[leetcode]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

算法思路：

简单一维DP。跟这道题比起来[leetcode]Unique Binary Search Trees II，弱爆了。

代码如下：

public class Solution {
    public int numTrees(int n) {
        if(n < 0) return 0;
        int[] hash = new int[n + 3];
        hash[0] = hash[1] = 1;
        hash[2] = 2;
        for(int i = 3; i <= n; i++){
            for(int j = 1; j <= i; j++){
                hash[i] += hash[j -1] * hash[i - j];
            }
        }
        return hash[n];
    }
}