标签：
The Unsolvable Problem
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
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
Sample Output
题意：求满足a+b=n，a与b没有公约数（互质），a*b尽可能地大的值
思路：
分情况讨论：
如果n是奇数
那么你通过n/=2求得它的中间数，那么a和b就应该为n与n+1
如果n是偶数
那么先求中间数n/=2，再判断此时的这个中间数是奇数还是偶数，如果是奇数，那与它相邻的两个数肯定不互质，可以排除，所以a，b
应该为n-2和n+2；如果是偶数，那么就选n-1和n+1即可
代码：
#include"iostream"
#include"stdio.h"
using namespace std;
int main()
{
int T;
cin>>T;
while(T--)
{
long long n; //max和n都必须是long long型
long long max;
cin>>n;
if(n==2) cout<<1<<endl;
else{
if(n%2==0)
{
n/=2;
if(n%2==0)
max=(n-1)*(n+1);
else
max=(n-2)*(n+2);
}
else
{
n/=2;
max=n*(n+1);
}
cout<<max<<endl;
}
}
return 0;
}
The Unsolvable Problem
标签：
原文地址：http://www.cnblogs.com/zsyacm666666/p/4654678.html
