Easy DP Question 53 of 224

How do you compute the nth Fibonacci number efficiently?

DSA interview set · Speak this in 60–90 seconds · Faridabad & Delhi NCR

PICTURE THIS: DATABASE INDEX

Without indexScan every row

With indexJump to keys

CostWrites slower

Simple meaning

Naive recursion is exponential because it recomputes subproblems.

WHY — DP instead of guessing?

Why interviewers care about DP:

This is a process

question about DP.

Panels listen for order,

trade-offs, and what you would actually do on a DSA project - not buzzwords.

Stay structured

Name the idea, why it exists, then one short example.

Close cleanly

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:

1
Naive recursion is exponential
because it recomputes subproblems.
2
Memoization or a bottom-up
pair of rolling variables computes each index once: O(n) time and O(1) extra space for the iterative form.
3
Matrix exponentiation is O(log
n) if they want a follow-up.
4
Give an example
One tiny concrete case you can say aloud.
5
Common mistake
What juniors usually get wrong.
6
Close
When you pick this over the alternative.

EXAMPLE — See it in action

Here's a short line you can speak, broken into clear beats:

Say this line

“Memoization or a bottom-up pair of rolling variables computes each index once: O”

Break into beats

Memoizationorabottomuppair

Speaking order

2987408337471632900

Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.

Key takeaway

Naive recursion is exponential because it recomputes subproblems. Memoization or a bottom-up pair of rolling variables computes each index once: O(n) time and O(1) extra space for the iterative form.