hdu 6298

Posted 2020-12-25 tingtin

Maximum Multiple

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1500    Accepted Submission(s): 650

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

 

 

Source

2018 Multi-University Training Contest 1

 

 

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 /*
  经过数学变形知：
  x=n/k1,y=n/k2,z=n/k3
  1/k1+1/k2+1/k3=1
 3 3 3
 2 4 4
 2 3 6
只有这三组解，可令k1<=k2<=k3来推、
最后的结果即x*y*z=n*n*n/(k1*k2*k3)

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 #include <cstring>
 5 #include <vector>
 6 #include <utility>
 7 #include <queue>
 8 using namespace std;
 9 typedef long long ll;
10 int t;
11 int main()
12 {    scanf("%d",&t);
13      ll n;
14     while(t--){
15     scanf("%lld",&n);
16     if(n%3==0){
17         printf("%lld
",n*n*n/27);
18         continue;
19     }
20     if(n%4==0){
21         printf("%lld
",n*n*n/32);
22     }
23     else{
24         printf("-1
");//n%6=0，那么n%3也一定=0
25     }
26              }
27 return 0;
28 }