Problem 272. Generalized N-Cards Problem

Created by @bmtran (Bryant Tran)

Solve Later

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Preface: This is a generalized version of the problem I presented <a href="http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem">here</a>.You have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?The sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).Example<pre> generalNCardsProblem(5,[-1 1])
 deck = [ 1 2 3 4 5 ]
 deck = [ 2 3 4 5 ]
 deck = [ 3 4 5 2 ]
 deck = [ 4 5 2 ]
 deck = [ 5 2 4 ]
 deck = [ 2 4 ]
 deck = [ 4 2 ]
 deck = [ 2 ]</pre><pre> generalNCardsProblem(5,[-1 1 1 -1])
 deck = [ 1 2 3 4 5 ]
 deck = [ 2 3 4 5 ]
 deck = [ 3 4 5 2 ]
 deck = [ 4 5 2 3 ]
 deck = [ 5 2 3 ]
 deck = [ 2 3 ]
 deck = [ 3 2 ]
 deck = [ 2 3 ]
 deck = [ 3 ]</pre>

Preface: This is a generalized version of the problem I presented <http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem here>.

You have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?

The sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).

*Example*

generalNCardsProblem(5,[-1 1])
    deck = [ 1 2 3 4 5 ]
    deck = [ 2 3 4 5 ]
    deck = [ 3 4 5 2 ]
    deck = [ 4 5 2 ]
    deck = [ 5 2 4 ]
    deck = [ 2 4 ]
    deck = [ 4 2 ]
    deck = [ 2 ]

generalNCardsProblem(5,[-1 1 1 -1])
    deck = [ 1 2 3 4 5 ]
    deck = [ 2 3 4 5 ]
    deck = [ 3 4 5 2 ]
    deck = [ 4 5 2 3 ]
    deck = [ 5 2 3 ]
    deck = [ 2 3 ]
    deck = [ 3 2 ]
    deck = [ 2 3 ]
    deck = [ 3 ]

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Problem 272. Generalized N-Cards Problem

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