LeetCode Brush Questions Actual Combat 96: Different Binary Search Trees

I won’t say more about the importance of algorithms. If you want to go to a big factory, you have to go through basic knowledge and business logic interview + algorithm interview. Therefore, in order to improve everyone's algorithmic ability, this official account will take you to do an algorithm question every day, and the question will be selected from LeetCode!

The problem I’m talking about today is called different binary search trees . Let’s look at the problem first:

https://leetcode-cn.com/problems/unique-binary-search-trees/

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

Title

Given an integer n, how many types of binary search trees with 1...n as nodes?

Sample

Problem solving

Recursive subproblems

Assuming that the number of binary sorted trees in n nodes is G (n), let f(i) be the number of binary search trees rooted at i, then

G(n)=f(1)+f(2)+f(3)+f(4)+...+f(n),

f(i)=G(i−1)∗G(n−i)

class Solution {
    public int numTrees(int n) {
        if (n == 0 || n == 1) return 1;
        int res = 0;
        for (int i = 1; i <= n; i++) {
            res += numTrees(i - 1) * numTrees(n - i);
        }
        return res;
    }
}

Dynamic programming

From dp[0], dp[1] gradually expand backward

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

Okay, that's all for today's article. If you feel that you have gained something, please read it or forward it. Your support is my biggest motivation.

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