hdu 6235 Permutation

Permutation

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 179    Accepted Submission(s): 132
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

16

 

Sample Output

1 3 2 6 4 5

 

题意：构造满足pi%(|pi-pi-2|）==0的序列。

思路：i和i+2的奇偶性是相同的，所以奇偶序列是互不干扰的。根据pi%(|pi-pi-2|）==0推出，只要奇子序列的数和偶子序列的数分别是相邻的自然数就行了。

#include <iostream>#include <cstdio>#include <cstring>using namespace std;int main(){    int t,n;    scanf("%d",&t);    while(t--)    {        scanf("%d",&n);        int num1=1,num2=(n+1)/2+1,i=1;        while(i<=n)        {            if(i%2==1)            {                if(i==1)                    printf("%d",num1++),i++;                else                    printf(" %d",num1++),i++;            }            if(i%2==0&&i<=n)                printf(" %d",num2++),i++;        }        printf("\n");    }    return 0;}