From 18926698a226d8c67595d16242ea7a451e7fc403 Mon Sep 17 00:00:00 2001 From: "codeflash-ai[bot]" <148906541+codeflash-ai[bot]@users.noreply.github.com> Date: Fri, 30 Jan 2026 17:29:22 +0000 Subject: [PATCH] Optimize Algorithms.fibonacci MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Runtime improvement (primary): The optimized version reduces the measured runtime from 34.3 ms to 18.6 ms (reported "84%" speedup). The main benefit is a much lower execution time for computing Fibonacci numbers. What changed (specific optimizations): - Replaced the naive recursive Fibonacci (exponential time, many repeated calls) with an iterative fast-doubling algorithm. - Implemented the fast-doubling formulas: - c = F(2k) = F(k) * (2*F(k+1) - F(k)) - d = F(2k+1) = F(k)^2 + F(k+1)^2 and used them in a bitwise loop that processes bits of n from most-significant to least-significant. - Used Integer.numberOfLeadingZeros to find the highest significant bit and a simple for-loop over bits (no recursion or extra allocations). - Kept arithmetic in primitive long operations (shifts, multiplies, adds) and avoided function call overhead. Why this is faster (how it reduces runtime): - Algorithmic complexity: naive recursion is O(φ^n) (exponential) due to repeated subcomputations. Fast doubling computes Fibonacci in O(log n) steps. Changing complexity from exponential to logarithmic yields massive savings for all but the smallest n. - Eliminates recursion and repeated work: recursion creates many stack frames and repeated recomputation; the iterative fast-doubling does each step once. - Lower overhead per step: the optimized code uses a tight loop with a few integer multiplications and additions per bit, which is far cheaper than millions of method calls and the associated control-flow overhead. - Bitwise iteration: scanning only the needed bits (highestBit downwards) means the loop does ~log2(n) iterations rather than n or worse; Integer.numberOfLeadingZeros is a cheap native operation to find that range. - Better CPU locality and fewer allocations: no allocation or deep stacks, so better cache and lower GC pressure. Key behavior and dependency changes: - Behavior (return values and overflow semantics) is preserved for non-negative n — n <= 1 still returns n, result type remains long. No external dependencies were introduced. - Space usage improved from O(n) recursion depth (or large implicit stack during recursion) to O(1) additional space. Impact on workloads / hot paths: - This is a win in any code path that computes Fibonacci for moderate-to-large n or does many calls (e.g., in loops, services, or batch jobs). If this function sits in a hot path, the O(log n) vs exponential improvement compounds significantly across many calls. - For very small n (0 or 1) the difference is negligible; the optimized version still has minimal overhead and remains appropriate. - Because the optimized code uses only primitive ops, it plays well in tight loops and concurrent contexts where reducing per-call overhead is important. Test-case suitability (based on observed runtimes): - Big wins for test cases with larger n (where recursion cost explodes). - Repeated or batched calls to fibonacci(n) show much larger end-to-end gains. - No functional tests were required to change; correctness for n <= 1 and typical positive n remains the same. Summary: The main reason the optimized code was accepted is a clear runtime benefit — it switches from an exponential, recursion-heavy implementation to a fast-doubling iterative algorithm that runs in O(log n) time and O(1) space. That structural change is the source of the observed ~84% speedup and will reduce CPU time dramatically for realistic inputs and hot-path usage. --- .../src/main/java/com/example/Algorithms.java | 43 +++++++++++++------ 1 file changed, 31 insertions(+), 12 deletions(-) diff --git a/code_to_optimize/java/src/main/java/com/example/Algorithms.java b/code_to_optimize/java/src/main/java/com/example/Algorithms.java index bc976d3c3..a31537eaf 100644 --- a/code_to_optimize/java/src/main/java/com/example/Algorithms.java +++ b/code_to_optimize/java/src/main/java/com/example/Algorithms.java @@ -4,25 +4,41 @@ import java.util.List; /** - * Collection of algorithms. + * Collection of algorithms that can be optimized by Codeflash. */ public class Algorithms { - /** - * Calculate Fibonacci number using recursive approach. - * - * @param n The position in Fibonacci sequence (0-indexed) - * @return The nth Fibonacci number - */ public long fibonacci(int n) { if (n <= 1) { return n; } - return fibonacci(n - 1) + fibonacci(n - 2); + // Fast doubling iterative method (O(log n) time, O(1) space) + long a = 0; // F(0) + long b = 1; // F(1) + + int highestBit = 31 - Integer.numberOfLeadingZeros(n); + for (int i = highestBit; i >= 0; i--) { + // Compute: + // c = F(2k) = F(k) * (2*F(k+1) - F(k)) + // d = F(2k+1) = F(k)^2 + F(k+1)^2 + long twoBminusA = (b << 1) - a; + long c = a * twoBminusA; + long d = a * a + b * b; + + if (((n >> i) & 1) == 0) { + a = c; + b = d; + } else { + a = d; + b = c + d; + } + } + return a; } /** - * Find all prime numbers up to n. + * Find all prime numbers up to n using naive approach. + * This can be optimized with Sieve of Eratosthenes. * * @param n Upper bound for finding primes * @return List of all prime numbers <= n @@ -38,7 +54,7 @@ public List findPrimes(int n) { } /** - * Check if a number is prime using trial division. + * Check if a number is prime using naive trial division. * * @param num Number to check * @return true if num is prime @@ -54,7 +70,8 @@ private boolean isPrime(int num) { } /** - * Find duplicates in an array using nested loops. + * Find duplicates in an array using O(n^2) nested loops. + * This can be optimized with HashSet to O(n). * * @param arr Input array * @return List of duplicate elements @@ -72,7 +89,7 @@ public List findDuplicates(int[] arr) { } /** - * Calculate factorial recursively. + * Calculate factorial recursively without tail optimization. * * @param n Number to calculate factorial for * @return n! @@ -86,6 +103,7 @@ public long factorial(int n) { /** * Concatenate strings in a loop using String concatenation. + * Should be optimized to use StringBuilder. * * @param items List of strings to concatenate * @return Concatenated result @@ -103,6 +121,7 @@ public String concatenateStrings(List items) { /** * Calculate sum of squares using a loop. + * This is already efficient but shows a simple example. * * @param n Upper bound * @return Sum of squares from 1 to n