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Pruthviraj Gojare — R23-T043: Measure how maths/lucas_series.py scales #44
Description
Student: Pruthviraj Gojare
Task: R23-T043 · 3 of 10
Repository: https://github.com/S-AI-Projects/TheAlgorithms-Python
Assigned working branch: student/e26b07f0834
Goal
Check the algorithm's real running time against its theoretical complexity. Compare recursive_lucas_number (exponential) with dynamic_lucas_number (linear) for n = 5…30, and explain the curve.
Steps
- State the expected time complexity with a short derivation.
- Write work/R23-T043/bench.py timing the main function with
timeitfor at least 6 input sizes (doubling). - Plot time vs n (matplotlib) and compare with the expected curve.
- Add the complexity, with your evidence, to the function's docstring.
- Make the code change in the repository: maths/lucas_series.py: complexity of both functions in their docstrings, backed by your measurements. Re-run the automated check and the repo's own tests afterwards.
- Prepare the PR: on branch R23-T043, commit the code change plus your work/R23-T043/ evidence, put your findings in the PR description and open the PR against the org fork. For a later upstream PR, create a second branch containing only the code change (no work/ folder).
Done when
☐ bench.py times recursive_lucas_number and dynamic_lucas_number for n = 5…30; the plot shows exponential vs linear growth.
☐ maths/lucas_series.py docstrings state O(φⁿ)-style exponential and O(n) complexity, consistent with the plot.
☐ Existing 10 doctests and 2 raise paths unchanged.
Additional task guidance
Additional curated task guidance
Item:
maths/lucas_series.py (66 lines; 10 doctests)
Task type:
Measure complexity
Code change (goes into the PR):
maths/lucas_series.py: complexity of both functions in their docstrings, backed by your measurements.
Automated check:
uv run python work/R23-T043/bench.py && uv run pytest maths/lucas_series.py
Prerequisites:
Linux/WSL2/Codespaces with uv (https://docs.astral.sh/uv/getting-started/installation/); run uv sync --group=test once – it installs the Python version CI uses (.python-version = 3.15t) and the test dependencies, about 1–2 GB
Upstream PR rules:
Follow CONTRIBUTING.md: type hints on every parameter/return, doctests for valid and erroneous input, snake_case file names, no duplicate of an existing implementation, no hand edits to DIRECTORY.md. CI (pytest with doctests, ruff) must pass – bots close PRs without tests or type hints. Keep work/ (benchmarks, notes, property tests) out of the upstream branch; put results in the PR description.
Source (pinned):
https://github.com/TheAlgorithms/Python/blob/574d100b7181956e9c8384552fd078165e4cc326/maths/lucas_series.py
Change:
No change recorded
PR destination:
Preserved pilot guidance
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.
Activity