LeetCode: Unique Binary Search Trees

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

---

We can observe that the problem can be divided into subproblems. Assume current root node is i, then all elements on the left side of i will be in the left subtree of root, and all elements of the right side of i will be in the right subtree of root. And the number of trees for root i will be number of left trees times number of right trees.

C++ Code:

/*
 * func: unique_BST
 * goal: find the total number of BSTs by given n nodes
 * @param n: the number of nodes
 * return: total number
 */
int unique_BST(int n){
    if(n <= 1){
        return 1;
    }
    int total = 0;
    for(int i=1; i<=n; ++i){
        total += unique_BST(i-1) * unique_BST(n-i);
    }
    return total;
}

Python Code:

# func: find the total number of BSTs
# @param n: input total number of nodes
# @return: total number of trees
def unique_BST(n):
    if n <= 1:
        return 1
    else:
        result = []
        result.append(1)
        result.append(1)
        for i in xrange(2, n+1):
            curr_result = 0
            for root in xrange(i):
                curr_result += result[root] * result[i-root-1]

            result.append(curr_result)
        return result[-1]