96 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

Solution

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

Notes

• Catalan number
• Note to use an array to keep record of numTrees(i < n ). Thus one doesn't have to evaluate numTrees(i) and numTrees(n-1-i) for every i.