2023-03-16

A Walk Through the Forest

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7995    Accepted Submission(s): 2943

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
Question:
From the starting point 1 to the end 2, find the number of such a path: if the distance from point A to 2 is greater than from point B to 2, and A can go from A to B. Ask a few ways like this.
code:
``` 1 //is not the shortest number of circuits. First Dijk get out of the shortest circuit of 2 to each point, search for the number of paths in memory
2 #include<iostream>
3 #include<cstdio>
4 #include<cstring>
5 #include<cmath>
6 using namespace std;
7 const int MAX=10000007;
8 int mp[1005][1005],dis[1005],vis[1005],path[1005];
9 int n,m;
10 void dijk()
11 {
12     for(int i=1;i<=n;i++)
13     {
14         dis[i]=mp[2][i];
15         vis[i]=0;
16     }
17     vis[2]=1;
18     for(int i=1;i<=n;i++)
19     {
20         int Min=MAX,sta=0; //STA is initialized to prevent J in the following, and the VIS [STA] array appears to cross the world.
21         for(int j=1;j<=n;j++)
22         {
23             if(!vis[j]&&dis[j]<Min)
24             {
25                 Min=dis[j];
26                 sta=j;
27             }
28         }
29         vis[sta]=1;
30         for(int j=1;j<=n;j++)
31         {
32             if(!vis[j]&&mp[sta][j]!=MAX&&dis[j]>dis[sta]+mp[sta][j])
33             dis[j]=dis[sta]+mp[sta][j];
34         }
35     }
36 }
37 int dfs(int x)
38 {
39     if(path[x]!=-1)  //memory
40     return path[x];
41     if(x==2)
42     return 1;
43     path[x]=0;
44     for(int i=1;i<=n;i++)
45     {
46         if(mp[x][i]!=MAX&&dis[x]>dis[i])
47         path[x]+=dfs(i);
48     }
49     return path[x];
50 }
51 int main()
52 {
53     int a,b,c;
54     while(scanf("%d",&n)&&n)
55     {
56         scanf("%d",&m);
57         for(int i=1;i<=n;i++)
58         for(int j=1;j<=n;j++)
59         mp[i][j]=i==j?0:MAX;
60         for(int i=0;i<m;i++)
61         {
62             scanf("%d%d%d",&a,&b,&c);
63             mp[a][b]=mp[b][a]=min(mp[a][b],c);
64         }
65         dijk();
66         memset(path,-1,sizeof(path));
67         int ans=dfs(1);
68         printf("%d\n",ans);
69     }
70     return 0;
71 }```
code:

Reprinted: https://www.cnblogs.com/- zhiyuan/p/6057362.html

source