96. Unique Binary Search Trees [LeetCode]

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

class Solution_96_1 {
public:
	int numTrees(int n) {
		vector f(n + 1, 0);
		f[0] = 1;
		f[1] = 1;
		for (int i = 2; i <= n; ++i) {
			for (int k = 1; k <= i; ++k)
				f[i] += f[k - 1] * f[i - k];
		}
		return f[n];
	}
};