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 Taking 1n as root respectively: 1 as root:  of trees  F0  Fn1   F0  1 2 as root:  of trees  F1  Fn2 3 as root:  of trees  F2  Fn3 ... n1 as root:  of trees  Fn2  F1 n as root:    of trees  Fn1  F0 So, the formulation is: Fn  F0  Fn1  F1  Fn2  F2  Fn3  ...  Fn2  F1  Fn1  F0 :type n: int :rtype: int
"""
Taking 1~n as root respectively:
1 as root: # of trees = F(0) * F(n-1)  // F(0) == 1
2 as root: # of trees = F(1) * F(n-2)
3 as root: # of trees = F(2) * F(n-3)
...
n-1 as root: # of trees = F(n-2) * F(1)
n as root:   # of trees = F(n-1) * F(0)

So, the formulation is:
F(n) = F(0) * F(n-1) + F(1) * F(n-2) + F(2) * F(n-3) + ... + F(n-2) * F(1) + F(n-1) * F(0)
"""

def num_trees(n):
    """
    :type n: int
    :rtype: int
    """
    dp = [0] * (n+1)
    dp[0] = 1
    dp[1] = 1
    for i in range(2, n+1):
        for j in range(i+1):
            dp[i] += dp[i-j] * dp[j-1]
    return dp[-1]
