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$O(n^4)$

 1 # include 
 2 using namespace std;
 3 
 4 typedef long long ll;
 5 const int M = 50;
 6 
 7 int n, h;
 8 ll f[M][M];
 9 
10 int main() {
11     cin >> n >> h;
12     f[0][0] = 1;
13     for (int i=1; i<=n; ++i)
14         for (int j=1; j<=i; ++j) {
15             for (int k=0; k<=i-1; ++k)
16                 for (int l=0; l<=j-1; ++l)
17                     f[i][j] += f[k][j-1]*f[i-k-1][l];
18             for (int k=0; k<=i-1; ++k)
19                 for (int l=0; l<=j-2; ++l)
20                     f[i][j] += f[k][j-1]*f[i-k-1][l];
21         }
22     ll ans = 0;
23     for (int i=h; i<=n; ++i) ans += f[n][i];
24     cout << ans;
25     return 0;
26 }

View Code

转载于:https://www.cnblogs.com/galaxies/p/codeforces9d.html