pat 甲级 1003 Emergency

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      

题意：

求单源点对最短路径数和最大的点权重之和。

思路：

floyd是办不到的，只能在dijstra算法上加计数dp类型的优化，统计从起点到当前节点的最短路径的条数和到该点为止

所能找到的最多的急救队的数。

#include<bits/stdc++.h>
using namespace std;
const int maxn = 550;
const int INF = 0x3f3f3f3f;
int m,n,st,ed;
int have[maxn];
int vis [maxn];
int e[maxn][maxn];
int dist[maxn];
int lead[maxn];
int diff[maxn];
int main()
{
    memset(vis,0,sizeof(vis));
    scanf("%d%d%d%d",&n,&m,&st,&ed);
    for(int i = 0;i < n;i++)
        scanf("%d",&have[i]);
    for(int i= 0;i < maxn;i++)
        for(int j = 0;j < maxn;j++)
            if(i != j)
                e[i][j] = INF;
            else
                e[i][j] = 0;
    for(int i =0;i < m;i++)
    {
        int a,b,l;
        scanf("%d%d%d",&a,&b,&l);
        e[a][b] = e[b][a] = l;
    }
    if(st == ed)//没有这个第二组样例是过不了的，卡了很久
    {
        printf("%d %d\n",1,have[st]);
        return 0;
    }
    for(int i = 0;i < n;i++)
    {
        diff[i] = 1;
        dist[i] = e[st][i];
        if(dist[i] != INF)
            lead[i] = have[st]+have[i];
    }
    dist[st] = 0;
    vis[st] = 1;
    for(int i = 1;i < n;i++)
    {
        int minn = INF;
        int v = 0;
        for(int j = 0;j < n;j++)
        {
            if(vis[j])continue;
            if(minn > dist[j])
            {
                minn = dist[j];
                v = j;
            }
        }
        if(v == ed)
        {
            printf("%d %d\n",diff[v],lead[v]);
            break;
        }
        vis[v] = 1;
        for(int j = 0;j < n;j++)
        {
            if(!vis[j]&&e[v][j]!=INF)
            {
                if(dist[j] > dist[v] + e[v][j])
                {
                    dist[j] = dist[v] + e[v][j];
                    lead[j] = lead[v] + have[j];
                    diff[j] = diff[v];
                }
                else if(dist[j] == dist[v]+e[v][j])
                {
                    diff[j]+= diff[v];
                    if(lead[v]+have[j]>lead[j])
                        lead[j] = lead[v] + have[j];
                }
            }
        }
    }
    return 0;
}