[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 == 0)
            return 0;
        
        int *num;
        num = new int[n + 1];
        num[0] = 1;
        num[1] = 1;
        for(int i = 2;i <= n;i++)
        {
            num[i] = 0;
            for(int j = 0;j < i;j++)
                num[i] += num[j] * num[i - 1 - j];
        }
        
        return num[n];
    }
};