A Walk Through the Forest
Time Limit: 2000/1000 MS
(Java/Others) Memory Limit: 65536/32768 K
(Java/Others)
Total Submission(s): 5306 Accepted
Submission(s): 1939
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
Recommend
Eddy | We have
carefully selected several similar problems for you: 2722 2962 2923 1116 2433
开始题意理解错了，以为求最短路径的数目。其实求的是在点1到点2的路径中，经过的路段Vij要求d[i]>d[j](d[i]为点i到到点2的最短路)，求满足要求的路径数。
最短路径：
先求出点2到其他店的最短路，然后记忆化搜索得解。
1 //31MS 820K 1533B G++
2 #include<iostream>
3 #include<vector>
4 #include<queue>
5 #define N 1005
6 #define inf 0x7fffffff
7 using namespace std;
8 struct node{
9 int v,d;
10 node(int a,int b){
11 v=a;d=b;
12 }
13 };
14 vector<node>V[N];
15 int vis[N],d[N];
16 int v;
17 int n,m;
18 int ans[N];
19 void dij(int s)
20 {
21 memset(vis,0,sizeof(vis));
22 for(int i=0;i<=n;i++)
23 d[i]=inf;
24 d[s]=0;
25 queue<int>Q;
26 Q.push(s);
27 vis[s]=1;
28 while(!Q.empty()){
29 int u=Q.front();
30 Q.pop();
31 vis[u]=0;
32 int m=V[u].size();
33 for(int i=0;i<m;i++){
34 int v=V[u][i].v;
35 int w=V[u][i].d;
36 if(d[v]>d[u]+w){
37 d[v]=d[u]+w;
38 if(!vis[v]){
39 vis[v]=1;
40 Q.push(v);
41 }
42 }
43 }
44 }
45 }
46 int dfs(int u)
47 {
48 if(u==2) return 1;
49 if(ans[u]!=0) return ans[u];
50 int m=V[u].size();
51 int cnt=0;
52 for(int i=0;i<m;i++){
53 int v=V[u][i].v;
54 int w=V[u][i].d;
55 if(d[v]<d[u])
56 cnt+=dfs(v);
57 }
58 return ans[u]=cnt;
59 }
60 int main(void)
61 {
62 int a,b,c;
63 while(scanf("%d",&n),n)
64 {
65 scanf("%d",&m);
66 memset(ans,0,sizeof(ans));
67 for(int i=0;i<=n;i++) V[i].clear();
68 for(int i=0;i<m;i++){
69 scanf("%d%d%d",&a,&b,&c);
70 V[a].push_back(node(b,c));
71 V[b].push_back(node(a,c));
72 }
73 dij(2);
74 printf("%d\n",dfs(1));
75 }
76 return 0;
77 }