from collections import defaultdict


def is_bipartite(graph: defaultdict[int, list[int]]) -> bool:
    """
    Check whether a graph is Bipartite or not using Depth-First Search (DFS).

    A Bipartite Graph is a graph whose vertices can be divided into two independent
    sets, U and V such that every edge (u, v) either connects a vertex from
    U to V or a vertex from V to U. In other words, for every edge (u, v),
    either u belongs to U and v to V, or u belongs to V and v to U. There is
    no edge that connects vertices of the same set.

    Args:
        graph: An adjacency list representing the graph.

    Returns:
        True if there's no edge that connects vertices of the same set, False otherwise.

    Examples:
        >>> is_bipartite(
        ...     defaultdict(list, {0: [1, 2], 1: [0, 3], 2: [0, 4], 3: [1], 4: [2]})
        ... )
        False
        >>> is_bipartite(defaultdict(list, {0: [1, 2], 1: [0, 2], 2: [0, 1]}))
        True
    """

    def depth_first_search(node: int, color: int) -> bool:
        visited[node] = color
        return any(
            visited[neighbour] == color
            or (
                visited[neighbour] == -1
                and not depth_first_search(neighbour, 1 - color)
            )
            for neighbour in graph[node]
        )

    visited: defaultdict[int, int] = defaultdict(lambda: -1)

    return all(
        not (visited[node] == -1 and not depth_first_search(node, 0)) for node in graph
    )


if __name__ == "__main__":
    import doctest

    result = doctest.testmod()

    if result.failed:
        print(f"{result.failed} test(s) failed.")
    else:
        print("All tests passed!")