96. Unique Binary Search Trees

目录

• 题目描述
• 方法1
• 方法2

题目描述

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

方法1

递归方法，这个解法Leecode会超时

class Solution {
public:
    int numTrees(int n) {

    	if(n == 0)
    		return 1;
    	int cnt = 0;
        //遍历根节点元素所有可能的情况
    	for(int i = 1;i <= n;i++)
    	{
    		cnt+=numTrees(i-1)*numTrees(n-i);
   
    	}
    	return cnt;        
    }
};

方法2

将上面的递归方法翻译成动态规划

class Solution {
public:
    int numTrees(int n) {

        if(n == 0)
            return 1;
        vector<int> dp(n+1,0);
        dp[0] = 1;
        //从小到大进行动态规划
        for(int i = 1;i <= n;i++)
        {   //遍历根节点元素所有可能的情况
            for(int j = 1;j <= i;j++)
            {
                dp[i]+=dp[j-1]*dp[i-j];
       
            }
        }
        return dp[n];        
    }
};