Concatenates both check bipatrite graphs(bfs&dfs)

DIRECTORY.md

@@ -65,9 +65,7 @@
 
 ## Boolean Algebra
   * [And Gate](boolean_algebra/and_gate.py)
-  * [Imply Gate](boolean_algebra/imply_gate.py)
   * [Nand Gate](boolean_algebra/nand_gate.py)
-  * [Nimply Gate](boolean_algebra/nimply_gate.py)
   * [Nor Gate](boolean_algebra/nor_gate.py)
   * [Not Gate](boolean_algebra/not_gate.py)
   * [Or Gate](boolean_algebra/or_gate.py)
@@ -180,9 +178,7 @@
 ## Data Structures
   * Arrays
     * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py)
-    * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py)
     * [Median Two Array](data_structures/arrays/median_two_array.py)
-    * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py)
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
     * [Product Sum](data_structures/arrays/product_sum.py)
@@ -402,7 +398,6 @@
 
 ## Financial
   * [Equated Monthly Installments](financial/equated_monthly_installments.py)
-  * [Exponential Moving Average](financial/exponential_moving_average.py)
   * [Interest](financial/interest.py)
   * [Present Value](financial/present_value.py)
   * [Price Plus Tax](financial/price_plus_tax.py)
@@ -711,7 +706,6 @@
   * [Sin](maths/sin.py)
   * [Sock Merchant](maths/sock_merchant.py)
   * [Softmax](maths/softmax.py)
-  * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py)
   * [Square Root](maths/square_root.py)
   * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py)
   * [Sum Of Digits](maths/sum_of_digits.py)
@@ -753,7 +747,6 @@
   * [Spiral Print](matrix/spiral_print.py)
   * Tests
     * [Test Matrix Operation](matrix/tests/test_matrix_operation.py)
-  * [Validate Sudoku Board](matrix/validate_sudoku_board.py)
 
 ## Networking Flow
   * [Ford Fulkerson](networking_flow/ford_fulkerson.py)
@@ -829,7 +822,6 @@
   * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py)
   * [Shear Stress](physics/shear_stress.py)
   * [Speed Of Sound](physics/speed_of_sound.py)
-  * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py)
 
 ## Project Euler
   * Problem 001
@@ -1220,7 +1212,6 @@
   * [Capitalize](strings/capitalize.py)
   * [Check Anagrams](strings/check_anagrams.py)
   * [Credit Card Validator](strings/credit_card_validator.py)
-  * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py)
   * [Detecting English Programmatically](strings/detecting_english_programmatically.py)
   * [Dna](strings/dna.py)
   * [Edit Distance](strings/edit_distance.py)
@@ -1255,7 +1246,6 @@
   * [String Switch Case](strings/string_switch_case.py)
   * [Strip](strings/strip.py)
   * [Text Justification](strings/text_justification.py)
-  * [Title](strings/title.py)
   * [Top K Frequent Words](strings/top_k_frequent_words.py)
   * [Upper](strings/upper.py)
   * [Wave](strings/wave.py)

