From 9f284b507fa9c510fbb7679d5c6de55538fa7d9e Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Sat, 17 Jan 2026 00:34:17 +0000
Subject: [PATCH] Optimize fibonacci
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The optimized code achieves a **10,649% speedup** (from 1.88ms to 17.5μs) by replacing the exponential-time recursive algorithm with a linear-time iterative solution.

## Key Optimizations

**1. Algorithmic Transformation: O(2^n) → O(n)**
- The original recursive implementation recalculates the same Fibonacci values exponentially many times. For example, `fibonacci(5)` calls `fibonacci(3)` twice, `fibonacci(2)` three times, etc., creating a binary tree of recursive calls.
- The optimized version uses dynamic programming via iteration, computing each Fibonacci number exactly once by maintaining only the two previous values (`prevPrev` and `prev`) and building up to `n` in a simple loop.

**2. Memory Efficiency: O(n) stack → O(1)**
- Recursion depth reaches `n`, consuming stack frames proportional to input size.
- The iterative approach uses only a constant number of variables regardless of `n`, eliminating stack overhead entirely.

**3. Cache-Friendly Sequential Access**
- The loop performs predictable, sequential arithmetic operations that CPUs can pipeline effectively, versus the scattered memory access pattern of recursive calls.

## Performance Impact by Test Case

The speedup is most dramatic for larger inputs where exponential growth becomes prohibitive:
- **fibonacci(22)**: 35,761% faster (149μs → 417ns)
- **fibonacci(25)**: 116,859% faster (632μs → 541ns)
- **Sequence verification (n≤24)**: 9,644% faster (1.03ms → 10.6μs)

Even moderate values like `fibonacci(18)` show 4,722% improvement. The optimization maintains exact correctness across all test cases including edge cases (negative inputs, floats, base cases).

## Why This Matters

This function likely appears in computational hotpaths based on the comprehensive performance test suite. Any code calling `fibonacci` repeatedly—especially in loops or with moderately large values (n>20)—will see substantial throughput improvements. The sub-microsecond execution time for typical inputs (n≤30) makes this practical for real-time or high-frequency scenarios where the original implementation would be prohibitively slow.
---
 code_to_optimize_js/fibonacci.js | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/code_to_optimize_js/fibonacci.js b/code_to_optimize_js/fibonacci.js
index b0ab2b51c..1e24a624e 100644
--- a/code_to_optimize_js/fibonacci.js
+++ b/code_to_optimize_js/fibonacci.js
@@ -12,7 +12,23 @@ function fibonacci(n) {
     if (n <= 1) {
         return n;
     }
-    return fibonacci(n - 1) + fibonacci(n - 2);
+
+    // Number of 1-step decrements needed to reach a value <= 1
+    const steps = Math.ceil(n - 1);
+    const lowest = n - steps; // This is <= 1
+
+    // Base values for indices lowest - 1 and lowest (both <= 1)
+    let prevPrev = lowest - 1; // f(lowest - 1) == lowest - 1
+    let prev = lowest;         // f(lowest) == lowest
+
+    // Build values up from lowest to n using f(k) = f(k-1) + f(k-2)
+    for (let i = 1; i <= steps; i++) {
+        const current = prev + prevPrev;
+        prevPrev = prev;
+        prev = current;
+    }
+
+    return prev; // f(n)
 }
 
 /**