96. Unique Binary Search Trees(dp)

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

 

Constraints:

• 1 <= n <= 19

 

class Solution {
public:
    int numTrees(int n) {
        vector<int> dp(n+1,0);
        int res;
        if(n == 1) return 1;
        if(n == 2 )return 2;
        dp[0] = 1;
        dp[1] = 1;
        dp[2] = 2;
        for(int i=3;i<=n;i++){
            for(int j=1;j<=i;j++)
            {
                dp[i] += dp[j-1]*dp[i-j];
            }            
        }
        return dp[n];
    }
};