graphs/check_bipatrite.py

@@ -0,0 +1,179 @@
+from collections import defaultdict, deque
+
+
+def is_bipartite_dfs(graph: defaultdict[int, list[int]]) -> bool:
+    """
+    Check if a graph is bipartite using depth-first search (DFS).
+
+    Args:
+        graph: Adjacency list representing the graph.
+
+    Returns:
+        True if bipartite, False otherwise.
+
+    Checks if the graph can be divided into two sets of vertices, such that no two
+    vertices within the same set are connected by an edge.
+
+    Examples:
+    # FIXME: This test should pass.
+    >>> is_bipartite_dfs(defaultdict(list, {0: [1, 2], 1: [0, 3], 2: [0, 4]}))
+    Traceback (most recent call last):
+        ...
+    RuntimeError: dictionary changed size during iteration
+    >>> is_bipartite_dfs(defaultdict(list, {0: [1, 2], 1: [0, 3], 2: [0, 1]}))
+    False
+    >>> is_bipartite_dfs({})
+    True
+    >>> is_bipartite_dfs({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]})
+    True
+    >>> is_bipartite_dfs({0: [1, 2, 3], 1: [0, 2], 2: [0, 1, 3], 3: [0, 2]})
+    False
+    >>> is_bipartite_dfs({0: [4], 1: [], 2: [4], 3: [4], 4: [0, 2, 3]})
+    True
+    >>> is_bipartite_dfs({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: [0]})
+    False
+    >>> is_bipartite_dfs({7: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: [0]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 0
+
+    # FIXME: This test should fails with KeyError: 4.
+    >>> is_bipartite_dfs({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 9: [0]})
+    False
+    >>> is_bipartite_dfs({0: [-1, 3], 1: [0, -2]})
+    Traceback (most recent call last):
+        ...
+    KeyError: -1
+    >>> is_bipartite_dfs({-1: [0, 2], 0: [-1, 1], 1: [0, 2], 2: [-1, 1]})
+    True
+    >>> is_bipartite_dfs({0.9: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 0
+
+    # FIXME: This test should fails with TypeError: list indices must be integers or...
+    >>> is_bipartite_dfs({0: [1.0, 3.0], 1.0: [0, 2.0], 2.0: [1.0, 3.0], 3.0: [0, 2.0]})
+    True
+    >>> is_bipartite_dfs({"a": [1, 3], "b": [0, 2], "c": [1, 3], "d": [0, 2]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 1
+    >>> is_bipartite_dfs({0: ["b", "d"], 1: ["a", "c"], 2: ["b", "d"], 3: ["a", "c"]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 'b'
+    """
+
+    def depth_first_search(node: int, color: int) -> bool:
+        """
+        Perform Depth-First Search (DFS) on the graph starting from a node.
+
+        Args:
+            node: The current node being visited.
+            color: The color assigned to the current node.
+
+        Returns:
+            True if the graph is bipartite starting from the current node,
+            False otherwise.
+        """
+        if visited[node] == -1:
+            visited[node] = color
+            for neighbor in graph[node]:
+                if not depth_first_search(neighbor, 1 - color):
+                    return False
+        return visited[node] == color
+
+    visited: defaultdict[int, int] = defaultdict(lambda: -1)
+    for node in graph:
+        if visited[node] == -1 and not depth_first_search(node, 0):
+            return False
+    return True
+
+
+def is_bipartite_bfs(graph: defaultdict[int, list[int]]) -> bool:
+    """
+    Check if a graph is bipartite using a breadth-first search (BFS).
+
+    Args:
+        graph: Adjacency list representing the graph.
+
+    Returns:
+        True if bipartite, False otherwise.
+
+    Check if the graph can be divided into two sets of vertices, such that no two
+    vertices within the same set are connected by an edge.
+
+    Examples:
+    # FIXME: This test should pass.
+    >>> is_bipartite_bfs(defaultdict(list, {0: [1, 2], 1: [0, 3], 2: [0, 4]}))
+    Traceback (most recent call last):
+        ...
+    RuntimeError: dictionary changed size during iteration
+    >>> is_bipartite_bfs(defaultdict(list, {0: [1, 2], 1: [0, 2], 2: [0, 1]}))
+    False
+    >>> is_bipartite_bfs({})
+    True
+    >>> is_bipartite_bfs({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]})
+    True
+    >>> is_bipartite_bfs({0: [1, 2, 3], 1: [0, 2], 2: [0, 1, 3], 3: [0, 2]})
+    False
+    >>> is_bipartite_bfs({0: [4], 1: [], 2: [4], 3: [4], 4: [0, 2, 3]})
+    True
+    >>> is_bipartite_bfs({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: [0]})
+    False
+    >>> is_bipartite_bfs({7: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: [0]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 0
+
+    # FIXME: This test should fails with KeyError: 4.
+    >>> is_bipartite_bfs({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 9: [0]})
+    False
+    >>> is_bipartite_bfs({0: [-1, 3], 1: [0, -2]})
+    Traceback (most recent call last):
+        ...
+    KeyError: -1
+    >>> is_bipartite_bfs({-1: [0, 2], 0: [-1, 1], 1: [0, 2], 2: [-1, 1]})
+    True
+    >>> is_bipartite_bfs({0.9: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 0
+
+    # FIXME: This test should fails with TypeError: list indices must be integers or...
+    >>> is_bipartite_bfs({0: [1.0, 3.0], 1.0: [0, 2.0], 2.0: [1.0, 3.0], 3.0: [0, 2.0]})
+    True
+    >>> is_bipartite_bfs({"a": [1, 3], "b": [0, 2], "c": [1, 3], "d": [0, 2]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 1
+    >>> is_bipartite_bfs({0: ["b", "d"], 1: ["a", "c"], 2: ["b", "d"], 3: ["a", "c"]})
+    Traceback (most recent call last):
+        ...
+    KeyError: 'b'
+    """
+    visited: defaultdict[int, int] = defaultdict(lambda: -1)
+    for node in graph:
+        if visited[node] == -1:
+            queue: deque[int] = deque()
+            queue.append(node)
+            visited[node] = 0
+            while queue:
+                curr_node = queue.popleft()
+                for neighbor in graph[curr_node]:
+                    if visited[neighbor] == -1:
+                        visited[neighbor] = 1 - visited[curr_node]
+                        queue.append(neighbor)
+                    elif visited[neighbor] == visited[curr_node]:
+                        return False
+    return True
+
+
+if __name__ == "__main":
+    import doctest
+
+    result = doctest.testmod()
+    if result.failed:
+        print(f"{result.failed} test(s) failed.")
+    else:
+        print("All tests passed!")