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Optimize gcd_recursive
The optimization replaces **recursion with iteration**, eliminating Python's function call overhead which is the primary bottleneck in recursive algorithms. **Key changes:** - `if b == 0: return a` + `return gcd_recursive(b, a % b)` → `while b: a, b = b, a % b` + `return a` - Removes 4,318 recursive function calls that were consuming 68.1% of the original runtime - Uses tuple unpacking for efficient variable swapping **Why it's faster:** Python function calls are expensive due to stack frame creation, parameter passing, and return value handling. The line profiler shows the recursive call consumed 1.991 microseconds (68.1% of total time). The iterative version eliminates this overhead entirely, executing the same mathematical operations in a tight loop. **Performance characteristics:** - **Best gains (25-50% faster)**: Cases requiring multiple iterations like coprime numbers, large number pairs, and Fibonacci-like sequences - **Modest gains (15-25% faster)**: Simple cases with fewer iterations - **Minimal/no gains**: Trivial cases that terminate immediately (e.g., `gcd(9, 0)`) The 16% overall speedup comes from removing Python's recursive overhead while preserving identical mathematical behavior.
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src/math/computation.py

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -1,5 +1,5 @@
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def gcd_recursive(a: int, b: int) -> int:
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"""Calculate greatest common divisor using Euclidean algorithm with recursion."""
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if b == 0:
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return a
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return gcd_recursive(b, a % b)
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while b:
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a, b = b, a % b
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return a

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