How do you compute the minimum cost of matrix-chain multiplication order?
PICTURE THIS: HOW TO EXPLAIN IT
Simple meaning
dp[i][j] is the min cost of multiplying matrices i..j, trying every split k.
WHY — DP instead of guessing?
Why interviewers care about DP:
question about DP.
trade-offs, and what you would actually do on a DSA project - not buzzwords.
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:
- 1dp[i][j] is the min
cost of multiplying matrices i..j, trying every split k.
- 2Time is O(n^3) and
space is O(n^2) for n matrices.
- 3This is the classic
interval-DP interview problem
- 4reconstructing the parenthesization stores
argmin k.
- 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
dp[i][j] is the min cost of multiplying matrices i..j, trying every split k. Time is O(n^3) and space is O(n^2) for n matrices.