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Add optimized Sieve of Eratosthenes algorithm#13617

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Naman-Vasudev wants to merge 8 commits intoTheAlgorithms:masterfrom
Naman-Vasudev:sieve_of_erastosthenes
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Add optimized Sieve of Eratosthenes algorithm#13617
Naman-Vasudev wants to merge 8 commits intoTheAlgorithms:masterfrom
Naman-Vasudev:sieve_of_erastosthenes

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@Naman-Vasudev
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Describe your change:

  • Add an algorithm

This PR adds an optimized implementation of the Sieve of Eratosthenes.
The optimization skips even numbers after 2 and uses a half-sized boolean array,
reducing both memory and time by approximately 50% compared to the standard sieve.

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work.
  • This PR only changes one algorithm file.
  • All function parameters and return values are annotated with type hints.
  • All functions have doctests that pass automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.

@algorithms-keeper algorithms-keeper bot added the require descriptive names This PR needs descriptive function and/or variable names label Oct 20, 2025
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Click here to look at the relevant links ⬇️

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from math import isqrt

def optimized_sieve(n: int) -> list[int]:

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Please provide descriptive name for the parameter: n

@algorithms-keeper algorithms-keeper bot added the awaiting reviews This PR is ready to be reviewed label Oct 20, 2025
@algorithms-keeper algorithms-keeper bot removed the require descriptive names This PR needs descriptive function and/or variable names label Oct 20, 2025
@algorithms-keeper algorithms-keeper bot added the tests are failing Do not merge until tests pass label Oct 20, 2025
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