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feat: add new Josephus file in Recursive directory #1728

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@Lonercode Lonercode commented Oct 10, 2024

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Describe your change:

As part of my contribution to hacktoberfest 2024, I have added a file recursively implementing the Josephus algorithm and its associated test to the Recursive directory. The Josephus algorithm is a counting-out game that returns the last number after removing every kth number in a circle. More on it can be found here

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new JavaScript files are placed inside an existing directory.
  • All filenames should use the UpperCamelCase (PascalCase) style. There should be no spaces in filenames.
    Example:UserProfile.js is allowed but userprofile.js,Userprofile.js,user-Profile.js,userProfile.js are not
  • All new algorithms have a URL in their comments that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.78%. Comparing base (ff314a2) to head (483f181).

Additional details and impacted files 
@@ Coverage Diff @@
## master #1728 +/- ##
==========================================
+ Coverage 84.76% 84.78% +0.01% 
==========================================
 Files 378 379 +1 
 Lines 19742 19767 +25 
 Branches 2955 2961 +6 
==========================================
+ Hits 16735 16760 +25 
 Misses 3007 3007

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return collection[0]
} else {
step = (step - 1) % collection.length
collection.splice(step, 1)
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@appgurueu appgurueu Oct 10, 2024

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This is $O(n)$ so you get $O(n^2)$ runtime, which is very naive. Wikipedia shows formulae that achieve $O(n)$ or $O(k\log{n})$ runtime, both of which are substantially better. And even besides those, I can pretty easily come up with $O(n \log{n})$ algorithms based on decremental data structures which support this "splice" operation in logarithmic time (such as an initially balanced k-nary tree augmented with counts).

This algorithm also doesn't really benefit from recursion. It would be clearer as a simple while loop:

while (collection.length > 1) { /* kill someone */ }
return collection[0]

const collection1 = [1]
const collection2 = []

it('should return 4 for step size of 3', () => {
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@appgurueu appgurueu Oct 10, 2024

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Repetitive tests of the form "should return X for Y" should use it.each

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Thanks for the review @appgurueu Alright. In that case would there be a need to modify it for the recursive directory.

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@appgurueu appgurueu appgurueu left review comments

@raklaptudirm raklaptudirm Awaiting requested review from raklaptudirm raklaptudirm is a code owner

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