[Leetcode] 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

Solution:

递归，由于是二叉查找树，先选择任一结点根结点，假设为结点i，则[1，i-1]范围的结点为结点i的左子树结点，[i+1，n]范围的结点为结点i的右子树结点，则以结点i为根结点的BST个数为左，右子树可构成BST个数的乘积，基于这个思路，可以写出以下递归程序。

public class Solution {
    public int numTrees(int n) {
        if (n < 3)
            return n;
        return numTrees(1, n);
    }
    private int numTrees(int start, int end) {
        // TODO Auto-generated method stub

        if (start >= end)
            return 1;
        int result = 0;
        for (int i = start; i <= end; ++i) {
            result += numTrees(start, i - 1) * numTrees(i + 1, end);
        }
        return result;
    }
}

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20150216

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

http://blog.csdn.net/linhuanmars/article/details/24761459