Day 44, #96 Unique Binary Search Trees

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 

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Catalan Number 

COME_BACK

class Solution {
public:
    int numTrees(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int ret = 1;
        for (int i = 2; i <= n; i++) {
            ret = 2*(2*i-1)*ret/(i+1);
        }
        return ret;
    }
};

DP

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