Bellman-Ford算法怎样通过追溯前驱节点来找到负权环的具体路径C++

要通过追溯前驱节点来找到负权环的具体路径，可以在Bellman-Ford算法的基础上进行一些修改。下面是一个用C++实现的示例代码：

#include <iostream>
#include <vector>

using namespace std;

struct Edge {
    int src, dest, weight;
};

vector<int> findNegativeCycle(vector<Edge>& edges, int V, int E, int source) {
    vector<int> dist(V, INT_MAX);
    vector<int> parent(V, -1);

    dist[source] = 0;

    int lastUpdatedVertex;

    // Relax all edges V-1 times
    for (int i = 1; i <= V - 1; i++) {
        lastUpdatedVertex = -1;
        for (int j = 0; j < E; j++) {
            int u = edges[j].src;
            int v = edges[j].dest;
            int weight = edges[j].weight;
            
            if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) {
                dist[v] = dist[u] + weight;
                parent[v] = u;
                lastUpdatedVertex = v;
            }
        }
    }

    // If there is no update in the last iteration, then there is no negative cycle
    if (lastUpdatedVertex == -1)
        return {};

    // Trace back the negative cycle using the parent array
    vector<int> cycle;
    int startVertex = lastUpdatedVertex;

    for (int i = 0; i < V; i++)
        startVertex = parent[startVertex];

    int currVertex = startVertex;
    cycle.push_back(currVertex);

    do {
        currVertex = parent[currVertex];
        cycle.push_back(currVertex);
    } while (currVertex != startVertex);

    return cycle;
}

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

    vector<Edge> edges(E);
    cout << "Enter the source, destination, and weight of each edge:\n";
    for (int i = 0; i < E; i++)
        cin >> edges[i].src >> edges[i].dest >> edges[i].weight;

    int source;
    cout << "Enter the source vertex: ";
    cin >> source;

    vector<int> cycle = findNegativeCycle(edges, V, E, source);

    if (cycle.empty()) {
        cout << "No negative cycle found.\n";
    } else {
        cout << "Negative cycle found: ";
        for (int vertex : cycle)
            cout << vertex << " ";
        cout << endl;
    }

    return 0;
}

在代码中，我们使用了`dist`数组来存储从起点到每个顶点的最短路径距离，使用`parent`数组来记录每个顶点的前驱节点。在算法的最后，我们通过追溯`parent`数组来找到负权环的具体路径。

请注意，这只是一个示例代码，并未进行详尽的输入验证和错误处理。在实际应用中，需要根据具体情况进行适当的修改和完善。