#Maximum Length-Bounded Disjoint Paths


    # Create a copy of the graph

    # Add a dummy node

    # Connect the dummy node to the target node

    # Find the maximum flow from the source to the dummy node

    # Find the paths based on the flow values

    # Filter paths based on maximum length constraint


# Example usage:

# Add edges to the graph

# Define source and target nodes

# Define maximum length

# Find maximum length-bounded disjoint paths

# Print the paths

if __name__ == '__main__':
    import networkx as nx
    def find_maximum_length_bounded_disjoint_paths(graph, source, target, max_length):
        modified_graph = graph.copy()
        dummy_node = 'dummy'
        modified_graph.add_node(dummy_node)
        for node in modified_graph.nodes():
            if node != target and node != dummy_node:
                modified_graph.add_edge(node, dummy_node, capacity=1)
        flow_value, flow_dict = nx.maximum_flow(modified_graph, source, dummy_node)
        paths = []
        for node in modified_graph.neighbors(dummy_node):
            if flow_dict[source][node] == 1:
                path = nx.shortest_path(graph, source=source, target=node)
                paths.append(path[:-1])  # Remove the dummy node from the path
        filtered_paths = [path for path in paths if len(path) <= max_length]
        return filtered_paths
    graph = nx.DiGraph()
    graph.add_edge('A', 'B')
    graph.add_edge('A', 'C')
    graph.add_edge('B', 'C')
    graph.add_edge('B', 'D')
    graph.add_edge('C', 'D')
    source = 'A'
    target = 'D'
    max_length = 3
    paths = find_maximum_length_bounded_disjoint_paths(graph, source, target, max_length)
    for path in paths:
        print("Path:", ' -> '.join(path))
