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Optimize perfect cube detection for large numbers with modular check #12981

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lighting9999
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@lighting9999 lighting9999 commented Sep 19, 2025 •
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  1. Added modular arithmetic checks to quickly eliminate numbers that cannot be perfect cubes: · Last digit check: Only digits 0-9 can be cube endings · Modulo 7 check: Cubes can only be 0, 1, or 6 mod 7 · Modulo 9 check: Cubes can only be 0, 1, or 8 mod 9
  2. Improved boundary estimation for very large numbers (n > 10^18): · Uses logarithmic approximation to calculate a reasonable upper bound · Reduces the binary search space significantly for extremely large values
  3. Optimized computation in the binary search loop: · Added a check to avoid expensive cubic calculations for very large mid values · Uses integer division to prevent overflow in comparisons
  4. Enhanced test coverage with comprehensive doctests: · Added tests for very large numbers (up to 10^300) · Included edge cases and error conditions · Maintained compatibility with existing tests

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?

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".

@lighting9999
Optimize perfect cube detection for large numbers with modular checks…
0c5ef1f 
… and improved boundary estimation

1. Added modular arithmetic checks to quickly eliminate numbers that cannot be perfect cubes:
   · Last digit check: Only digits 0-9 can be cube endings
   · Modulo 7 check: Cubes can only be 0, 1, or 6 mod 7
   · Modulo 9 check: Cubes can only be 0, 1, or 8 mod 9
2. Improved boundary estimation for very large numbers (n > 10^18):
   · Uses logarithmic approximation to calculate a reasonable upper bound
   · Reduces the binary search space significantly for extremely large values
3. Optimized computation in the binary search loop:
   · Added a check to avoid expensive cubic calculations for very large mid values
   · Uses integer division to prevent overflow in comparisons
4. Enhanced test coverage with comprehensive doctests:
   · Added tests for very large numbers (up to 10^300)
   · Included edge cases and error conditions
   · Maintained compatibility with existing tests
@lighting9999 lighting9999 changed the title Optimize perfect cube detection for large numbers with modular checks… Optimize perfect cube detection for large numbers with modular check Sep 19, 2025
@algorithms-keeper algorithms-keeper bot added the tests are failing Do not merge until tests pass label Sep 19, 2025
@algorithms-keeper algorithms-keeper bot added the awaiting reviews This PR is ready to be reviewed label Sep 19, 2025
@algorithms-keeper algorithms-keeper bot removed the tests are failing Do not merge until tests pass label Sep 19, 2025
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@cclauss Can you help me review the PR?

cclauss
cclauss reviewed Sep 19, 2025
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cclauss commented Sep 19, 2025

As discussed in CONTRIBUTING.md, do not add tests and code in the same pull request. First, create a pull request that adds tests to the existing algorithm. After that has landed, create a second pull request that changes the algorithm and modifies test results where the new algorithm generated different results than the old algorithm.

lighting9999
lighting9999 commented Sep 20, 2025
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I have just completed the suggested changes, what should I do now?

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@mindaugl mindaugl mindaugl approved these changes

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