2013多校联合3 G The Unsolvable Problem（hdu 4627）

2013-07-30 20:35 388人阅读 评论(0) 收藏 举报

http://acm.hdu.edu.cn/showproblem.php?pid=4627

The Unsolvable Problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 230    Accepted Submission(s): 136

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.

标准签到题，先特判n==2的情况，否则若n为奇数，则答案显然是n/2 和 n/2+1，若n为偶数设n=2*k，若k为偶数，则答案为k-1,k+1,否则答案为k-2,k+2。

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <algorithm>
#define ll long long
using namespace std;
int main()
{
    //freopen("dd.txt","r",stdin);
    ll n,ncase;
    cin>>ncase;
    while(ncase--)
    {
        cin>>n;
        if(n==2)
        cout<<1<<endl;
        else
        {
            if(n%2)
            cout<<(n/2)*(n-n/2)<<endl;
            else
            {
                if((n/2)%2==0)
                cout<<(n/2-1)*(n/2+1)<<endl;
                else
                cout<<(n/2-2)*(n/2+2)<<endl;
            }
        }
    }
    return 0;
}
一开始用暴力，唉，挂了，但是为什么是这样呢，想了半天终于明白了。