堆优化版dijkstra算法

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; }