CTRICK - Card Trick
The magician shuffles a small pack of cards, holds it face down and performs the following procedure:
- 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.
- 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.
- Three cards are moved one at a time…
- 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…
Input: 2 4 5 Output: 2 1 4 3 3 1 4 5 2
How can we prove that such configuration of cards will always exist for all values of n??
Last edit: 2016-07-31 16:21:52
segment Trees.... ; )
Basant kumar bhala:
1.39s with linked lists
loved it after solving the problem tried the whole new approach :) =D
Try with segment trees :)
Solving this problem with BIT gives real pleasure :)
very good question
how to solve this with BIT??