hdu6298[多校第一场A]

链接:hdu6298[多校第一场A]

题解

• 显然$n=\frac{n}{a}+\frac{n}{b}+\frac{n}{c},a|n,b|n,c|n$
• 约分之后是$1=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
• $$1=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{1}{2}+\frac{1}{4}+\frac{1}{4}$$
• 显然要使得$\frac{n^3}{abc}$最大只有右面两种情况可能，即n%3==0||n%4==0成立才有解，且前者优先

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#define rep(i,x,y) for(register int i=x;i<=y;++i)
#define repd(i,x,y) for(register int i=x;i>=y;--i)
#define ll long long
using namespace std;
int n,T;
int main(){
	scanf("%d",&T);
	while(T--&&~scanf("%d",&n)){
		if(n%3==0){
			n/=3;
			printf("%lld\n",1ll*n*n*n);
		}
		else if(n%4==0){
			printf("%lld\n",1ll*n*n*n/32);
		}
		else puts("-1");
	}
	return 0;
}