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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.
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.
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.
5 2
1 2
2 3
3 4
2 5
4
5 3
1 2
2 3
3 4
4 5
2
In the first sample the pairs of vertexes at distance 2 from each other are (1, 3), (1, 5), (3, 5) and (2, 4).
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 }
CodeForces 161D Distance in Tree
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原文地址：http://www.cnblogs.com/crackpotisback/p/4842343.html
