[LeetCode] Unique Binary Search Trees

问题：

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

分析：

一道比较简单的题，可以通过recursion解决。对于一个range[1, n]，我们让每一个元素i当一次root，然后recursively计算range[1, i-1]和range[i+1, end]，两个结果相乘即可。即left subtree的种数乘以right subtree的种树。只需要小心一点边界情况即可。

代码：（O(n logn)）

class Solution{public:int numTreesHelper(int start, int end) {if (start >= end) return 1;int result = 0;for (int i = start; i <= end; i ++) {result += (numTreesHelper(start, i - 1) * numTreesHelper(i + 1, end));}return result;}int numTrees(int n) {return numTreesHelper(1, n);}};