This one wrecked me more than I want to admit.
Start by clarifying the ambiguous formats and assumptions (e.g., two-digit year mapping, timezone defaults) before diving into the algorithm. Then outline a modular pipeline: parsing and validation, normalization to UTC ISO 8601, and business-day difference calculation with weekend/holiday exclusion. Emphasize edge cases like leap years, DST transitions, and invalid inputs, and discuss trade-offs between using built-in libraries versus custom logic.
Pro tip: Mention that you would use a battle-tested library like dateutil or pandas for parsing, but implement the business-day logic manually to handle custom holidays and ensure auditability—this shows you balance efficiency with control, which is crucial in finance.
Ask about ambiguous formats (e.g., MM/DD vs DD/MM), two-digit year mapping (e.g., 00-68 -> 2000-2068, 69-99 -> 1969-1999), timezone defaults, and the fixed holiday set. Confirm that invalid inputs should raise errors.
Use a robust parser (e.g., dateutil) with explicit format hints, validate dates (leap years, month/day ranges), and handle timezone offsets. Return errors for unparseable or invalid dates.
Convert parsed datetimes to UTC, then format as ISO 8601 strings (e.g., 'YYYY-MM-DDTHH:MM:SSZ'). Ensure consistency and handle DST transitions correctly.
Given two normalized dates, calculate the number of business days between them, excluding weekends and the fixed holiday set. Use a loop or vectorized approach, and consider performance for large ranges.
Test with edge cases (leap years, ambiguous formats, timezone conversions) and discuss trade-offs: library vs custom code, performance vs accuracy, and handling of holidays.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Classic DP but the state space constraint is what makes it annoying.
Model the problem as an integer linear program (ILP) where decision variables represent the number of each bundle and individual item purchased. Use a solver or dynamic programming to find the minimum cost solution that exactly meets all target quantities, ensuring no oversupply. Return the cost and the combination, or -1 if infeasible.
Pro tip: In a hedge fund context, emphasize that you would first validate the problem's feasibility and consider the trade-off between exact ILP solutions and faster heuristics, especially if the problem size grows or real-time decisions are needed.
Let x_j be the number of times bundle j is used, and y_i be the number of individual units of item i purchased. Constraints: for each item i, sum over bundles containing i of (quantity in bundle * x_j) + y_i = target_i, and all variables are non-negative integers.
Minimize total cost = sum over bundles of (bundle price * x_j) + sum over items of (unit price_i * y_i).
For small instances (up to 6 item types), use an ILP solver (e.g., PuLP, OR-Tools) or dynamic programming. If the number of bundles is large, consider branch-and-bound or column generation.
If the solver finds no feasible solution, return -1. Otherwise, extract the optimal cost and the corresponding values of x_j and y_i to report the combination.
Mention that for larger problems, exact methods may be slow, so heuristics (e.g., greedy, local search) or approximations could be used, but they may not guarantee optimality. Also note that the problem is NP-hard in general.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Geometry problems always make me nervous and this was no exception.
Start by defining the seven states clearly and the conditions that distinguish them using squared distances. Then outline an algorithm that computes squared distance between centers, compares with squared radii sums/differences, and handles epsilon for near-tangency. Finally, describe how to compute intersection points when the circles intersect at two points.
Pro tip: Emphasize that using squared distances avoids square roots and precision loss, and that epsilon should be relative to the scale of the inputs to handle floating-point comparisons robustly.
List the states: separate, touching externally, intersecting, one inside another (non-concentric), internally tangent, concentric (different radii), concentric equal. Clearly state the geometric conditions for each.
Compute squared distance between centers (d²) and squared radii (r1², r2²). Compare d² with (r1+r2)² and (r1-r2)² to classify without square roots.
Introduce a small epsilon to treat cases where d² is close to (r1+r2)² or (r1-r2)² as tangent. Use relative epsilon based on the magnitude of the values to avoid scale issues.
For intersecting circles, calculate the intersection points using the standard formula: find the distance from center1 to the radical line, then offset along the perpendicular. Return coordinates.
Test with concentric equal circles, one circle inside another, external tangency, and near-tangency. Ensure epsilon handling does not misclassify distinct states.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.