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feat: add new Josephus file in Recursive directory#1728

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Lonercode wants to merge1 commit intoTheAlgorithms:master
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Lonercode
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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 foundhere

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

Checklist:

  • I have readCONTRIBUTING.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 butuserprofile.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 containsFixes: #{$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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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 simplewhile loop:

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

const collection1 = [1]
const collection2 = []

it('should return 4 for step size of 3', () => {
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Repetitive tests of the form "should return X for Y" should useit.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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@appgurueuappgurueuappgurueu left review comments

@raklaptudirmraklaptudirmAwaiting requested review from raklaptudirmraklaptudirm is a code owner

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@Lonercode@codecov-commenter@appgurueu
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