HDU 4027 The Unsolvable Problem

The Unsolvable Problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 486    Accepted Submission(s): 280

Problem Description

There are many unsolvable problem in the world.It could be about one or about zero.But this time it is about bigger number. Given an integer n(2 <= n <= 10⁹).We should find a pair of positive integer a, b so that a + b = n and [a, b] is as large as possible. [a, b] denote the least common multiplier of a, b.

 

Input

The first line contains integer T(1<= T<= 10000),denote the number of the test cases. For each test cases,the first line contains an integer n.

 

Output

For each test cases,print the maximum [a,b] in a line.

 

Sample Input

3

2

3

4

 

Sample Output

1

2

3

 

 多校第三场1008

先特判n=2的情况。

然后如果n=2k+1，那么答案就是k*(k+1)

如果n=2k，那么进一步讨论。

　　如果k为奇数，那么答案是(k-2)*(k+2)

　　如果k为偶数，那么答案是(k-1)*(k+1)

#include<iostream>

using namespace std;

int main()
{
    int t;

    cin>>t;

    while(t--)
    {
        long long x;

        cin>>x;

        if(x==2)
            cout<<1<<endl;
        else if(x%2==1)
            cout<<(x/2)*(x/2+1)<<endl;
        else if((x/2)%2==1)
            cout<<(x/2-2)*(x/2+2)<<endl;
        else
            cout<<(x/2-1)*(x/2+1)<<endl;
    }

    return 0;
}