Bellman_Ford算法总结

知识概览

Bellman_Ford算法适合解决存在负权边的最短路问题，时间复杂度为O(nm)。
在存在负权边的最短路问题中，Bellman_Ford算法的效率虽然不如SPFA算法，但是Bellman_Ford算法能解决SPFA算法不能解决的经过不超过k条边的最短路问题。

例题展示

题目链接

853. 有边数限制的最短路 - AcWing题库高质量的算法题库https://www.acwing.com/problem/content/855/

代码

#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int N = 510, M = 10010;

int n, m, k;
int dist[N], backup[N];

struct Edge {
    int a, b, w;
} edges[M];

void bellman_ford()
{
    memset(dist, 0x3f, sizeof dist);
    dist[1] = 0;
    
    for (int i = 0; i < k; i++)
    {
        memcpy(backup, dist, sizeof dist);
        for (int j = 0; j < m; j++)
        {
            int a = edges[j].a, b = edges[j].b, w = edges[j].w;
            dist[b] = min(dist[b], backup[a] + w);
        }
    }
}

int main()
{
    scanf("%d%d%d", &n, &m, &k);
    
    for (int i = 0; i < m; i++)
    {
        int a, b, w;
        scanf("%d%d%d", &a, &b, &w);
        edges[i] = {a, b, w};
    }
    
    bellman_ford();
    
    if (dist[n] > 0x3f3f3f3f / 2) puts("impossible");
    else printf("%d\n", dist[n]);
    
    return 0;
}