, 5, 6]
+        >>> dg.bfs(1)
+        [1, 3, 4, 5, 6]
+        >>> dg.bfs()
+        [0, 1, 2, 3, 4, 5, 6]
+        """
         d = deque()
         visited = []
         if s == -2:
+            if self.graph.get(s, None):
+                pass  # -2 is a node
+            elif len(self.graph) > 0:
                 s = next(iter(self.graph))
+            else:
+                return []  # Graph empty
         d.append(s)
         visited.append(s)
+        # Run bfs
         while d:
             s = d.popleft()
             if len(self.graph[s]) != 0:
@@ -300,41 +383,59 @@ class Graph:
 
     # if no destination is meant the default value is -1
     def dfs(self, s=-2, d=-1):
-        if s == d:
-            return []
+        """
+        Performs depth first search from s to find d.
+        Returns the path s->d as a list.
+        Returns dfs from s if d is not found
+        >>> ug = Graph()
+        >>> ug.dfs()
+        []
+        >>> ug.add_pair(1,1)
+        >>> ug.dfs(1,1)
+        [1]
+        >>> ug = Graph()
+        >>> ug.add_pair(0,1)
+        >>> ug.add_pair(0,2)
+        >>> ug.add_pair(1,3)
+        >>> ug.add_pair(1,4)
+        >>> ug.add_pair(1,5)
+        >>> ug.add_pair(2,5)
+        >>> ug.add_pair(5,6)
+        >>> ug.dfs(0,6)
+        [0, 2, 5, 6]
+        >>> ug.dfs(1,6)
+        [1, 5, 6]
+        >>> ug.dfs()
+        [0, 2, 5, 6, 1, 4, 3]
+        >>> ug.dfs(1,0)
+        [1, 5, 6, 2, 0]
+        """
         stack = []
         visited = []
         if s == -2:
+            if self.graph.get(s, None):
+                pass  # -2 is a node
+            elif len(self.graph) > 0:
                 s = next(iter(self.graph))
-        stack.append(s)
-        visited.append(s)
-        ss = s
-
-        while True:
-            # check if there is any non isolated nodes
-            if len(self.graph[s]) != 0:
-                ss = s
-                for node in self.graph[s]:
-                    if visited.count(node[1]) < 1:
-                        if node[1] == d:
-                            visited.append(d)
-                            return visited
             else:
-                            stack.append(node[1])
-                            visited.append(node[1])
-                            ss = node[1]
+                return []  # Graph empty
+        stack.append(s)
+
+        # Run dfs
+        while len(stack) > 0:
+            s = stack.pop()
+            if visited.count(s) == 1:
+                continue
+            else:
+                visited.append(s)
+            # If reached d, return
+            if s == d:
                 break
 
-            # check if all the children are visited
-            if s == ss:
-                stack.pop()
-                if len(stack) != 0:
-                    s = stack[len(stack) - 1]
-            else:
-                s = ss
-
-            # check if se have reached the starting point
-            if len(stack) == 0:
+            # add not visited child nodes to stack
+            for _, ss in self.graph[s]:
+                if visited.count(ss) < 1:
+                    stack.append(ss)
         return visited
 
     # c is the count of nodes you want and if you leave it or pass -1 to the function
@@ -350,10 +451,39 @@ class Graph:
                     self.add_pair(i, n, 1)
 
     def bfs(self, s=-2):
+        """
+        Performs breadth first search from s
+        Returns list.
+        >>> ug = Graph()
+        >>> ug.bfs()
+        []
+        >>> ug.add_pair(1,1)
+        >>> ug.bfs(1)
+        [1]
+        >>> ug = Graph()
+        >>> ug.add_pair(0,1)
+        >>> ug.add_pair(0,2)
+        >>> ug.add_pair(1,3)
+        >>> ug.add_pair(1,4)
+        >>> ug.add_pair(1,5)
+        >>> ug.add_pair(2,5)
+        >>> ug.add_pair(5,6)
+        >>> ug.bfs(0)
+        [0, 1, 2, 3, 4, 5, 6]
+        >>> ug.bfs(1)
+        [1, 0, 3, 4, 5, 2, 6]
+        >>> ug.bfs()
+        [0, 1, 2, 3, 4, 5, 6]
+        """
         d = deque()
         visited = []
         if s == -2:
+            if self.graph.get(s, None):
+                pass  # -2 is a node
+            elif len(self.graph) > 0:
                 s = next(iter(self.graph))
+            else:
+                return []  # Graph empty
         d.append(s)
         visited.append(s)
         while d:

