CTRICK - Card Trick

The magician shuffles a small pack of cards, holds it face down and performs the following procedure:

  1. The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.
  2. Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.
  3. Three cards are moved one at a time…
  4. This goes on until the nth and last card turns out to be the n of Spades.

This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 20000.


On the first line of the input is a single positive integer, telling the number of test cases to follow. Each case consists of one line containing the integer n.


For each test case, output a line with the correct permutation of the values 1 to n, space separated. The first number showing the top card of the pack, etc…



2 1 4 3
3 1 4 5 2

hide comments
sHaShAnK sHeKhAr: 2015-07-23 10:22:51

How can we prove that such configuration of cards will always exist for all values of n??

rini22: 2015-07-10 09:15:31

Last edit: 2016-07-31 16:21:52
i_am_looser: 2015-05-29 20:55:02

segment Trees.... ; )

Basant kumar bhala: 2015-03-01 08:31:14

1.39s with linked lists

mkrjn99: 2015-01-26 06:19:59

nlog^2(n) :D

CoNtRaDiCtIoN: 2014-12-13 21:18:30

loved it after solving the problem tried the whole new approach :) =D

Bumbler: 2014-10-31 20:51:44

Try with segment trees :)

knight: 2014-10-20 22:12:01

Solving this problem with BIT gives real pleasure :)

Ankit Verma: 2014-10-15 19:31:34

very good question

Dharmendra Verma: 2014-09-08 01:40:51

how to solve this with BIT??

Added by:Camilo Andrés Varela León
Time limit:3.279s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Nordic Collegiate Contest 2006