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

Summary: dynamic programming

    int numTrees(int n) {
        vector<int> nums;
        nums.push_back(0);
        for(int i = 1; i <= n; i ++) {
            if(i == 1){
                nums.push_back(1);
            }else if(i == 2){
                int num = i * nums[i - 1];
                nums.push_back(num);
            }else if(i >= 3){
                int num = 0;
                for(int j = 1; j <= i; j ++)
                    num += (nums[j - 1] == 0 ? 1 : nums[j - 1]) * (nums[i - j] == 0 ? 1 : nums[i - j]);
                nums.push_back(num);
            }
        }
        return nums[n];
    }