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[1010], t[1010][10010], p[1010][1010];
int vis[1010];
void dijkstra()
{
    memset(vis, 0, sizeof(vis));
    for(int i = 1; i <= n; i++){
        dist[i] = INF;
    }
    dist[1] = 0;
    for(int i = 1; i <= n; i++){
        int mini = INF, k = -1;
        for(int j = 1; j <= n; j++){
            if(!vis[j]&&mini > dist[j]){
                mini = dist[j];
                k = j;
            }
        }
        vis[k] = 1;
        for(int j = 1; 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 = 1; i <= n; i++){
            for(int j = 1; j <= n; j++){
                if(i == j) t[i][j] = 0, p[i][j] = 0;
                else t[i][j] = INF; p[i][j] = INF;
            }
        }
        for(int i = 0; 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=0;
        for(int i = 2; 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 = 1; 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 0;
}

 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[10010];
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[10010];
void dijkstra()
{
    priority_queue<P, vector<P>, greater<P> > q;
    for(int i = 1; i <= n; i++) dist[i] = INF;
    dist[1] = 0;
    q.push(P(0, 1));
    while(!q.empty()){
        P p = q.top(); q.pop();
        int v = p.second;
        if(dist[v] < p.first) continue;
        for(int i = 0; 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 = 0; i <= n; i++){
            G[i].clear();
        }
        for(int i = 0; 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 = 0;
        for(int i = 2; i <= n; i++){
            int mini = INF;
            for(int j = 0; 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 0;
}