A Walk Through the Forest

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 10172    Accepted Submission(s): 3701

Problem Description

Jimmy experiences a lot of stress at work these days, especially since his accident made working difficult. To relax after a hard day, he likes to walk home. To make things even nicer, his office is on one side of a forest, and his house is on the other. A nice walk through the forest, seeing the birds and chipmunks is quite enjoyable.
The forest is beautiful, and Jimmy wants to take a different route everyday. He also wants to get home before dark, so he always takes a path to make progress towards his house. He considers taking a path from A to B to be progress if there exists a route from B to his home that is shorter than any possible route from A. Calculate how many different routes through the forest Jimmy might take.

Input

Input contains several test cases followed by a line containing 0. Jimmy has numbered each intersection or joining of paths starting with 1. His office is numbered 1, and his house is numbered 2. The first line of each test case gives the number of intersections N, 1 < N ≤ 1000, and the number of paths M. The following M lines each contain a pair of intersections a b and an integer distance 1 ≤ d ≤ 1000000 indicating a path of length d between intersection a and a different intersection b. Jimmy may walk a path any direction he chooses. There is at most one path between any pair of intersections.

Output

For each test case, output a single integer indicating the number of different routes through the forest. You may assume that this number does not exceed 2147483647

Sample Input

5 6
1 3 2
1 4 2
3 4 3
1 5 12
4 2 34
5 2 24
7 8
1 3 1
1 4 1
3 7 1
7 4 1
7 5 1
6 7 1
5 2 1
6 2 1
0

Sample Output

2
4

Source

University of Waterloo Local Contest 2005.09.24

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题目意思：

这道题不是求最短路的条数！！！

注意了

题目是说如果A到终点的距离大于B到终点的距离，那么我们认为A到B是满足条件的路径

问你满足条件的路的条数

分析：

先用终点做起点然后求单源最短路，得到每个点到终点的距离

然后通过记忆化搜索，搜满足条件的路径数目！！！

主要是题目意思难懂，很容易误解成为求1到2的最短路条数

code：

#include<iostream>
#include<stdio.h>
#include<memory.h>
using namespace std;
#define max_v 1005
#define INF 9999999
int n,m;
int vis[max_v];
int dis[max_v];
int e[max_v][max_v];
int dp[max_v];
void init()
{
    memset(vis,0,sizeof(vis));
    for(int i=0;i<=n;i++)
    {
        for(int j=0;j<=n;j++)
        {
            e[i][j]=INF;
        }
        dp[i]=-1;
        dis[i]=INF;
    }
}
void Dijkstra(int s)
{
    for(int i=1;i<=n;i++)
        dis[i]=e[s][i];
    dis[s]=0;
    for(int i=1;i<=n;i++)
    {
        int index,mindis=INF;
        for(int j=1;j<=n;j++)
        {
            if(!vis[j]&&dis[j]<mindis)
            {
                mindis=dis[j];
                index=j;
            }
        }
        vis[index]=1;
        for(int j=1;j<=n;j++)
            if(dis[index]+e[index][j]<dis[j])
                dis[j]=dis[index]+e[index][j];
    }
}
int dfs(int v)
{
    if(dp[v]!=-1)
        return dp[v];
    if(v==2)
        return 1;
    int sum=0;
    for(int i=1;i<=n;i++)
        if(dis[v]>dis[i]&&e[v][i]!=INF)
             sum+=dfs(i);
    dp[v]=sum;
    return dp[v];
}
int main()
{
    while(~scanf("%d",&n))
    {
        if(!n)
            break;
        scanf("%d",&m);
        init();
        for(int i=0;i<m;i++)
        {
            int x,y,z;
            scanf("%d %d %d",&x,&y,&z);
            if(e[x][y]>z)
                e[x][y]=e[y][x]=z;
        }
        Dijkstra(2);
        printf("%d\n",dfs(1));
    }
    return 0;
}

原文地址：https://www.cnblogs.com/yinbiao/p/9451042.html