Explain time complexity with a simple example

The short version: time complexity refers to a measure of how an algorithm's running time grows with input size. A quick example makes it concrete — A single nested loop over n items runs in O(n²) time.

How to approach it step by step

Once one example makes sense, the method generalises: count the dominant repeated operation and express it in Big O notation. In a visual interactive session the example is built on screen piece by piece, so you see which quantity changes at each step instead of only reading a final answer. Ask for a harder variant and the explanation adapts on the spot.

Worked example

A single nested loop over n items runs in O(n²) time.

The mistake most learners make

Counting constants and lower order terms that Big O deliberately ignores.

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