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Faster sieve_of_eratosthenes.py implementation & memo optimized#13109

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Sumit210106 wants to merge 2 commits intoTheAlgorithms:masterfrom
Sumit210106:master
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Faster sieve_of_eratosthenes.py implementation & memo optimized#13109
Sumit210106 wants to merge 2 commits intoTheAlgorithms:masterfrom
Sumit210106:master

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Describe your change:

This PR optimizes the existing prime_sieve implementation:

  • Skips all even numbers after 2 to reduce iterations.
  • Marks only odd multiples starting from i*i.
  • Collects primes efficiently after marking.
  • Preserves existing doctests and interface.
  • Improves runtime and keeps memory usage low.

This makes the algorithm faster while keeping outputs identical to the previous version.

  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- doctests preserved.
  • Add an 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.
  • 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 enhancement This PR modified some existing files awaiting reviews This PR is ready to be reviewed labels Oct 2, 2025
@algorithms-keeper algorithms-keeper Bot added the tests are failing Do not merge until tests pass label Oct 2, 2025
@Sumit210106 Sumit210106 closed this Oct 2, 2025
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