Free Interview Resources
Free practice questions, preparation advice, and expert insights for Computer Science interviews at Imperial College London.
Real Computer Science interview questions in the style Imperial College London asks. Try answering each one aloud before you reveal the hint.
You have a 3-litre jug and a 5-litre jug, an unlimited water supply and no other measuring marks. Describe a procedure that leaves exactly 4 litres in the 5-litre jug, and convince me it terminates.
Problem-Solving
Hint
Treat each jug state as a pair and search reachable states; the key move is repeatedly filling one jug and pouring into the other until it overflows. A strong candidate frames it as a small state-transition graph rather than trial and error.
Given an unsorted array of n distinct integers, how would you find the two elements whose difference is smallest? Give a naive method first, then improve it, and state the cost of each.
Problem-Solving
Hint
Start with the O(n^2) all-pairs comparison, then realise that after sorting the closest pair must be adjacent, giving O(n log n). Justify why non-adjacent pairs cannot beat the best adjacent gap.
You are given a stream of numbers one at a time and can store only a fixed amount of memory. How would you return a uniformly random one of the n numbers seen so far, at any point, without knowing n in advance?
Problem-Solving
Hint
This is reservoir sampling: keep the current pick with probability 1/i when the i-th item arrives. Ask the candidate to prove by induction that every item ends up with probability 1/n.
I have a chessboard with two diagonally opposite corner squares removed, leaving 62 squares, and a set of dominoes each covering exactly two adjacent squares. Can the board be tiled completely? Prove your answer.
Problem-Solving
Hint
Colour the board like a chessboard: each domino covers one black and one white square, but the two removed corners share a colour. The parity mismatch makes a full tiling impossible.
Design a data structure that supports push, pop and retrieving the current minimum, all in O(1) time. How do you handle duplicate minima?
Problem-Solving
Hint
Keep an auxiliary stack of running minima alongside the main stack. Probe whether the candidate pushes onto the min-stack on equal values so that duplicate minima pop correctly.
Structured interviews that combine technical problem-solving with motivation and personal statement discussion.
Imperial interviews vary by department. Engineering and Computing tend to be technical with problem-solving elements. Medicine uses a Multiple Mini Interview (MMI) format with several short stations. Most interviews last 15-30 minutes and may include a presentation or group exercise.
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
What does it mean to say an algorithm is O(n log n)? Why do we deliberately ignore constant factors and lower-order terms in that notation?
entryHint
Push for the formal definition: there exist c and n0 such that the running time is bounded above by c times n log n beyond n0. A good answer distinguishes asymptotic growth from real-world constants and explains why the abstraction is useful.
Explain the difference between a stack and a queue. Give one concrete situation where using the wrong one would produce clearly wrong behaviour.
entryHint
LIFO versus FIFO. A strong example is undo history (needs a stack) versus a print job or breadth-first traversal (needs a queue); getting these swapped reverses the intended order.
Why is binary search O(log n), and what property must the input have for it to work at all? What happens to its guarantees if that property is only approximately true?
midHint
Each comparison halves the search space, so the depth is log base 2 of n. The array must be sorted on the search key; if ordering is violated the invariant breaks and correctness is lost, not just performance.
What is recursion, and how is it related to mathematical induction? Take the factorial or Fibonacci definition and show me the correspondence.
midHint
A recursive definition mirrors a base case plus an inductive step. The candidate should see that proving a recursive function correct is essentially an induction proof, and mention the base case as both the termination guard and the induction anchor.
Explain the difference between a problem being decidable and a problem being tractable. Where does the halting problem sit, and where does a problem like Boolean satisfiability sit?
hardHint
Decidability is about whether any algorithm exists at all; tractability is about whether one runs in polynomial time. The halting problem is undecidable; SAT is decidable but believed intractable (NP-complete), which is a different kind of difficulty.
Your statement mentions a programming project you built independently. Talk me through a design decision where you chose one approach over another, and what you would change if you rebuilt it now.
entryHint
Reward a specific trade-off (data structure, library, architecture) with honest reflection. Weak answers describe features; strong answers reason about alternatives and their consequences.
You say you enjoy mathematics as well as computing. Give me an example of a mathematical idea that changed how you think about a computing problem.
entryHint
Look for a genuine link, for example modular arithmetic behind hashing, graphs behind networks, or logic behind circuit design. The point is showing that maths is a tool they actually reach for.
You listed a book or article about computer science that you read beyond the syllabus. What claim in it did you find least convincing, and why?
midHint
This tests critical reading rather than name-dropping. A strong candidate can summarise an argument and then push back on it with a reason, not just praise the author.
You mention teaching yourself a topic outside your school curriculum. What was the hardest concept to grasp, and what finally made it click?
midHint
Probe metacognition: how they diagnose their own misunderstanding and what resource or reframing resolved it. This reveals independent-learning ability that a mathematically demanding course demands.
Imperial's degree is heavily theoretical and proof-oriented, not just coding. What in your experience so far suggests you will enjoy the mathematical side, not only building things?
hardHint
Test course fit honestly. The best answers cite a moment of pleasure in abstraction or proof, and acknowledge realistically that theory and engineering are different skills they are prepared to develop.
How many piano tuners are there in London? Reason it out loud; I care about the method, not the exact number.
midHint
A classic estimation problem: build up from population, pianos per household, tunings per year, and a tuner's annual capacity. Reward explicit assumptions and a sanity check at the end.
If I gave you access to every book ever written as plain text, how would you decide whether two of them were written by the same author, without being told anything about the authors?
midHint
Look for feature extraction: word-length distributions, function-word frequencies, sentence structure, then a similarity or clustering step. The insight is turning a fuzzy question into measurable quantities.
Suppose you could add one extra instruction to a computer's processor that does not currently exist. What would you choose, and what would break or become harder as a result?
hardHint
There is no right answer; the interviewer is testing whether the candidate reasons about trade-offs, for instance an instruction that speeds one task but complicates the hardware, security, or compiler. Reward awareness that every abstraction has a cost.
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Book Mock Interview →Watch & Learn
Helps applicants understand the Department of Computing learning environment and student perspective.
Useful for context on Imperial's campus and student life without presenting it as admissions evidence.
Applicant-facing context from the department's YouTube channel; use alongside official course pages.
Targets a common TMUA Paper 2 logic weakness; use as supplementary, not official, preparation.
General institutional context for applicants considering Imperial. Published September 2025, current for 2027 entry cycle.
All videos are the property of their respective creators.
Further Reading
by UAT-UK
Primary free resource for TMUA-style practice; historic papers remain useful because content specification and question style are unchanged.
by UAT-UK
Current source for TMUA dates, format, scoring, registration and candidate support.
by Imperial College London
Confirms which Imperial departments require TMUA and links applicants to registration/preparation guidance.
by Imperial College London
Canonical page for course structure, entry requirements and application details.
by Imperial College London
Explains the structured UCAS personal-statement prompts for 2027 entry.