When does greedy coin change work, and when does it fail?
PICTURE THIS: HOW TO EXPLAIN IT
Simple meaning
Taking the largest coin that does not exceed the remainder is optimal for canonical systems like US coins.
WHY — Greedy instead of guessing?
Why interviewers care about Greedy:
on Greedy.
the situation, the default choice, and one exception - that reads as experience.
Name the idea, why it exists, then one short example.
End with when you use it and one common pitfall.
STEPS — What happens step by step?
Before you speak the answer, walk the interviewer through these steps:
- 1Taking the largest coin
that does not exceed the remainder is optimal for canonical systems like US coins.
- 2It fails on some
sets, for example coins 1, 3, 4 and amount 6, where 3+3 beats 4+1+1.
- 3If greedy is not
proven, use DP in O(amount * coins) time.
- 4Give an example
One tiny concrete case you can say aloud.
- 5Common mistake
What juniors usually get wrong.
- 6Close
When you pick this over the alternative.
EXAMPLE — See it in action
Here's a short line you can speak, broken into clear beats:
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
Taking the largest coin that does not exceed the remainder is optimal for canonical systems like US coins. It fails on some sets, for example coins 1, 3, 4 and amount 6, where 3+3 beats 4+1+1.