"""
QUESTION:
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
ANSWER:
DP
"""
class Solution(object):
    def numTrees(self, n):
        """
        :type n: int
        :rtype: int
        """
        dp = [1] + [0]*n
        for i in xrange(1,n+1):
            for j in xrange(i):
                dp[i] += dp[j]*dp[i-1-j]
        return dp[-1]

if __name__ == '__main__':
    print  Solution().numTrees(10)