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Optimize Node.has_loop to use constant auxiliary space - #15607

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iamshresthraj:optimize-has-loop
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iamshresthraj:optimize-has-loop

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Describe your change

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Optimize Node.has_loop in data_structures/linked_list/has_loop.py to use Floyd's tortoise-and-hare cycle-finding algorithm:

  • Uses two pointers (slow and fast) to detect cycles.
  • Compares node references (is) rather than values.
  • Reduces auxiliary space complexity from (n)$ to (1)$ while maintaining (n)$ time complexity.
  • Accurately detects acyclic lists, self-loops, loops back to earlier nodes/head, loops involving the final node, and lists with duplicate node values.

Fixes #15576

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 Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues, then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

@algorithms-keeper algorithms-keeper Bot added awaiting reviews This PR is ready to be reviewed enhancement This PR modified some existing files labels Oct 19, 2026

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Optimize Node.has_loop to use constant auxiliary space instead of O(N) space

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