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 = 50;

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

int main() {
    cin >> n >> h;
    f[0][0] = 1;
    for (int i=1; i<=n; ++i)
        for (int j=1; j<=i; ++j) {
            for (int k=0; k<=i-1; ++k)
                for (int l=0; l<=j-1; ++l)
                    f[i][j] += f[k][j-1]*f[i-k-1][l];
            for (int k=0; k<=i-1; ++k)
                for (int l=0; l<=j-2; ++l)
                    f[i][j] += f[k][j-1]*f[i-k-1][l];
        }
    ll ans = 0;
    for (int i=h; i<=n; ++i) ans += f[n][i];
    cout << ans;
    return 0;
}