Unique_Binary_Search_Tree.cpp

/*
Problem:
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
*/

class Solution {
public:
    int numTrees(int n) 
    {
        vector<int> result(n+1,0);
        result[0] = 1;
        result[1] = 1;
        for (int i = 2; i <= n; i++)
        {
            for (int j = 0; j < i; j++)
            {
                result[i] += result[j]*result[i-j-1]; 
            }
        }
        return result[n];
    }
};