A Walk Through the Forest

A Walk Through the Forest_spfa&&dfs

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 11 Accepted Submission(s) : 8

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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

Sample Output

2
4

假设 A 和 B 是相连的，当前在 A 处，如果 A 到终点的距离大于 B 到终点的距离，则可以从 A 通往 B 处，问满足这种的条件的路径条数。

分析：1、spfa以终点开始求到各点的最短距离；

2、直接DFS记忆化搜索。

#include<iostream>
#include<stdio.h>
#include<queue>
#include<string.h>
using namespace std;
const int N=1005;
const int inf=0x7777777;
int mp[N][N];
int n,m;
int vis[N];
int num[N],dis[N];
void init()
{
    memset(num,0,sizeof(num));
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=n;j++)
        {
            mp[i][j]=inf;
        }
        mp[i][i]=0;
    }

}
void spfa(int s)
{
    queue<int>qu;
    memset(vis,0,sizeof(vis));
    for(int i=1;i<=n;i++) dis[i]=inf;
    dis[s]=0,vis[s]=1;
    qu.push(s);
    while(!qu.empty())
    {
        int t=qu.front();
        qu.pop();
        vis[t]=0;
        for(int i=1;i<=n;i++)
        {
            if(dis[i]>dis[t]+mp[t][i])
            {
                dis[i]=dis[t]+mp[t][i];
                if(!vis[i])
                {
                    vis[i]=1;
                    qu.push(i);
                }
            }
        }
    }
}
int dfs(int s)
{
    if(num[s]) return num[s];
    if(s==2) return 1;
    int sum=num[s];
    for(int i=1;i<=n;i++)
    {
        if(mp[s][i]<inf&&dis[s]>dis[i])
        {
            if(num[i]) sum=sum+num[i];
            else sum+=dfs(i);
        }
    }
    num[s]=sum;
    return num[s];
}
int main()
{
    while(cin>>n,n)
    {
        cin>>m;
        init();
        for(int i=1;i<=m;i++)
        {
            int a,b,c;
            cin>>a>>b>>c;
            mp[a][b]=mp[b][a]=c;
        }
        spfa(2);
        cout<<dfs(1)<<endl;
    }
}