用c++编写：定义有向图用分支界限算法求tsp最优解

下面是使用C++编写的分支限界算法来解决Traveling Salesman Problem（TSP）的最优解：

#include <iostream>
#include <vector>
#include <algorithm>
#include <limits>

using namespace std;

const int INF = numeric_limits<int>::max();

// 有向图的表示
class Graph {
public:
    int vertices;
    vector<vector<int>> adjacencyMatrix;

    Graph(int v) : vertices(v) {
        adjacencyMatrix.resize(v, vector<int>(v, 0));
    }

    void addEdge(int source, int destination, int weight) {
        adjacencyMatrix[source][destination] = weight;
    }
};

// 分支限界算法求解TSP
class TSP {
public:
    int solve(Graph& graph) {
        vector<int> path;
        int optimalPath = INF;
        vector<bool> visited(graph.vertices, false);
        path.push_back(0); // 从节点0开始

        solveUtil(graph, path, visited, 0, optimalPath);

        return optimalPath;
    }

private:
    void solveUtil(Graph& graph, vector<int>& path, vector<bool>& visited, int cost, int& optimalPath) {
        if (path.size() == graph.vertices) {
            // 更新最优路径
            optimalPath = min(optimalPath, cost + graph.adjacencyMatrix[path.back()][0]);
            return;
        }

        int last = path.back();
        for (int i = 0; i < graph.vertices; i++) {
            if (!visited[i]) {
                visited[i] = true;
                path.push_back(i);

                // 计算当前路径的代价
                int currentCost = cost + graph.adjacencyMatrix[last][i];

                // 剪枝，如果当前路径代价已经大于最优路径，则不再继续搜索
                if (currentCost < optimalPath) {
                    solveUtil(graph, path, visited, currentCost, optimalPath);
                }

                path.pop_back();
                visited[i] = false;
            }
        }
    }
};

int main() {
    int vertices, edges;
    cout << "Enter the number of vertices: ";
    cin >> vertices;
    cout << "Enter the number of edges: ";
    cin >> edges;

    Graph graph(vertices);

    cout << "Enter the edges (source, destination, weight):" << endl;
    for (int i = 0; i < edges; i++) {
        int source, destination, weight;
        cin >> source >> destination >> weight;
        graph.addEdge(source, destination, weight);
    }

    TSP tsp;
    int optimalPath = tsp.solve(graph);

    cout << "Optimal TSP path length: " << optimalPath << endl;

    return 0;
}

这段代码实现了使用分支限界算法求解TSP的最优路径。你可以输入图的顶点数和边数，然后依次输入每条边的起点、终点和权重。程序将输出最优TSP路径的长度。请确保输入的图是有向图，并且权重都是非负整数。

希望这能帮到你！如果还有其他问题，请随时提问。