朴素版dijkstra算法

dijkstra算法用来处理无负权边的图,是单源最短路的算法

对于自环,因为是非负权边,所以不用考虑,不会走的

对于重边,在加入数组时,应仅加入最小的那条边

朴素版dijkstra算法一般用在稠密图,时间复杂度是O(n^2 + m),稠密图也就是边数m ~ 点数n^2级别的图

#pragma optimize(2)
#include<bits/stdc++.h>
#include<unordered_map>
#define endl '\n'
#define int int64_t
using namespace std;
const int  N = 1e4 + 10;
struct edge { int v, w; };
vector<edge>e[N];
int d[N],vis[N],m,n,s;
void dijkstra(int s) {
    for (int i = 0; i <= n; ++i) d[i] = INT_MAX;
    d[s] = 0;
    for (int i = 0; i < n; ++i) {
         int u = 0;
         for (int j = 1; j <= n; ++j) 
             if (!vis[j] && d[u] > d[j]) u = j;
         vis[u] = 1;//出圈
         for (auto k : e[u]) {
             int v = k.v, w = k.w;
             d[v] = min(d[v], d[u] + w);
         }
    }
}
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;
}