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Longest Strictly Increasing Subsequence DSA Interview

Given a sequence of integers, find the length of the longest subsequence (not necessarily contiguous) whose elements are strictly increasing.

Mock Interview with AI

1. Problem Statement

You are given a sequence of integers. Find the length of the longest subsequence, not necessarily contiguous, whose elements are strictly increasing.

2. Live Coding Format

Choose Python, JavaScript, Java, or C++, then solve while explaining your reasoning to the live interviewer.

Validation uses handwritten tests only. The MVP does not compile or run code, and it does not provide AI algorithm completion.

3. Key Focus Areas

1
Problem clarification and contract
2
Approach exploration and optimality
3
Think-aloud communication and pacing
4
Implementation correctness
5
Code quality and language fluency
6
Handwritten tests and dry run
7
Debugging and self-correction
8
Complexity analysis
9
Follow-up performance

4. What Strong Candidates Should Demonstrate

✓Clarify strictness of the ordering and behavior on empty or fully non-increasing input before coding.
✓Explain an O(n^2) DP baseline and improve to an O(n log n) patience-sorting approach.
✓Think aloud while implementing careful DP or binary-search-based tail tracking.
✓Validate with explicit expected outputs and a top-to-bottom handwritten dry run.
✓Analyze time and space complexity and handle a bounded follow-up modification.

Evaluation Guide

This is an evaluation framework, not a single model answer. Strong designs may make different choices when their assumptions and trade-offs are explicit.

Problem clarification and contract

10%

Senior signals

✓Clarifies that the subsequence need not be contiguous, confirms strict increase (no equal adjacent values in the subsequence), and asks what to return for an empty array.
✓Confirms whether values can repeat in the original array even though the subsequence must be strictly increasing.

Staff-level signals

◆Asks about expected input size to justify pursuing the logarithmic-factor improvement.

Common red flags

×Codes immediately while assuming the subsequence must be contiguous without confirming.

Approach exploration and optimality

20%

Senior signals

✓Explains the O(n^2) DP baseline where dp[i] is the longest increasing subsequence ending at index i, identifies the pairwise comparison cost, and improves to the O(n log n) patience-sorting approach using a maintained array of smallest tail values per length.
✓Explains why binary search over the tails array correctly finds where a new value should replace or extend the sequence.

Staff-level signals

◆Discusses why the tails array does not directly represent an actual valid subsequence, only its length, unless parent pointers are also tracked.

Common red flags

×Starts implementation without explaining an approach even after one interviewer prompt.

Think-aloud communication and pacing

10%

Senior signals

✓Explains the plan before coding and narrates the DP recurrence or tails-array invariant while implementing.
✓Paces the core solution to leave time for validation and the follow-up.

Common red flags

×Writes substantial code silently and cannot explain what the code is doing.

Implementation correctness

25%

Senior signals

✓Implements a correct O(n^2) DP or O(n log n) tails-array solution that produces the correct length for strictly increasing subsequences.
✓Handles an empty array, a single element, a fully non-increasing array (answer 1), and a fully strictly increasing array (answer n).
✓Provides a convincing invariant argument for why the chosen approach yields the true maximum length.

Common red flags

×Confuses non-decreasing with strictly increasing, producing an incorrect result for arrays with equal adjacent values.
×Final code contains a material correctness bug that the candidate does not identify.

Code quality and language fluency

15%

Senior signals

✓Produces readable, language-appropriate code with clear DP array or tails-array variable names and correct binary search boundary handling if used.

Common red flags

×Contains off-by-one errors in binary search bounds or syntax-level incoherence that prevents credible reasoning.

Handwritten validation, dry run, and debugging

10%

Senior signals

✓Provides explicit inputs and expected outputs before tracing the code from top to bottom, showing DP values or tails-array evolution.
✓Covers an empty array, single element, all equal or non-increasing values, and all strictly increasing values.
✓Finds and fixes an error independently, then re-validates the affected path.

Common red flags

×Claims the code works without a representative trace.

Complexity analysis and follow-up

10%

Senior signals

✓States quadratic time for the DP baseline versus O(n log n) time for the tails-array approach, and auxiliary space for each, comparing the two.

Staff-level signals

◆Discusses when the simpler quadratic DP might be acceptable in practice despite being asymptotically worse.

Common red flags

×Cannot state the complexity of the implemented solution.
×Fails a reasonable follow-up despite having at least five minutes and receiving bounded clarification.

Trade-offs to articulate

The O(n^2) DP approach is simple to reason about and reconstruct but scales poorly for large inputs.
The O(n log n) tails-array approach is faster but the tails array itself is not a valid subsequence, only a length-tracking structure.
Reconstructing an actual subsequence from the tails-array approach requires additional parent-pointer bookkeeping.

Practice follow-up questions

1.Coding follow-up: modify the solution to reconstruct and return one actual longest strictly increasing subsequence, not just its length.
2.Verbal extension: how would the approach change if you needed the longest non-decreasing subsequence instead of strictly increasing?

Want interactive feedback?

Practice this problem in the live coding workspace while the interviewer probes your clarification, algorithm, implementation, complexity, and handwritten tests.

Start Interview

Core Concepts

Dynamic ProgrammingBinary SearchArraysComplexity Analysis