12.spfa判断负环

 

 spfa算法判断负环时间复杂度最坏nm

#include <bits/stdc++.h>
using namespace std;
const int N = 10010;
int h[N], e[N], ne[N], idx, w[N];
int dist[N], cnt[N];
//dist数组存储每个点到1号点的最短路的距离
//cnt数组存储这个最短路的边数
bool st[N];
int n, m;
void add(int a, int b, int c) {
    e[idx] = b;
    w[idx] = c;
    ne[idx] = h[a];
    h[a] = idx++;
}
bool spfa() {
    memset(dist, 0x3f, sizeof dist);
    dist[1] = 0;
    queue<int> q;
    for (int i = 1; i <= n; i++) { //把所有点放进队列
        q.push(i);
        st[i] = true;
    }
    while (q.size()) {
        int t = q.front();
        q.pop();
        st[t] = false;
        for (int i = h[t]; i != -1; i = ne[i]) {
            int j = e[i];
            if (dist[j] > dist[t] + w[i]) {
                dist[j] = dist[t] + w[i];
                cnt[j] = cnt[t] + 1;
                //从1到t的边数加上这一条边
                if (cnt[j] >= n) { //抽屉原理
                    return true;
                }
                if (!st[j]) {
                    q.push(j);
                    st[j] = true;
                }
            }
        }
    }
    return false;
}
int main() {
    memset(h, -1, sizeof h);
    cin >> n >> m;
    while (m--) {
        int a, b, c;
        cin >> a >> b >> c;
        add(a, b, c);
    }
    if (spfa()) {
        cout << "Yes" << endl;
    } else {
        cout << "No" <<endl;
    }
    return 0;
}