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