PAT甲级1003. Emergency (25)（Dijkstra变形）

叁歲伎倆 2022-05-30 09:06 180阅读 0赞

# 1003. Emergency (25) #

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

As an emergency rescue team leader of a city, you are given a special map of your country. The map shows several scattered cities connected by some roads. Amount of rescue teams in each city and the length of each road between any pair of cities are marked on the map. When there is an emergency call to you from some other city, your job is to lead your men to the place as quickly as possible, and at the mean time, call up as many hands on the way as possible.

**Input**

Each input file contains one test case. For each test case, the first line contains 4 positive integers: N (<= 500) - the number of cities (and the cities are numbered from 0 to N-1), M - the number of roads, C1 and C2 - the cities that you are currently in and that you must save, respectively. The next line contains N integers, where the i-th integer is the number of rescue teams in the i-th city. Then M lines follow, each describes a road with three integers c1, c2 and L, which are the pair of cities connected by a road and the length of that road, respectively. It is guaranteed that there exists at least one path from C1 to C2.

**Output**

For each test case, print in one line two numbers: the number of different shortest paths between C1 and C2, and the maximum amount of rescue teams you can possibly gather.  
All the numbers in a line must be separated by exactly one space, and there is no extra space allowed at the end of a line.

**Sample Input**

5 6 0 2
    1 2 1 5 3
    0 1 1
    0 2 2
    0 3 1
    1 2 1
    2 4 1
    3 4 1

**Sample Output**

2 4

思路：最主要是road和pmax数组   road数组是从开始点到终点最短路条数，pmax是从起点到终点所有最短路中最大的人数和

#include<cstdio>
    #include<algorithm>
    using namespace std;
    
    const int maxn=550;
    const int INF=0x3f3f3f3f;
    int mp[maxn][maxn], vis[maxn], dis[maxn], city[maxn], pmax[maxn], road[maxn];
    int n, m, c1, c2;
    void Dijkstra(int s){
        pmax[s]=city[s];
        road[s]=1;
        for(int i=0; i<n; i++)
            dis[i]=mp[s][i];
        dis[s]=0;//很重要的初始化；
        for(int i=0; i<n; i++)
        {
            int mm=INF, id;
            for(int j=0; j<n; j++)
            {
                if(!vis[j] && dis[j]<mm)
                    mm=dis[id=j];
            }
            vis[id]=1;
            for(int j=0; j<n; j++)
            {
    
                if(dis[j]>dis[id]+mp[id][j])
                {
                    dis[j]=dis[id]+mp[id][j];
                    road[j]=road[id];
                    pmax[j]=pmax[id]+city[j];
                }
                else if(dis[j]==dis[id]+mp[id][j])
                {
                    road[j]+=road[id];
                    pmax[j]=max(pmax[j], pmax[id]+city[j]);
                }
            }
        }
    
    }
    
    int main(){
    
        scanf("%d%d%d%d", &n, &m, &c1, &c2);
        for(int i=0; i<n; i++)
            scanf("%d", city+i);
        int u, v, w;
    
        for(int i=0; i<n; i++)
            for(int j=0; j<n; j++)
                mp[i][j]=INF;//很重要的初始化，一定不要将i==j的情况初始化为0
    
        for(int i=0; i<m; i++)
        {
            scanf("%d%d%d", &u, &v, &w);
            if(w<mp[u][v])
                mp[u][v]=mp[v][u]=w;
        }
    
        Dijkstra(c1);
    
        printf("%d %d\n", road[c2], pmax[c2]);
        return 0;
    }