text: /*
  Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?
  
  Example:
  
  Input: 3
  Output: 5
  Explanation:
  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
  */
  class Solution {
  public:
      int numTrees(int n) {
          if (n < 1) return 0;
          vector<int> dp(n + 1, 0);
          dp[0] = dp[1] = 1;
          for (int i = 2; i <= n; ++i) {
              for (int j = 1; j <= i; ++j) {
                  dp[i] += dp[j - 1] * dp[i - j];
              }
          }
          return dp[n];
      }
  
      void test() {
          assert(numTrees(3) == 5);
      }
  };