searches/exponential_search.py

@@ -0,0 +1,113 @@
+#!/usr/bin/env python3
+
+"""
+Pure Python implementation of exponential search algorithm
+
+For more information, see the Wikipedia page:
+https://en.wikipedia.org/wiki/Exponential_search
+
+For doctests run the following command:
+python3 -m doctest -v exponential_search.py
+
+For manual testing run:
+python3 exponential_search.py
+"""
+
+from __future__ import annotations
+
+
+def binary_search_by_recursion(
+    sorted_collection: list[int], item: int, left: int = 0, right: int = -1
+) -> int:
+    """Pure implementation of binary search algorithm in Python using recursion
+
+    Be careful: the collection must be ascending sorted otherwise, the result will be
+    unpredictable.
+
+    :param sorted_collection: some ascending sorted collection with comparable items
+    :param item: item value to search
+    :param left: starting index for the search
+    :param right: ending index for the search
+    :return: index of the found item or -1 if the item is not found
+
+    Examples:
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 0, 0, 4)
+    0
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 15, 0, 4)
+    4
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 5, 0, 4)
+    1
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 6, 0, 4)
+    -1
+    """
+    if right < 0:
+        right = len(sorted_collection) - 1
+    if list(sorted_collection) != sorted(sorted_collection):
+        raise ValueError("sorted_collection must be sorted in ascending order")
+    if right < left:
+        return -1
+
+    midpoint = left + (right - left) // 2
+
+    if sorted_collection[midpoint] == item:
+        return midpoint
+    elif sorted_collection[midpoint] > item:
+        return binary_search_by_recursion(sorted_collection, item, left, midpoint - 1)
+    else:
+        return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
+
+
+def exponential_search(sorted_collection: list[int], item: int) -> int:
+    """
+    Pure implementation of an exponential search algorithm in Python.
+    For more information, refer to:
+    https://en.wikipedia.org/wiki/Exponential_search
+
+    Be careful: the collection must be ascending sorted, otherwise the result will be
+    unpredictable.
+
+    :param sorted_collection: some ascending sorted collection with comparable items
+    :param item: item value to search
+    :return: index of the found item or -1 if the item is not found
+
+    The time complexity of this algorithm is O(log i) where i is the index of the item.
+
+    Examples:
+    >>> exponential_search([0, 5, 7, 10, 15], 0)
+    0
+    >>> exponential_search([0, 5, 7, 10, 15], 15)
+    4
+    >>> exponential_search([0, 5, 7, 10, 15], 5)
+    1
+    >>> exponential_search([0, 5, 7, 10, 15], 6)
+    -1
+    """
+    if list(sorted_collection) != sorted(sorted_collection):
+        raise ValueError("sorted_collection must be sorted in ascending order")
+
+    if sorted_collection[0] == item:
+        return 0
+
+    bound = 1
+    while bound < len(sorted_collection) and sorted_collection[bound] < item:
+        bound *= 2
+
+    left = bound // 2
+    right = min(bound, len(sorted_collection) - 1)
+    return binary_search_by_recursion(sorted_collection, item, left, right)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Manual testing
+    user_input = input("Enter numbers separated by commas: ").strip()
+    collection = sorted(int(item) for item in user_input.split(","))
+    target = int(input("Enter a number to search for: "))
+    result = exponential_search(sorted_collection=collection, item=target)
+    if result == -1:
+        print(f"{target} was not found in {collection}.")
+    else:
+        print(f"{target} was found at index {result} in {collection}.")