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堆优化的dijkstra算法用于稀疏图,也就是m~n级别的图,算法时间复杂度O(mlog(n))

vis数组的用处:堆优化是按照距离来进行排序,可能会出现距离已经被优化的点,和原先没被优化的距离同时进入了堆,也就是堆内的元素数实际上不等于顶点数,而是边数,vis就是为了处理上述可能被重复更新的点

#pragma optimize(2)
#include<bits/stdc++.h>
#include<unordered_map>
#define endl '\n'
#define int int64_t
using namespace std;
const int  N = 1e5 + 10;
struct edge { int v, w; };
vector<edge>e[N];
int d[N],vis[N],m,n,s;
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>>q;
void dijkstra(int s) {for (int i = 0; i <= n; ++i) d[i] = INT_MAX;d[s] = 0; q.push({ 0,s });while (q.size()) {int u = q.top().second; q.pop();if (vis[u]) continue;vis[u] = 1;for (auto k : e[u]) {if (d[k.v] > d[u] + k.w) {d[k.v] = d[u] + k.w;q.push({ d[k.v],k.v });}}}
}
signed main() {ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);cin >> n >> m >> s;for (int i = 1; i <= m; ++i) {int a, b, c; cin >> a >> b >> c;e[a].push_back({ b,c });}dijkstra(s);for (int i = 1; i <= n; ++i) cout << d[i] << " ";return 0;
}