25 original quant programming interview questions with explained answers on algorithms, Python, data structures, numerical accuracy and reproducibility.
A quant implementation needs a clear contract: correct outputs, controlled numerical error and suitable performance on the intended workload. These examples combine algorithmic reasoning with Python behaviour, streaming calculations and numerical methods. State the input and data-structure assumptions whenever you give a complexity bound; expected, amortised and worst-case costs are different claims.
Clarify duplicate handling, index conventions, empty inputs and required precision. A fast implementation of an ambiguous contract is difficult to evaluate.
Explain which elements are visited and what state is retained. Include preprocessing and auxiliary space instead of quoting a complexity label alone.
Floating-point representation, convergence conditions and random-number generation affect the result. Use stable formulations and record enough context to reproduce a simulation.
Try each question before reading its answer. These original teaching examples remain free to read on this page.
Attach each complexity claim to its access pattern and assumptions.
A sorted random-access array contains n elements. What is binary search's worst-case comparison complexity?
Answer: O(log n).
Explanation: Each comparison discards about half the remaining interval. The random-access assumption matters when translating the method to another data structure.
Without preprocessing or additional structure, what is the worst-case time to find an item in an unsorted array of n elements?
Answer: O(n).
Explanation: An adversary can place the item last or omit it. Sorting or indexing introduces a different preprocessing and query trade-off.
Is a hash-table lookup guaranteed to take O(1) time?
Answer: No; average performance is often O(1), while worst-case behaviour depends on implementation and collisions.
Explanation: State the hashing and load assumptions. Expected performance is a different claim from a per-operation worst-case guarantee.
Why does general comparison sorting require Ω(n log n) comparisons in the worst case?
Answer: A comparison decision tree must distinguish n! input orders.
Explanation: A binary tree with n! leaves needs depth at least log₂(n!). Non-comparison methods rely on extra assumptions about keys.
What does stability mean for a sorting algorithm?
Answer: Records with equal sort keys retain their relative input order.
Explanation: Stability matters when prior ordering carries information or when performing several sorting passes. It is separate from speed and memory use.
Choose state that avoids repeated work while preserving the required output order.
How can you find two values summing to a target in an unsorted array using expected linear time?
Answer: Scan while storing previously seen values in a hash set; check the complement before inserting.
Explanation: Checking first prevents using the same position twice. Expected O(n) time costs O(n) auxiliary space under ordinary hashing assumptions.
How can you remove duplicate identifiers while preserving their first occurrence?
Answer: Scan in order, keep a set of seen identifiers and emit only the first unseen record.
Explanation: A set alone may lose required ordering across languages or implementations. Make the output-order contract explicit.
Two sorted arrays have lengths m and n. Give the time complexity of merging them into a sorted output.
Answer: O(m + n).
Explanation: Compare the current heads and advance one pointer. Each element is read and emitted at most once.
For a stream of n values with k much smaller than n, how can you retain the largest k?
Answer: Maintain a min-heap of size at most k.
Explanation: Replace the heap minimum when a larger value arrives. Processing takes O(n log k) time and O(k) space.
Which data structure validates balanced parentheses in a single pass?
Answer: A stack, or a depth counter for one bracket type.
Explanation: Opening brackets push and closing brackets must match the top. Reject premature closings and require an empty stack at the end.
A recurrence or rolling summary can replace repeated computation and reduce memory.
A staircase can be climbed in steps of size 1 or 2. If f(0) = f(1) = 1, give the recurrence for f(n).
Answer: f(n) = f(n − 1) + f(n − 2) for n ≥ 2.
Explanation: Classify paths by their final step. Retaining just the previous two counts gives O(n) time and O(1) auxiliary space.
How can many static inclusive array range-sum queries be answered in O(1) time after preprocessing?
Answer: Build prefix sums P with P[0] = 0; return P[r + 1] − P[l].
Explanation: O(n) preprocessing avoids rescanning each interval. The extra leading zero makes index boundaries explicit.
How can you update a moving mean of the last k values in O(1) time per observation?
Answer: Maintain the window sum, add the new value and subtract the outgoing value.
