ANIKET KUMAR NISHAD — R50-T039: Measure the work done by liouvilleFunction (LiouvilleFunction.js) [Maths/LiouvilleFunction.js] #39

Student: ANIKET KUMAR NISHAD

Task: R50-T039 · 9 of 10
Repository: https://github.com/S-AI-Projects/TheAlgorithms-JavaScript
Assigned working branch: student/e26b07f0789

Goal

Work on Maths/LiouvilleFunction.js. Measure the scaling of liouvilleFunction on valid inputs while checking correctness. Distinguish algorithm operations from process startup, I/O and compilation. Fixture: Use the smallest valid input and one ordinary input for liouvilleFunction from Maths/LiouvilleFunction.js. Write the literal inputs and independently calculated expected outputs in the tests before editing the implementation. The check must name the source line establishing each precondition.

Steps

1. Read Maths/LiouvilleFunction.js, especially liouvilleFunction near line 20. Record its public inputs, result, mutation behavior and any external dependencies before changing it.
2. Define input size for this algorithm. Select three increasing sizes within a short CPU-only run; use operation counts if timing is dominated by overhead or the domain is fixed.
3. Use fixed seeds, fresh inputs and five repetitions per size. Check outputs outside the timed interval and report median plus range.
4. Implement work/R50-T039/check.py as a focused runner that executes the new checks and propagates failures. Native check to incorporate: run the repository test script in non-watch mode after installing from its lockfile; for browser-only code use a browser test instead of plain Node. Record the actual command and nonzero test count.
5. Create the checks specified below and run python3 work/R50-T039/check.py. Save inputs, expected versus actual results and tool versions in work/R50-T039/; a check must exit non-zero when an assertion fails.
6. Commit the repository change on branch R50-T039; prepare a PR to the organisation fork explaining the result and linking the checks. Keep each task independently reviewable. Remove work/R50-T039/ from a later upstream branch.

Done when

☐ The checked behavior is tied to liouvilleFunction in Maths/LiouvilleFunction.js; every assertion has an explicit expected value.
☐ Use the smallest valid input and one ordinary input for liouvilleFunction from Maths/LiouvilleFunction.js. Write the literal inputs and independently calculated expected outputs in the tests before editing the implementation. The check must name the source line establishing each precondition.
☐ Existing supported behavior and the public interface are preserved unless a failing regression demonstrates and documents a defect.
☐ The complexity statement names its input-size variable and distinguishes worst-case claims from observations.
☐ No pass/fail threshold depends on wall-clock speed; all measured cases pass correctness checks.

Submission checklist

• Complete this task and its checks.
• Add the required evidence and link your pull request here.
• Select this S-AI-Projects fork as the PR base repository.
• Request instructor review.

Keep this PR focused on this task. Do not submit assignment PRs to the upstream repository.