check_bipatrite.py

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!")