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Optimize Lucas Number Calculation with Matrix Exponentiation #13131

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Optimize Lucas Number Calculation with Matrix Exponentiation #13131

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@lighting9999 lighting9999 commented Oct 3, 2025 •
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Describe your change:

  1. Added matrix_power_lucas_number function:
    · Implements matrix exponentiation algorithm for O(log n) time complexity
    Maintains the same interface as existing functions

  2. Key features:
    Uses 2x2 matrix multiplication with fast exponentiation
    Handles base cases (n=0, n=1) directly

  • 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
fix this py is to slow Problem
348b81d 
1. Added matrix_power_lucas_number function:
   · Implements matrix exponentiation algorithm for O(log n) time complexity
   · Maintains the same interface as existing functions
   · Includes comprehensive doctests matching the existing patterns
2. Key features:
   · Uses 2x2 matrix multiplication with fast exponentiation
   · Handles base cases (n=0, n=1) directly
   · Proper type annotations for all internal functions
   · Maintains backward compatibility
@algorithms-keeper algorithms-keeper bot added enhancement This PR modified some existing files awaiting reviews This PR is ready to be reviewed labels Oct 3, 2025
@algorithms-keeper algorithms-keeper bot added the tests are failing Do not merge until tests pass label Oct 3, 2025
@lighting9999 lighting9999 changed the title fix this py is to slow Problem Optimize Lucas Number Calculation with Matrix Exponentiation Oct 3, 2025
@algorithms-keeper algorithms-keeper bot removed the tests are failing Do not merge until tests pass label Oct 3, 2025
@algorithms-keeper algorithms-keeper bot added the tests are failing Do not merge until tests pass label Oct 3, 2025
@algorithms-keeper algorithms-keeper bot removed the tests are failing Do not merge until tests pass label Oct 3, 2025
@lighting9999
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@cclauss Can you help me review these two PRs? One is #13128, and the other is #13131.

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