96. Unique Binary Search Trees

题目描述

Given n, how many structurally unique BST's(binary search trees) that store values 1...n?

For example,
Givenn= 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

解题方法

        int[] dp = new int[n + 1];
        dp[0] = 1;
        dp[1] = 1;
        for(int i = 2; i <= n; i++){   //注意等號
            for(int j = 0; j < i ; j++){
                dp[i] += dp[j] * dp[i - 1 - j];
            }
        }

        return dp[n];