我们希望1到X和X到1都是最短路,有个难点是多个起点到终点的最短路,就要用到反向建边,反向建一个图,然后跑1到x的最短路,得到的结果就是x到1的最短路,因为这条路径是反着的,我们扭回来就正好是x到1了。
在形式上不要写的像我一样,可以用vector模拟静态邻接链表。
时间复杂度O(mlogn)
#include <iostream>
#include <queue>
#include <algorithm>
#include <string.h>
using namespace std;
typedef long long ll;
#define IOS ios::sync_with_stdio(false),cin.tie(0);
#define endl cout<<"\n";
const int N = 1e3 + 7;
const int M = 1e5 + 7;
struct node {
int to, next, c;
} e1[M], e2[M];
int h1[N], h2[N];
int cnt1, cnt2;
void add1(int x, int y, int z) {
e1[++cnt1].c = z;
e1[cnt1].to = y;
e1[cnt1].next = h1[x];
h1[x] = cnt1;
return;
}
void add2(int x, int y, int z) {
e2[++cnt2].c = z;
e2[cnt2].to = y;
e2[cnt2].next = h2[x];
h2[x] = cnt2;
return;
}
int n, m;
int d1[N];
int d2[N];
int vis[N];
priority_queue<pair<int, int>> q;
void dij(int s, int flag) {
memset(vis, 0, sizeof vis);
while (q.size())q.pop();
int* dist = flag == 0 ? d1 : d2;
dist[s] = 0;
q.push({0, s});
while (!q.empty()) {
int x = q.top().second;
q.pop();
if (vis[x])continue;
vis[x] = 1;
//cout<<"pok\n";
int* h = flag == 0 ? h1 : h2;
node* e = flag == 0 ? e1 : e2;
for (int i = h[x]; i; i = e[i].next) {
int v = e[i].to;
if (dist[v] >= dist[x] + e[i].c) {
dist[v] = dist[x] + e[i].c;
q.push({-1 * dist[v], v});
}
}
}
return;
}
void solve() {
cin >> n >> m;
for (int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
add1(a, b, c); //正向建边
add2(b, a, c); //反向建边
}
memset(d1, 0x3f3f3f3f, sizeof d1);
memset(d2, 0x3f3f3f3f, sizeof d2);
dij(1, 0);
dij(1, 1);
int ans = 0;
for (int i = 2; i <= n; i++) {
ans += d1[i] + d2[i];
}
cout << ans;
}
int main() {
//IOS;
int T = 1;
//cin>>T;
while (T--)solve();
return 0;
}



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