Bellman ford算法，c++代码

Bellman-Ford算法是一种用于解决单源最短路径问题的算法，它可以处理边权值为负数的情况。下面是C语言实现的代码：

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>

#define MAX_VERTICES 1000
#define MAX_EDGES 2000

typedef struct Edge {
    int source;
    int destination;
    int weight;
} Edge;

Edge edges[MAX_EDGES];

int distances[MAX_VERTICES];
int parents[MAX_VERTICES];

int num_vertices;
int num_edges;

void bellman_ford(int source) {
    // 初始化距离数组和前驱数组
    for (int i = 0; i < num_vertices; i++) {
        distances[i] = INT_MAX;
        parents[i] = -1;
    }
    distances[source] = 0;

    // 对每条边进行V-1次松弛操作
    for (int i = 1; i <= num_vertices - 1; i++) {
        for (int j = 0; j < num_edges; j++) {
            Edge edge = edges[j];
            int u = edge.source;
            int v = edge.destination;
            int w = edge.weight;
            if (distances[u] != INT_MAX && distances[u] + w < distances[v]) {
                distances[v] = distances[u] + w;
                parents[v] = u;
            }
        }
    }

    // 检测负权环
    for (int i = 0; i < num_edges; i++) {
        Edge edge = edges[i];
        int u = edge.source;
        int v = edge.destination;
        int w = edge.weight;
        if (distances[u] != INT_MAX && distances[u] + w < distances[v]) {
            printf("Graph contains a negative-weight cycle\n");
            return;
        }
    }

    // 输出结果
    for (int i = 0; i < num_vertices; i++) {
        printf("Vertex %d, distance = %d, parent = %d\n", i, distances[i], parents[i]);
    }
}

int main() {
    // 从文件读取图的信息
    FILE *fp = fopen("graph.txt", "r");
    fscanf(fp, "%d %d", &num_vertices, &num_edges);
    for (int i = 0; i < num_edges; i++) {
        fscanf(fp, "%d %d %d", &edges[i].source, &edges[i].destination, &edges[i].weight);
    }
    fclose(fp);

    // 执行Bellman-Ford算法
    bellman_ford(0);

    return 0;
}

其中，`num_vertices`和`num_edges`分别表示图中的顶点数和边数，`distances`和`parents`分别表示每个顶点到源点的最短距离和最短路径上的前驱顶点，`edges`数组保存了每条边的起点、终点和权值。`bellman_ford`函数实现了Bellman-Ford算法的主要逻辑，首先对距离数组和前驱数组进行初始化，然后对每条边进行V-1次松弛操作，最后检测负权环并输出结果。