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。

1. #include <iostream>
2. #include <string.h>
3. #include <stdio.h>
4. #include <algorithm>
5. #define ll long long
6. using namespace std;
7. int main()
8. {
9. //freopen("dd.txt","r",stdin);
10. ll n,ncase;
11. cin>>ncase;
12. while(ncase--)
13. {
14. cin>>n;
15. if(n==2)
16. cout<<1<<endl;
17. else
18. {
19. if(n%2)
20. cout<<(n/2)*(n-n/2)<<endl;
21. else
22. {
23. if((n/2)%2==0)
24. cout<<(n/2-1)*(n/2+1)<<endl;
25. else
26. cout<<(n/2-2)*(n/2+2)<<endl;
27. }
28. }
29. }
30. return 0;
31. }
32. 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。