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
采用1维DP来做，以n为分类标准，建造数组，作为存储空间。
注意，对于任意的输入m，m == for all inv in m, number of trees for m += matrix[inv -1] * matrix[m - inv];  [1 , m )

public class Solution {
    public int numTrees(int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        //[....)
        if(n < 1) return 0;
        else{
            int[] matrix = new int[n + 1];
            matrix[0] = 1;
            matrix[1] = 1;
            for(int inv = 2; inv < n + 1; inv ++){
                    int sum = 0;
                    for(int m = 1; m < inv + 1; m ++){
                        sum += matrix[m -1] * matrix[inv - m];
                    }
                    matrix[inv] = sum;
            }
            return matrix[n];
        }
    }
}

 第二遍： 

public class Solution {
    public int numTrees(int n) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(n <= 0) return 0;
        int[] map = new int[n + 1];
        map[0] = 1;
        map[1] = 1;
        for(int i = 2; i <= n; i ++)
            for(int j = 1; j <= i; j ++)//root integer
                map[i] += map[j - 1] * map[i - j];
        return map[n];
    }
}