codeforces9D How many trees?

传送门：http://codeforces.com/problemset/problem/9/D

【题解】

树形dp，f(i,j)表示i个节点，高度为j的方案数，枚举左子树大小和哪一个子树高度为j-1即可。

不加任何优化时间复杂度$O(n^4)$

 # include <bits/stdc++.h>
 using namespace std;

 typedef long long ll;
 const int M = ;

 int n, h;
 ll f[M][M];

 int main() {
     cin >> n >> h;
     f[][] = ;
     for (int i=; i<=n; ++i)
         for (int j=; j<=i; ++j) {
             for (int k=; k<=i-; ++k)
                 for (int l=; l<=j-; ++l)
                     f[i][j] += f[k][j-]*f[i-k-][l];
             for (int k=; k<=i-; ++k)
                 for (int l=; l<=j-; ++l)
                     f[i][j] += f[k][j-]*f[i-k-][l];
         }
     ll ans = ;
     for (int i=h; i<=n; ++i) ans += f[n][i];
     cout << ans;
     return ;
 }