PAT–1003 Emergency 最短路径的迪杰斯特拉算法,加上边的权重问题

1001-高同学

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问题描述:

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.

 

这道题是无向无负边权的问题,用迪杰斯特拉算法就能很好的解决。如果不太懂迪杰斯特拉算法,可以看我的另一篇博文:

迪杰斯特拉讲解

AC代码如下:

#include <bits/stdc++.h>

using namespace std;
const int INF = 10000000;           ///最大值
const int maxv = 1000;          ///最大节点数
int G[maxv][maxv];              ///邻接矩阵
int d[maxv];        ///存放最短路径
int weight[maxv];               ///点权重
int vis[maxv] = {false};
int w[maxv] ;
///邻接矩阵的深度优先遍历
int n;
int num[maxv] = {0};
void Djskl(int s)
{
    for(int i=0; i<maxv; i++)
        d[i] = INF;
    memset(w,0,sizeof(w));
    d[s] = 0;
    w[s] = weight[s];
    num[s] = 1;
    for(int i=0; i<n; i++)
    {
        int u = -1,MIN = INF;
        for(int j=0; j<n; j++)
        {
            if(vis[j] == false && d[j] < MIN)
            {
                u = j;
                MIN = d[j];
            }
        }
        if(u == -1)
            return ;
        vis[u] = true;
        for(int v = 0; v<n; v++)
        {
            if(vis[v] == false && G[u][v] != INF )
            {
                if(d[u] + G[u][v] < d[v])
                {
                    d[v] = d[u] + G[u][v];
                    if(w[u] + weight[v] > w[v] )
                    {
                        w[v] = w[u] + weight[v];
                    }
                    num[v] = num[u];
                }
                else if(d[u] + G[u][v] == d[v])
                {
                    num[v] += num[u] ;
                    if(w[u] + weight[v] > w[v] )
                    {
                        w[v] = w[u] + weight[v];
                    }
                }
            }
        }
    }
}


int main()
{
    cin>>n;
    int m,s,dis;
    cin>>m>>s>>dis;
    for(int i=0; i<maxv; i++)
        for(int j=0; j<maxv; j++)
        {
             G[i][j] = INF;
        }
    int u,v,wn;
    for(int i=0; i<n; i++)
    {
        int x;
        cin>>x;
        weight[i] = x;
    }
    for(int i=0; i<m; i++)
    {
        cin>>u>>v>>wn;
        G[u][v] = wn;
        G[v][u] = wn;
    }
    Djskl(s);
    cout<<num[dis]<<" ";
    cout<<w[dis]<<endl;
    return 0;
}

 

拜师教育学员文章:作者:1001-高同学, 转载或复制请以 超链接形式 并注明出处 拜师资源博客
原文地址:《PAT–1003 Emergency 最短路径的迪杰斯特拉算法,加上边的权重问题》 发布于2018-07-22

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