单源最短路：Dijksra

单源最短路，时间复杂度\(O(nlog(n+m))\)

不适用于有负权边的图

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct edge
{
    int to, w;
};
vector<vector<edge>> adj;
vector<int> dis;
vector<bool> vis;
int n, m, start;

bool operator<(const edge a, const edge b) // 大根堆：重载小于号
{
    return a.w > b.w;
}

bool cmp(const edge a, const edge b)
{
    return a.w > b.w;
}

void dijkstra(int start)
{
    dis[start] = 0;

    priority_queue<edge> pq;
    pq.push({start, 0});

    while (!pq.empty())
    {
        auto [u, now] = pq.top();
        pq.pop();

        if (vis[u])
            continue;

        vis[u] = 1;
        for (auto [to, w] : adj[u])
        {

            if (!vis[to] and dis[u] + w < dis[to])
            {
                dis[to] = dis[u] + w;
                pq.push({to, dis[to]});
            }
        }
    }
}

void add(int a, int b, int w)
{
    adj[a].push_back({b, w});
}

int main()
{

    cin >> n >> m >> start;

    dis.resize(n + 1, INT_MAX);
    vis.resize(n + 1, 0);
    adj.resize(n + 1);
    for (int i = 0; i < m; ++i)
    {
        int a, b, w;
        cin >> a >> b >> w;
        add(a, b, w);
    }

    dijkstra(start);
    for (int i = 1; i <= n; ++i)
        cout << dis[i] << ' ';

    cout << '\n';

    return 0;
}