Problem 1506. Maximum Intra-Vector Swaps

Created by Richard Zapor

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This Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.The processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.Example Sequences:<pre class="language-matlab">[3 1 2], [2 1 3], [1 2 3] Score 2
[3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]
</pre>Input: n (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31)Output: Vector of values 1:nExample:Input: 5 Output: [3 1 4 5 2]Score: 7A minimum cumulative score of 531 for the 17 cases is required to Pass.Final Score = 2531 - sum(scores)Hints:Usage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n>9.Request: If Code is implemented external then please post as a block comment.Faster Code Block than fliplr:<pre class="language-matlab">function count=process_seq(seq)
 count=0;
 while seq(1)>1
 count=count+1;
 seq(1:seq(1))=seq(seq(1):-1:1);
 end
end
</pre>

This Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.

The processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.

*Example Sequences:*

[3 1 2], [2 1 3], [1 2 3] Score 2
  [3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]

*Input:* n  (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31)

*Output:* Vector of values 1:n

Example:

Input: 5  Output: [3 1 4 5 2]

Score: 7

A minimum cumulative score of 531 for the 17 cases is required to Pass.

Final Score = 2531 - sum(scores)

*Hints:*

Usage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n>9.

Request: If Code is implemented external then please post as a block comment.

Faster Code Block than fliplr:

function count=process_seq(seq)
   count=0;
   while seq(1)>1
    count=count+1;
    seq(1:seq(1))=seq(seq(1):-1:1);
   end
  end

Solve

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Last Solution submitted on Jul 16, 2019

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1 Comment

Jean-Marie Sainthillier on 17 Jul 2013

Wonderful problem

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Problem 1506. Maximum Intra-Vector Swaps

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Problem 1506. Maximum Intra-Vector Swaps

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