dji最短路模板

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<ll, int> pli;  // {距离, 节点}

const ll INF = 1e18;

// 邻接表: graph[u] = {{v, w}, ...} 表示u到v有权重为w的边
vector<vector<pair<int, ll>>> graph;
vector<ll> dist;
vector<int> parent;  // 用于记录最短路径

// Dijkstra算法
// n: 节点数(0-indexed), start: 起点
// 返回从start到各点的最短距离数组
void dijkstra(int n, int start) {
   dist.assign(n, INF);
   parent.assign(n, -1);
   dist[start] = 0;
   
   priority_queue<pli, vector<pli>, greater<pli>> pq;
   pq.push({0, start});
   
   while (!pq.empty()) {
       auto [d, u] = pq.top();
       pq.pop();
       
       // 如果当前距离大于已记录距离，跳过
       if (d > dist[u]) continue;
       
       for (auto [v, w] : graph[u]) {
           if (dist[u] + w < dist[v]) {
               dist[v] = dist[u] + w;
               parent[v] = u;
               pq.push({dist[v], v});
           }
       }
   }
}

// 获取从start到target的最短路径(节点列表)
vector<int> getPath(int target) {
   vector<int> path;
   if (dist[target] == INF) return path;  // 不可达
   
   for (int u = target; u != -1; u = parent[u]) {
       path.push_back(u);
   }
   reverse(path.begin(), path.end());
   return path;
}

// ========== 使用示例 ==========
int main() {
   ios::sync_with_stdio(false);
   cin.tie(nullptr);
   
   int n, m, s;  // n个点, m条边, 起点s
   cin >> n >> m >> s;
   s--;  // 转为0-indexed
   
   graph.resize(n);
   
   for (int i = 0; i < m; i++) {
       int u, v;
       ll w;
       cin >> u >> v >> w;
       u--; v--;  // 转为0-indexed
       graph[u].push_back({v, w});
       // 如果是无向图，加上: graph[v].push_back({u, w});
   }
   
   dijkstra(n, s);
   
   // 输出到各点的最短距离
   for (int i = 0; i < n; i++) {
       cout << (dist[i] == INF ? -1 : dist[i]) << " ";
   }
   cout << endl;
   
   // 示例: 输出到某点的路径
   // vector<int> path = getPath(target);
   
   return 0;
}