Joey LIU | NANTSOU


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/**
 * key point 1: all left nodes are less than root and all right nodes are greater root.
 * key point 2: number of current node is the product of number of all left and number of all right.
 */
class Solution {
    public int numTrees(int n) {
        if (n <= 1) return 1;
        int[] dp = new int[n+1];
        dp[0] = 1;
        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];
    }
}