Coding
AI Prompt for Complexity Analysis
Analyze time and space complexity with this AI prompt: Big-O of your code explained intuitively, bottlenecks identified, and scaling predictions.
The prompt
Role: You are a complexity analyst who makes Big-O intuitive and practical. Context: Language: [LANGUAGE]. My level: [YOUR_LEVEL]. Code: [CODE] Task: 1) Determine the time complexity with step-by-step reasoning (count the operations per loop level, recurrence relation if recursive). 2) Determine the space complexity including call stack and auxiliary structures. 3) Explain what the Big-O MEANS practically: "if input doubles, runtime roughly X" with concrete numbers for [REALISTIC_SIZES, e.g. n=1k, 1M]. 4) Identify the dominant term — which part to optimize first. 5) State the best/average/worst cases if they differ. Format: Time analysis with reasoning, then space, then the practical scaling table, then the optimization target, then case analysis. Ask the AI to sanity-check the analysis empirically: a tiny benchmark script doubling the input size and confirming the predicted growth curve. Theory you can measure is theory you can trust. Constraints: Show the reasoning, not just the answer — I want to learn the method. Use [REALISTIC_SIZES] for the scaling intuition. Distinguish Big-O from real-world constants where it matters.
Variables to fill in
Replace each [variable] in the prompt with your own details:
[LANGUAGE] [YOUR_LEVEL] [CODE] [REALISTIC_SIZES]
Example input
CODE=recursive Fibonacci, LANGUAGE=Python, LEVEL=beginner, GOAL=understand Big-O intuitively
How to use this prompt
Paste the code you want analyzed — abstract complexity questions get abstract answers. Ask for the intuitive explanation, not just the symbol.
Tips for the best results
- Ask for the scaling table with your actual data sizes — it makes Big-O concrete.
- Have it identify the dominant term; that is your optimization target.
- Request the recurrence-relation derivation for recursive code to learn the method.
Frequently asked questions
Can it analyze my code's complexity?
It analyzes YOUR code's actual complexity with an intuitive explanation, then shows the optimized version's complexity for contrast.
What is amortized complexity?
The average cost per operation over a sequence — like dynamic array appends being O(1) amortized despite occasional O(n) resizes. Ask the prompt to explain with your code.