HDU6298-2018ACM暑假多校联合训练1001-Maximum Multiple

Posted 2020-12-25 qq965921539

题意大致是给你一个整数n，让你确定是否有三个正整数x,y,z既能被n整除，又能x+y+z=n,并使xyz最大

从中根据规律可以看出，只有被3或被4整除的数才能满足题目要求

被3整除的最大值为n^3/3^3

被4整除的最大值为n^3/(2*4*4)

Problem Description

Given an integer n, Chiaki would like to find three positive integers x, y and z such that: n=x+y+z, x∣n, y∣n, z∣n and xyz is maximum.

 

 

Input

There are multiple test cases. The first line of input contains an integer T (1≤T≤106), indicating the number of test cases. For each test case:
The first line contains an integer n (1≤n≤106).

 

 

Output

For each test case, output an integer denoting the maximum xyz. If there no such integers, output ?1 instead.

 

 

Sample Input

3 1 2 3

 

 

Sample Output

-1 -1 1

 

 1 #include <iostream>
 2 
 3 using namespace std;
 4 
 5 int main()
 6 {
 7     ios::sync_with_stdio(false);
 8     int t;
 9     cin >> t;
10     while (t--)
11     {
12         long long n;
13         cin >> n;
14         if (n % 3 == 0)
15             cout << (n / 3)*(n / 3)*(n / 3) << endl;
16         else if (n % 4 == 0)
17             cout << (n / 2)*(n / 4)*(n / 4) << endl;
18         else
19             cout << "-1" << endl;
20     }
21     return 0;
22 }