51Nod－1412－AVL树的种类(树形dp)

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状态转移方程

1、dp[i][k] += dp[i - 1 - j][k - 1] * dp[j][k - 1]
2、dp[i][k] += 2 * dp[i - 1 - j][k - 2] * dp[j][k - 1]

#include<bits\stdc++.h>using namespace std;typedef long long ll;#define pb push_back#define MOD 1000000007const int MAXN = 2001;const int tier = 11;typedef long long ll;ll dp[MAXN][tier];void init(){    dp[0][0] = 1;    dp[1][1] = 1;    for (int i = 2; i < MAXN; i++)    {        for (int k = 2; k < tier; k++)        {            for (int j = 0; j < i; j++)            {                dp[i][k] += dp[i - j - 1][k - 1] * dp[j][k - 1];                dp[i][k] %= MOD;                dp[i][k] += 2 * dp[i - j - 1][k - 2] * dp[j][k - 1];                dp[i][k] %= MOD;            }        }    }}int main(){    int n;    init();    while (scanf("%d", &n) == 1)    {        ll ans = 0;        for (int i = 1; i < tier; i++)        {            ans += dp[n][i];            ans %= MOD;        }        printf("%I64d\n", ans);    }    return 0;}

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