#Stacker-Crane



    # Add required edges with high weight

    # Find the Eulerian circuit in the augmented graph

    # Check if the circuit satisfies the constraints

# Example usage:




if __name__ == '__main__':
    import networkx as nx
    def directed_chinese_postman(graph, required_edges, bound):
        augmented_graph = graph.copy()
        for edge in required_edges:
            u, v, weight = edge
            augmented_graph.add_edge(u, v, weight=weight)
        eulerian_circuit = nx.eulerian_circuit(augmented_graph)
        total_length = sum(augmented_graph[u][v]['weight'] for u, v in eulerian_circuit)
        if total_length <= bound:
            return eulerian_circuit
        else:
            return None
    graph = nx.DiGraph()
    graph.add_edge('A', 'B', weight=2)
    graph.add_edge('B', 'C', weight=3)
    graph.add_edge('C', 'D', weight=4)
    graph.add_edge('D', 'A', weight=5)
    graph.add_edge('D', 'B', weight=1)
    required_edges = [('A', 'B', 2), ('D', 'B', 1)]
    bound = 12
    path = directed_chinese_postman(graph, required_edges, bound)
    if path is not None:
        total_length = sum(graph[u][v]['weight'] for u, v in path)
        print("Directed Chinese Postman Path:", path)
        print("Total Length:", total_length)
    else:
        print("No feasible solution within the specified bound.")
