树形DP入门题 cf 161D

题意:给你一棵树，让你求树上有多少点之间的距离是为k

思路

距离为k的个数为cnt

dp[i][j]:距离i点距离为j的点的个数

son 为i儿子

cnt += dp[i][j] * dp[son][k-j-1]

dp[i][j] += dp[son][j-1]

初始化dp[i][0]=1;

/********************************************
Author         :Crystal
Created Time   :
File Name      :
********************************************/
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <climits>
#include <string>
#include <vector>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <sstream>
#include <cctype>
using namespace std;
typedef long long ll;
typedef pair<int ,int> pii;
#define MEM(a,b) memset(a,b,sizeof a)
#define CLR(a) memset(a,0,sizeof a);
const int inf = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
//#define LOCAL
int n,k;
int cnt = 0;
int dp[50005][505];
std::vector<int> vertic[50005];
void dfs(int u,int pre){
	dp[u][0]=1;
	for(int i=0;i<vertic[u].size();i++){
		int v = vertic[u][i];
		if(v!=pre){
			dfs(v,u);
			for(int j=0;j<k;j++){
				cnt += dp[u][j]*dp[v][k-j-1];
			}
			for(int j=0;j<k;j++){
				dp[u][j+1]+=dp[v][j];
			}
		}
	}
}
int main()
{
#ifdef LOCAL
	freopen("in.txt", "r", stdin);
//	freopen("out.txt","w",stdout);
#endif
	cin >> n >> k;
	for(int i=1;i<=n-1;i++){
		int u,v;cin >> u >> v;
		vertic[u].push_back(v);
		vertic[v].push_back(u);
	}
	dfs(1,0);
	cout << cnt << endl;
	return 0;
}