Explanation: A queue or ring buffer stores outgoing values. Handle the initial partial window separately and consider floating-point drift.
In Python, why can rows = [[0] * 3] * 2 be dangerous to mutate?
Answer: Both row entries refer to the same inner list.
Explanation: Changing one row changes the shared object visible through the other. A comprehension creates separate row lists.
Why use a Python generator when processing a very large file once?
Answer: It yields items lazily and can avoid storing the entire dataset.
Explanation: Memory savings depend on downstream consumers also streaming. Converting the generator immediately to a list removes that advantage.
Reason about object identity, iteration contracts and approximation errors separately.
Why is adding keys to a Python dictionary while iterating over it problematic?
Answer: Changing its size can raise a runtime error and invalidates the iteration contract.
Explanation: Iterate over a snapshot or collect updates for a later pass. Distinguish changing values from changing the set of keys.
A continuous function changes sign on an interval of width 1. How many bisection steps make the bracket width at most 1/1024?
Answer: 10.
Explanation: Each step halves the bracket, so its width becomes 2^(−k). Continuity and a sign change ensure a root remains bracketed.
State Newton's update for solving f(x) = 0.
Answer: x_next = x − f(x)/f′(x), when the derivative is nonzero.
Explanation: It follows the tangent line to its root. Convergence is local under suitable conditions; a small derivative can make the step unstable.
Why can subtracting nearly equal floating-point numbers lose relative accuracy?
Answer: Leading significant digits cancel, exposing rounding error in the small difference.
Explanation: Look for an algebraically equivalent stable form. More decimal output does not restore lost information.
Why can adding many tiny values to a large floating-point accumulator lose contributions?
Answer: Some increments are below the accumulator's representable spacing.
Explanation: Pairwise or compensated summation can reduce error. The issue is arithmetic precision, not the mathematical commutativity of addition.
Use workload measurements, explicit edge cases and reproducibility to connect an algorithm to a dependable implementation.
Why might an O(n²) algorithm beat an O(n log n) algorithm on a very small input?
Answer: Constant factors, setup cost and memory access can dominate at small n.
Explanation: Asymptotic notation describes growth, not a stopwatch result for every input. Benchmark the realistic workload after checking correctness.
What edge cases deserve attention in a binary-search implementation?
Answer: Empty and one-element arrays, absent targets, endpoints, duplicates and the chosen return contract.
Explanation: These expose interval and off-by-one mistakes. Define whether duplicates return any, first or last matching position.
What should you record to reproduce a stochastic computation?
Answer: The seed, generator and version, inputs, algorithm and relevant environment.
Explanation: A seed alone does not fix changing code, data or generator behaviour. Parallel execution can also alter draw order.
Two workers read a counter, increment locally and write it back. What can go wrong?
Answer: An update can be lost because both workers read the same old value.
Explanation: The read-modify-write sequence needs synchronisation or an atomic operation. Independent-looking instructions do not make the sequence atomic.
Before optimising a pricing routine, what should you clarify?
Answer: Required accuracy, valid inputs, error behaviour, workload and latency or throughput objective.
Explanation: Optimisation needs a measurable target and correctness boundary. A faster routine with uncontrolled numerical error does not satisfy a pricing contract.
Each question has its own page with a short answer and a credit to its source. Hints and full worked solutions are in the question bank with a free account.
Our bank summary dated contains 69 Programming/Algorithms entries in the bank. Counts describe entries in our curated practice bank, including its source and classification choices. They do not measure employer interview frequency, candidate success rates or how often any one question is asked.
The public examples above were written for these guides. They illustrate the techniques and are not a reproduction or ranking of the bank's sourced questions. The dashboard's broader bank combines sourced questions, worked answers where available and references for book entries without a reproduced solution.
| Subtopic | Bank entries |
|---|---|
| C++ | 31 |
| Algorithms | 18 |
| Numerical Methods | 11 |
| Sorting & Searching | 6 |
| Data Structures | 2 |
| Dynamic Programming | 1 |
Bank difficulty labels: 49 easy · 20 medium.
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