96 Unique Binary Search Trees

链接：https://leetcode.com/problems/unique-binary-search-trees/
问题描述：
Given n, how many structurally unique BST’s (binary search trees) that store values 1…n?

For example,
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

Hide Tags Tree Dynamic Programming

给出一个数字n，求1—n，n个数字生成称多少种二叉搜索树。n个数组生成二叉树的数量可以慢慢分解为n-1，n-2，n-3……1能生成多少二叉树。

class Solution {
public:
    int numTrees(int n) {
        if(n<3)return n;
        int *arr=new int[n+1];
        memset(arr,0,sizeof(int)*(n+1));
        arr[0]=1;
        arr[1]=1;
        arr[2]=2;
        for(int i=2;i<=n;i++)
        {
            for(int j=0;j<i;j++)
            arr[i]+=arr[j]*arr[i-j-1];
        }
        int result=arr[n];
        delete arr;
        return result;
    }
};