← Capital One Interview Insights
The greedy insight is to sort employees by cost and fill the cheapest ones first, only pulling in contractors once you've exhausted cheaper options.
Model the problem as a min-cost selection: each employee offers up to cap hours at their rate, and contractors offer unlimited hours at a fixed rate. Sort all available hour-blocks by rate, greedily take the cheapest hours until H is met, and prove optimality via an exchange argument. Implement with a priority queue or sorting to achieve O(n log n).
Pro tip: Explicitly state the greedy choice property and exchange argument—interviewers at Capital One value rigorous correctness proofs as much as the algorithm itself. Also, clarify edge cases like insufficient total capacity or ties in rates.
Confirm that employee overtime hours are capped per employee, contractor hours are unlimited at a fixed rate, and we must exactly meet H hours. Ask about tie-breaking or if fractional hours are allowed.
Represent each employee as a supply of up to cap_i hours at rate r_i, and contractors as unlimited supply at rate r_c. The goal is to select H hours minimizing total cost.
Sort all employee rate-capacity pairs by rate ascending; treat contractor rate as a fallback. Greedily allocate hours from the cheapest source until H is reached, using a priority queue if needed.
Use an exchange argument: any optimal solution can be transformed into the greedy solution without increasing cost, because replacing a more expensive hour with a cheaper available hour reduces cost.
Sorting takes O(n log n); allocation takes O(n) with a simple loop or O(n log n) with a heap. Provide pseudocode or actual code, and discuss handling insufficient capacity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, restate the original algorithm and its complexity to establish a baseline. Then, explain how to incorporate per-employee tiered rates by splitting each employee's hours into two segments and applying different rates, and how to enforce a global cap on contractor hours by adding a constraint that may require sorting or a greedy approach. Finally, analyze the new time and space complexity, highlighting any additional sorting or data structures needed.
Pro tip: Emphasize that the global cap introduces a resource allocation problem that may require a greedy strategy or dynamic programming, and discuss trade-offs between optimality and efficiency. Mention that in practice, such constraints often lead to a knapsack-like problem, so clarifying assumptions about whether hours are divisible or not is crucial.
Briefly describe the original algorithm for calculating overtime without tiered rates or global caps, including its time and space complexity.
Explain that for each employee, you split their hours into two parts: up to t[i] hours at the lower rate and any remaining hours at the higher rate. This can be done in O(1) per employee, so overall O(n) for n employees.
Introduce a global constraint that the total hours assigned to contractors cannot exceed a cap. This may require prioritizing which contractors get hours based on cost or other criteria, potentially involving sorting or a greedy algorithm.
Determine the new time and space complexity. If sorting is needed to allocate hours under the cap, complexity may increase to O(n log n). If a more complex optimization is required (e.g., knapsack), it could be pseudo-polynomial or exponential, so discuss trade-offs.
Mention assumptions such as whether hours are divisible, whether the cap applies to all contractors or a subset, and how the algorithm behaves if the cap is exceeded. Highlight potential alternative approaches and their implications.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sort by rate: employee 2 at 35, employee 4 at 45, contractor at 50, employee 1 at 55, employee 3 at 60.
First, clarify the problem: we need to allocate H=120 hours among employees and contractors to minimize total cost, given each employee's capacity and rate, and contractor rate=50. Then, model it as a cost minimization problem: use employees with rates below 50 first, up to their capacities, and fill remaining hours with contractors. Finally, compute the total cost and verify that all constraints are satisfied.
Pro tip: Always state your assumptions and walk through the logic step-by-step, even if you can compute the answer mentally. This demonstrates structured thinking and ensures the interviewer can follow your reasoning.
Identify that H=120 hours must be allocated, each employee has a maximum capacity, and contractors can work unlimited hours at rate 50. The goal is to minimize total cost.
List employee rates: 55, 35, 60, 45. Compare each to the contractor rate of 50. Employees with rates below 50 (35 and 45) are cheaper; those above (55 and 60) are more expensive.
Assign as many hours as possible to the cheapest employee (rate 35) up to their capacity (20 hours), then to the next cheapest (rate 45) up to their capacity (12 hours). This uses 32 hours total.
After using 32 hours, 88 hours remain. The next cheapest option is contractors at rate 50, so assign all remaining 88 hours to contractors.
Calculate total cost: (20*35) + (12*45) + (88*50) = 700 + 540 + 4400 = 5640. Verify that total hours sum to 120 and no capacity is exceeded.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.