Unique Binary Search Trees [LEETCODE]

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

 

 

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Since its a binary tree, so a recursive solution is reasonable.

For a root i, its unique BST number is equal to its left child's unique BST number multiple  its right child's unique BST number.

 

class Solution {
public:
    int numTrees(int n) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        return numTrees(1,n);
    }
    int numTrees(int start, int end){
        //pick a root
        if(start >= end){
            return 1;
        }
        int total = 0;
        for(int i = start; i <= end; i++){
            total += numTrees(start, i-1) * numTrees(i+1, end);
        }
        return total;
        
    }
};