The order and ideas for answering questions come from Code Caprice, website address: https://programmercarl.com
343. Integer split - LeetCode
Given a positive integer n
, split it into k
the sum of positive integersk >= 2
( ) and maximize the product of these integers.
Returns the largest product you can get .
输入: n = 2
输出: 1
解释: 2 = 1 + 1, 1 × 1 = 1。
import java.util.Scanner;
/**
* @author light
* @Description 整数拆分
* @create 2023-09-14 18:19
*/
public class IntegerBreakTest {
public static void main(String[] args) {
Scanner input=new Scanner(System.in);
int n=input.nextInt();
System.out.println(integerBreak(n));
}
public static int integerBreak(int n) {
//dp[i] 为正整数 i 拆分后的结果的最大乘积
int[] dp = new int[n+1];
dp[2] = 1;
for(int i = 3; i <= n; i++) {
for(int j = 1; j <= i-j; j++) {
// 这里的 j 其实最大值为 i-j,再大只不过是重复而已,
//并且,在本题中,我们分析 dp[0], dp[1]都是无意义的,
//j 最大到 i-j,就不会用到 dp[0]与dp[1]
dp[i] = Math.max(dp[i], Math.max(j*(i-j), j*dp[i-j]));
// j * (i - j) 是单纯的把整数 i 拆分为两个数 也就是 i,i-j ,再相乘
//而j * dp[i - j]是将 i 拆分成两个以及两个以上的个数,再相乘。
}
}
return dp[n];
}
}
96. Different binary search trees - LeetCode
Given an integer , how many binary search treesn
are there that consist of exactly n
n nodes and whose node values are different from 1
to ? Returns the number of binary search trees that satisfy the question.n
/**
* @author light
* @Description 不同的二叉搜索树
*
* @create 2023-09-14 18:49
*/
public class NumTreesTest {
public int numTrees(int n) {
//1 确认dp数组及其含义:dp[i]:输入【i】,共有dp[i]种不同的二叉搜索树
//也可以理解是i个不同元素节点组成的二叉搜索树的个数为dp[i] ,都是一样的。
//dp[i] += dp[以j为头结点左子树节点数量] * dp[以j为头结点右子树节点数量]
//j相当于是头结点的元素,从1遍历到i为止。
int[] dp=new int[n+1];
dp[0]=1;
for (int i = 1; i <=n; i++) {
for (int j = 1; j <=i; j++) {
dp[i]+=dp[j-1]*dp[i-j];
}
}
return dp[n];
}
}