/*
 * @lc app=leetcode id=96 lang=java
 *
 * [96] Unique Binary Search Trees
 */

// @lc code=start
class Solution {
    /**
     * dp[n] = dp[n-1] + dp[1]+dp[n-2]
     * 
     * @param n
     * @return
     */
    public int numTrees(int n) {
        int[] dp = new int[n+1];
        for(int i=1; i<=n; i++) {
            dp[i] = 0;
        }
        dp[1] = 1;
        for(int i=2; i<=n; i++) {
            for(int j=0; j<=i-1;j++) {
                int left = j>0?dp[j]:1;
                int right = i-1-j>0?dp[i-1-j]:1;
                dp[i] += left*right;
            }
        }
        return dp[n];
    }
}
// @lc code=end