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Qube Research & Technologies·Software Engineer·Onsite - Coding / Algorithms·Senior

SeniorPrefer not to say
Jun 2026

Summary

Two pretty dense technical problems for a software engineering role at Qube RT. The flat_map question was a full design-and-implement exercise and the wealth redistribution one was more algorithmic with a proof requirement. Felt like a take-home or a very long onsite coding session.

Questions Asked (2)

Q1

Design and implement a flat_map container backed by a sorted array of key-value pairs, supporting the full standard associative container API including iterators, insert/erase, copy/move semantics, and equality comparison. Explain your design choices and complexity trade-offs compared to tree-based maps.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

This was a lot.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements and constraints, then outline the core data structure (sorted array of key-value pairs) and how it supports the full associative container API. Discuss the design choices, including iterator invalidation, complexity trade-offs, and when a flat_map is preferable to tree-based maps.

Pro tip: Emphasize that flat_map excels for small to medium-sized containers due to cache locality and low memory overhead, but degrades for frequent insertions/deletions. Mention that many standard libraries (e.g., Boost, Abseil) provide flat_map implementations, so referencing real-world usage shows practical awareness.

1. Clarify Requirements and Constraints

Ask about expected container size, operation frequency, and performance priorities to tailor the design. Confirm that the API must match std::map, including iterators, insert/erase, copy/move, and equality.

2. Design the Core Data Structure

Choose a sorted dynamic array (e.g., std::vector) of key-value pairs. Explain how to maintain sorted order via binary search for lookup and insertion position, and how to handle duplicates (if allowed).

3. Implement the Associative Container API

Detail iterator design (random-access, const and non-const), insert/erase operations (shifting elements), and special member functions (copy/move, equality). Discuss exception safety and allocator awareness.

4. Analyze Complexity and Trade-offs

Compare time complexities: O(log n) lookup, O(n) insert/erase due to shifting, versus O(log n) for tree-based maps. Highlight memory and cache benefits, and when flat_map is advantageous.

5. Summarize and Conclude

Recap key design decisions, mention potential optimizations (e.g., bulk construction, hinted insert), and state appropriate use cases for flat_map versus tree-based maps.

Key Points to Mention

  • Sorted array storage with binary search for O(log n) lookup
  • Insert/erase require O(n) shifting, but can be optimized with bulk operations
  • Iterator invalidation rules: insert/erase invalidate iterators at or after the modification point
  • Memory efficiency and cache locality compared to node-based trees
  • Copy/move semantics and equality comparison implementation
  • Use cases: small containers, read-heavy workloads, or when memory is constrained

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.

Q2

Given an array of integers representing individual wealth (can be negative, zero, or positive), design an algorithm to redistribute wealth through pairwise integer transfers so that the final values are as equal as possible. Define your objective formally, determine the optimal target value under integer constraints, output the transfer sequence, and prove correctness with complexity analysis.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The 'define your objective' part tripped me up more than the algorithm itself.

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AI HintsAI Generated

Suggested Approach

Start by formally defining the objective as minimizing the maximum absolute deviation from a target value, then determine the optimal integer target by considering the sum modulo n. Design a greedy algorithm that repeatedly transfers from the wealthiest to the poorest until all are within one unit of the target, and prove its correctness by showing each transfer reduces the total deviation.

Pro tip: Emphasize that the optimal target is either floor(avg) or ceil(avg) depending on the remainder, and that the greedy approach achieves the minimum number of transfers. Also, discuss how to handle negative wealth and ensure the algorithm terminates efficiently.

1. Formalize the objective

Define the goal as minimizing the maximum absolute difference between any final wealth and a target value, or equivalently minimizing the sum of absolute deviations. Note that the target must be an integer, and the total sum is invariant.

2. Determine the optimal target

Compute the total sum S and n = length of array. The optimal target is either floor(S/n) or ceil(S/n). If S is divisible by n, the target is S/n; otherwise, some elements will be floor(S/n) and others ceil(S/n) to minimize deviation.

3. Design the redistribution algorithm

Use a greedy approach: repeatedly find the current maximum and minimum wealth, transfer 1 unit (or the minimum of excess and deficit) from max to min, and update. Continue until all values are within 1 of the target. This ensures each transfer reduces the total absolute deviation.

4. Prove correctness and analyze complexity

Prove that the greedy algorithm achieves the minimum possible maximum deviation by showing that any transfer from a surplus to a deficit reduces the sum of absolute deviations, and the algorithm terminates when no further reduction is possible. Analyze time complexity: naive implementation O(n^2) or O(n log n) with heaps, and space O(n).

Key Points to Mention

  • The objective is to minimize the maximum absolute deviation from the target, not necessarily to make all values equal if the sum is not divisible by n.
  • The optimal target is either floor(avg) or ceil(avg), and the choice depends on the remainder when sum is divided by n.
  • Greedy transfer from richest to poorest is optimal because it reduces the total absolute deviation by 2 per unit transferred (or 1 if only one unit needed).
  • The algorithm terminates in at most the total surplus (sum of positive deviations) transfers, which is bounded by n * max_deviation.
  • Complexity can be improved to O(n log n) using a max-heap and min-heap, or O(n) if using a two-pointer approach after sorting.
  • Edge cases: all zeros, all equal, negative wealth, and large n require careful handling to avoid infinite loops.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.