Commit fc037c0
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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.1 parent a45e450 commit fc037c0
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