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feat: add O(log n) lucas number implementation using matrix exponentiation #907
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feat: add O(log n) lucas number implementation using matrix exponentiation #907
technusm1
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commits into
TheAlgorithms:master
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technusm1:update-lucas-series-implementation
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...ation Added dynamic_lucas_number_logn function that uses matrix exponentiation to compute Lucas numbers in logarithmic time complexity, compared to the existing O(n) and O(n) recursive implementations. Updated module exports to include the new function and added comprehensive test coverage for all three implementations.
Codecov Report
✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.32%. Comparing base (4eec0b7) to head (f9597ed).
Additional details and impacted files
@@ Coverage Diff @@ ## master #907 +/- ## ======================================= Coverage 95.32% 95.32% ======================================= Files 319 319 Lines 20807 20832 +25 ======================================= + Hits 19834 19859 +25 Misses 973 973
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Use iterator with enumerate() instead of range-based indexing to satisfy clippy::needless_range_loop lint.
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Summary
Added
dynamic_lucas_number_lognfunction that uses matrix exponentiation to compute nth Lucas number in O(log n) time complexity, compared to the existing O(n) dynamic programming and O(n) recursive implementations.Changes
Test plan
The implementation uses fast matrix exponentiation with the recurrence relation matrix [[1,1],[1,0]] to achieve logarithmic time complexity.