Maximum Multiple

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3241 Accepted Submission(s): 1344

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：n = x+ y + z, 需要满足 x|n, y|n, z|n (整除关系)，输出xyz的最大值，若不存在，输出-1

设 n/x = r n/y = s n/z = t ， r <= s <= t

所以1/r + 1/s + 1/t = 1

所以r <= 3

当r=3 s,t = (3,3)

当r=2 s,t = (4, 4) , (3, 6)

所以三种情况

n/3 n/3 n/3

n/2 n/4 n/4

n/2 n/3 n/6 (没有第一种大，舍去)

所以就判是否能整除3 或 4

 #include <iostream>

 #include <stdio.h>

 #include <math.h>

 #include <string.h>

 #include <stdlib.h>

 #include <string>

 #include <vector>

 #include <set>

 #include <map>

 #include <queue>

 #include <algorithm>

 #include <sstream>

 #include <stack>

 using namespace std;

 #define rep(i,a,n) for (int i=a;i<n;i++)

 #define per(i,a,n) for (int i=n-1;i>=a;i--)

 #define pb push_back

 #define mp make_pair

 #define all(x) (x).begin(),(x).end()

 #define fi first

 #define se second

 #define SZ(x) ((int)(x).size())

 #define FO freopen("in.txt", "r", stdin)

 #define lowbit(x) (x&-x)

 #define mem(a,b) memset(a, b, sizeof(a))

 typedef vector<int> VI;

 typedef long long ll;

 typedef pair<int,int> PII;

 const ll mod=;

 const int inf = 0x3f3f3f3f;

 ll powmod(ll a,ll b) {ll res=;a%=mod;for(;b;b>>=){if(b&)res=res*a%mod;a=a*a%mod;}return res;}

 ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}

 //head

 int _, n;

 int main() {

     for(scanf("%d", &_);_;_--) {

         scanf("%d", &n);

         if(n% == ) printf("%lld\n", 1ll * n * n * n / );

         else if(n% == ) printf("%lld\n", 1ll * n * n * n / );

         else puts("-1");

     }

 }

巴特西

HDU6298 Maximum Multiple （多校第一场1001）

Maximum Multiple

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