spfa算法是bellman_ford的队列优化版本, bfs实现

优化的是dist[b] = min(dist[b], dist[a]+w)
因为只有dist[a]更新之后变小, dist[b]更新之后才有可能变小
需要st[i]数组，保证队列里面只有一个i;

spfa是优化版的bellman_ford算法

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

using namespace std;
const int N = 1e5 + 10;
int h[N], e[N], w[N], ne[N], idx;
int n, m;
queue<int> q;
int st[N], dist[N];

void add(int a, int b, int c) {
    e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++;
}

int spfa() {
    memset(dist, 0x3f, sizeof dist);
    dist[1] = 0;
    q.push(1);
    st[1] = 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];
                if (!st[j]) {
                    st[j] = true;
                    q.push(j);
                }
            }
        }
    }
    // int dist[n]=t;
    if (dist[n] > 0x3f3f3f3f / 2) return -1;
    else return dist[n];
}

int main() {
    memset(h, -1, sizeof h);
    cin >> n >> m;
    for (int i = 0; i < m; i++) {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        add(a, b, c);
    }
    int t = spfa();
    if (t == -1) cout << "impossible" << endl;
    else cout << t << endl;
}