[LeetCode] Unique Binary Search Tree

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

解题思路：

设有n个结点的二叉查找树有b[n]个，则设想对一个排好序的list，我们从第一个元素开始枚举根节点。对于每一个根节点，这棵二叉查找树的可能是b[left] * b[right], left < n, right < n。

故我们只需要取b[0] = 0, b[1] = 1, 然后迭代计算b[i]即可。

class Solution {
public:
    int numTrees(int n) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(n == )
            return ;

        int *num;
        num = new int[n + ];
        num[] = ;
        num[] = ;
        for(int i = ;i <= n;i++)
        {
            num[i] = ;
            for(int j = ;j < i;j++)
                num[i] += num[j] * num[i -  - j];
        }

        return num[n];
    }
};