HDU 6298 Maximum Multiple （数学推理）

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Maximum Multiple

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 5670 Accepted Submission(s): 2096

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

题目大意：

给一个数 n 已知 n = x + y + z

且 x，y，z都能被 n 整除

求 x * y * z 的最大值

思路：讨论 n 的因子情况再判断

实际上只要考虑能被3整除和能被4整除

n 的最大因子 k 大于4时如果 k 不能被3或4整除不存在 k = x+y+z 且 k 是 x，y，z 的倍数

（是我自己总结的话如果有错的话望大佬们指出）

AC代码：

#include<stdio.h>
#include <bits/stdc++.h>
using namespace std;

int main()
{
    int t;
    long long a, b;
    scanf("%d", &t);
    while (t--) {
        scanf("%lld", &a);
        long long ans = -1;
        if (a % 3 == 0) {
            b = a / 3;
            ans = b * b * b;
        } else if (a % 4 == 0) {
            b = a / 4;
            ans = max(ans, b * b * b * 2);
        }
        printf("%lld\n", ans);
    }
    return 0;
}