#Leetcode# 96. Unique Binary Search Trees

https://leetcode.com/problems/unique-binary-search-trees/

 

Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?

Example:

Input: 3
Output: 5
Explanation:
Given n = 3, there are a total of 5 unique BST's:

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

代码：

class Solution {
public:
    int numTrees(int n) {
        vector<int> dp(n + 1, 0);
        dp[0] = 1;
        dp[1] = 1;
        for(int i = 2; i <= n; i ++) {
            for(int j = 0; j < i; j ++) 
                dp[i] += dp[j] * dp[i - j - 1];
        }
        return dp[n];
    }
};

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

long long mod = 1e9 + 7;

int main() {
    int n;
    long long sum;
    long long dp[3005];
    dp[0] = 1; dp[1] = 1; dp[2] = 2; dp[3] = 5;
    for(int i = 4; i <= 3000; i ++) {
        int tem = i;
        int cnt = tem / 2;
        sum = 0;
        for(int j = 0; j < cnt; j ++)
            sum += (dp[j] * dp[tem - 1 - j] * 2) % mod;
        if(tem % 2 == 1)
            sum += (dp[cnt] * dp[cnt]) % mod;
        dp[i] += sum % mod;
    }
    while(~scanf("%d", &n))
        printf("%lld\n", dp[n]);
    return 0;
}

 

　　

卡特兰数 人生中第二次遇见 好吧我还是认不出