spfa

原理

见《进阶指南》第353页。

模板题

洛谷-P3371-【模板】单源最短路径（弱化版）

#include <iostream>
#include <cstring>
#include <queue>
#define inf 0x3f3f3f3f
using namespace std;

const int N = 10010, M = 500010;
struct edge {
    int to, next, w;
};
edge e[M];
int idx, head[N];
int n, m, s;
int dis[N];
bool mark[N];

void add_edge (int u, int v, int w) {
    e[idx].w = w;
    e[idx].to = v;
    e[idx].next = head[u];
    head[u] = idx ++ ;
}
void spfa () {
    memset(dis, 0x3f, sizeof(dis));
    
    queue<int> q;
    dis[s] = 0;
    q.push(s);
    mark[s] = true;
    while (!q.empty()) {
        int cur = q.front();
        q.pop();
        mark[cur] = false;
        for (int i = head[cur]; i != -1; i = e[i].next) {
            int to = e[i].to, w = e[i].w;
            if (dis[cur] + w < dis[to]) {
                dis[to] = dis[cur] + w;
                if (mark[to] == false) {
                    q.push(to);
                    mark[to] = true;
                }
            }
        }
    }
}

int main () {
    memset(head, -1, sizeof(head));
    scanf("%d%d%d", &n, &m, &s);
    for (int i = 1, u, v, w; i <= m; ++ i) {
        scanf("%d%d%d", &u, &v, &w);
        add_edge(u, v, w);
    }
    spfa();
    for (int i = 1; i <= n; ++ i)
        printf("%d ", dis[i] == inf ? (1ll << 31) - 1 : dis[i]);
    return 0;
}