Aizu2249 Road Construction（dijkstra优化+思路 好题）

https://vjudge.net/problem/Aizu-2249

感觉这题和2017女生赛的Deleting Edge思路很像，都是先找最短路，然后替换边的。

但是这题用最朴素的dijkstra的话memory limit exceed了，看了下超了约7倍无望。。。

不得已这时候不得不学dijkstra的堆优化了。

 #include<iostream>
 #include<cstdio>
 #include<queue>
 #include<cstring>
 #include<algorithm>
 #include<cmath>
 #include<stack>
 #define lson l, m, rt<<1
 #define rson m+1, r, rt<<1|1
 #define INF 0x3f3f3f3f
 typedef unsigned long long ll;
 using namespace std;
 int n, m, a, b, d, c;
 int dist[], t[][], p[][];
 int vis[];
 void dijkstra()
 {
     memset(vis, , sizeof(vis));
     for(int i = ; i <= n; i++){
         dist[i] = INF;
     }
     dist[] = ;
     for(int i = ; i <= n; i++){
         int mini = INF, k = -;
         for(int j = ; j <= n; j++){
             if(!vis[j]&&mini > dist[j]){
                 mini = dist[j];
                 k = j;
             }
         }
         vis[k] = ;
         for(int j = ; j <= n; j++){
             if(!vis[j]&&dist[j] > dist[k]+t[k][j]){
                 dist[j] = dist[k]+t[k][j];
             }
         }
     }
 }
 int main()
 {
     while(cin >> n >> m){
         if(!n&&!m) break;
         for(int i = ; i <= n; i++){
             for(int j = ; j <= n; j++){
                 if(i == j) t[i][j] = , p[i][j] = ;
                 else t[i][j] = INF; p[i][j] = INF;
             }
         }
         for(int i = ; i < m; i++){
             cin >> a >> b >> d >> c;
             t[a][b] = d; t[b][a] = d;
             p[a][b] = c; p[b][a] = c;
         }
         dijkstra();
         int sum=;
         for(int i = ; i <= n; i++){//这里记得要从2开始，从一开始下面无法更新mini，而且反正i=1的时候mini也是0，就直接跳过了
             int mini = INF;
             for(int j = ; j <= n; j++){
                 if((dist[i] == dist[j]+t[j][i])&&mini>p[j][i]){
                     mini = p[j][i];
                 }
             }
             sum += mini;
         }
         cout << sum << endl;
     }
     return ;
 }

优先队列、vector容器、pair优化

 #include<iostream>
 #include<cstdio>
 #include<queue>
 #include<cstring>
 #include<algorithm>
 #include<cmath>
 #include<stack>
 #define lson l, m, rt<<1
 #define rson m+1, r, rt<<1|1
 #define INF 0x3f3f3f3f
 typedef unsigned long long ll;
 using namespace std;
 int n, m, a, b, d, c;
 int dist[];
 struct edge{
     int to, d, cost;
     //edge(int a, int b, int c):to(a),d(b),cost(c){ }
 };
 typedef pair<int, int> P;
 vector<edge> G[];
 void dijkstra()
 {
     priority_queue<P, vector<P>, greater<P> > q;
     for(int i = ; i <= n; i++) dist[i] = INF;
     dist[] = ;
     q.push(P(, ));
     while(!q.empty()){
         P p = q.top(); q.pop();
         int v = p.second;
         if(dist[v] < p.first) continue;
         for(int i = ; i < G[v].size(); i++){
             edge e = G[v][i];
             if(dist[e.to] > dist[v]+e.d){
                 dist[e.to] = dist[v]+e.d;
                 q.push(P(dist[e.to], e.to));
             }
         }
     }
 }
 int main()
 {
     while(cin >> n >> m){
         if(!n&&!m) break;
         for(int i = ; i <= n; i++){
             G[i].clear();
         }
         for(int i = ; i < m; i++){
             cin >> a >> b >> d >> c;
             G[a].push_back(edge{b, d, c});
             G[b].push_back(edge{a, d, c});
         }
         dijkstra();
         /*for(int i = 1; i <= n; i++){
             cout << dist[i] << " ";
         }*/
         int sum = ;
         for(int i = ; i <= n; i++){
             int mini = INF;
             for(int j = ; j < G[i].size(); j++){
                 edge e = G[i][j];
                 if(dist[e.to]+e.d == dist[i]){//这里注意，一开始e.d错放到等式右边了
                     mini = min(mini, e.cost);
                 }
             }
             sum += mini;
         }
         cout << sum << endl;
     }
     return ;
 }