Permutation

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 1190    Accepted Submission(s): 756
Special Judge
 

Problem Description

A permutation p1,p2,...,pn of 1,2,...,n is called a lucky permutation if and only if pi≡0(mod|pi−pi−2|) for i=3...n.

Now you need to construct a lucky permutation with a given n.

 

Input

The first line is the number of test cases.

For each test case, one single line contains a positive integer n(3≤n≤105).

 

Output

For each test case, output a single line with n numbers p1,p2,...,pn.

It is guaranteed that there exists at least one solution. And if there are different solutions, print any one of them.

 

Sample Input

1

6

Sample Output

1 3 2 6 4 5

 

同余定理

a≡0(mod b)即等于a%b==0;

如果要保证 pi≡0(mod|pi−pi−2|) ，那么保证 pi - pi-2 == 1即可。

代码：

#include<iostream>
#include<algorithm>
#include<cstring>
#include<string>
#include<cstdio>
#include<cmath>
#include<set>
#include<map>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define mem(a,b) memset(a,b,sizeof(a))
#define closeio std::ios::sync_with_stdio(false)

int a[100005];

int main()
{
	int t,n,i;
	cin>>t;
	while(t--)
	{
		cin>>n;
		int s=1;
		for(i=1;i<=n;i+=2)
		{
			a[i]=s;
			s++;
		}
		for(i=2;i<=n;i+=2)
		{
			a[i]=s;
			s++;
		}
		for(i=1;i<=n;i++)
		{
			cout<<a[i];
			if(i!=n)
				cout<<" ";
		}
		cout<<endl;
	}
	return 0;
}