CodeForces 161D Distance in Tree

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Distance in TreeTime Limit: 3000msMemory Limit: 524288KBThis problem will be judged on CodeForces. Original ID: 161D
64-bit integer IO format: %I64d      Java class name: (Any) 

A tree is a connected graph that doesn‘t contain any cycles.

The distance between two vertices of a tree is the length (in edges) of the shortest path between these vertices.

You are given a tree with n vertices and a positive number k. Find the number of distinct pairs of the vertices which have a distance of exactly k between them. Note that pairs (v,u) and (u, v) are considered to be the same pair.

 Input

The first line contains two integers n and k (1 ≤ n ≤ 50000, 1 ≤ k ≤ 500) — the number of vertices and the required distance between the vertices.

Next n - 1 lines describe the edges as "ai bi" (without the quotes) (1 ≤ ai, bi ≤ n, ai ≠ bi), where ai and bi are the vertices connected by the i-th edge. All given edges are different.

 Output

Print a single integer — the number of distinct pairs of the tree‘s vertices which have a distance of exactly k between them.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

 Sample Input
Input

5 2
1 2
2 3
3 4
2 5

Output

4

Input

5 3
1 2
2 3
3 4
4 5

Output

2

Hint

In the first sample the pairs of vertexes at distance 2 from each other are (1, 3), (1, 5), (3, 5) and (2, 4).

 SourceVK Cup 2012 Round 1 解題：樹形dp dp[u][i]表示從子樹到u為根長度為i的路徑數目 

 1 #include <bits/stdc++.h> 2 using namespace std; 3 const int maxn = 50010; 4 vector<int>g[maxn]; 5 int dp[maxn][505],n,k,ret; 6 void dfs(int u,int fa){ 7     for(int i = 1; i <= k; ++i) dp[u][i] = 0; 8     dp[u][0] = 1; 9     for(int i = g[u].size()-1; i >= 0; --i){10         if(g[u][i] == fa) continue;11         dfs(g[u][i],u);12         for(int j = 0; j < k; ++j) ret += dp[u][j]*dp[g[u][i]][k - j - 1];13         for(int j = 1; j <= k; ++j) dp[u][j] += dp[g[u][i]][j-1];14     }15 }16 int main(){17     int u,v;18     while(~scanf("%d%d",&n,&k)){19         for(int i = ret = 0; i < maxn; ++i) g[i].clear();20         for(int i = 1; i < n; ++i){21             scanf("%d%d",&u,&v);22             g[u].push_back(v);23             g[v].push_back(u);24         }25         dfs(1,0);26         printf("%d\n",ret);27     }28     return 0;29 }

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CodeForces 161D Distance in Tree