complexity

Prompt file imported from Mkhod51/NeetCode150 (.claude/commands/complexity.md). Fill in {{arguments}} before use. Copyright stays with the author.

Constraint (CLAUDE.md): only analyse a problem the human has ALREADY solved. Explaining the complexity of code they have written is allowed. Never reveal the optimal complexity, the approach or any code for a problem that is not yet solved, and never write or improve their solution.

Target file: {{arguments}}

Steps:

1. Check the problem is solved: run python3 scripts/check_file.py {{arguments}}.

   • If it FAILS (TODO fields, or the file does not run), STOP. Tell the human this command only analyses solved problems, and that revealing the optimal now would spoil the exercise. Offer /hint instead. Do not state the optimal complexity or the approach.

2. Measure the real running time (this benchmarks THEIR code, which is allowed):

   • If the file has no bench() function, add a small one at the bottom using helpers.complexity (pick a generator that matches the method's inputs, e.g. random_ints, sorted_ints, random_string; return a tuple from make_input for multi-argument methods). This is measurement code, not solution logic.
   • Run python3 scripts/benchmark.py {{arguments}} and read the table and the estimated growth.

3. Read the human's stated Time complexity and Space complexity from the docstring. Note if the measured growth disagrees with what they wrote (for example they wrote O(n) but it scales like O(n^2)), and ask them about it.

4. Compare against the optimal. Because the problem is solved, you may state the optimal time and space complexity for it and say whether they matched.

   • If they matched the optimal: say so plainly and stop.
   • If their solution is slower than optimal: name the gap in complexity terms only (for example "yours is O(n^2) time, the optimal is O(n)"). Explain in one or two sentences, in words, what is costing the extra time. Do NOT write or describe the full better algorithm outright. Offer a choice: a graduated /hint toward the faster idea, or set the docstring Revisit field to yes so they redo it later. Then run python3 scripts/progress.py if you changed the field.

Never edit their Solution code. You are analysing and comparing, not fixing.