51nod 1412 AVL树的种类(dp)

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #include<queue>
 5 using namespace std;
 6 typedef long long ll;
 7 const int mod = 1e9+7;
 8 const int N = 2001;
 9 ll dp[N][16];//dp[i][k]  i:节点数, k:深度
10 void solve(){
11     int i, j, k;
12     dp[0][0] = dp[1][1] = 1;
13     for(i = 2; i < N; ++i){
14         for(k = 2; k < 16; ++k){
15             for(j = 0; j < i; ++j){
16                 //j为右子树的节点数,左右子树节点之和为i-1
17                 //左右子树深度相同
18                 dp[i][k] += dp[i-1-j][k-1] * dp[j][k-1];
19                 //左右子树深度差一
20                 dp[i][k] += 2 * dp[i-1-j][k-2] * dp[j][k-1];
21                 dp[i][k] %= mod;
22             }
23         }
24     }
25 }
26 int main(){
27     int n, i;
28     ll ans = 0;
29     solve();
30     scanf("%d", &n);
31     for(i = 1; i < 16; ++i){
32         ans += dp[n][i];
33     }
34     ans %= mod;
35     printf("%lld\n", ans);
36     return 0;
37 }