Summary
Robinhood software engineer coding round with two problems, both heavier on implementation than I expected. The calendar layout one especially had more edge cases than it looked like at first glance.
Questions Asked(2)
This one looked manageable until I started thinking about what 'group' actually means when you have chains of overlapping events.
Suggested Approach
Model this as a graph coloring / interval scheduling problem: sort events by start time, then use a greedy column-assignment pass to place each event in the earliest available column that doesn't conflict with an already-placed overlapping event. After assigning columns, do a second pass to compute the total columns needed per overlap group by identifying connected components of mutually overlapping events.
Clarify Assumptions & Define Overlap
Ask whether events whose end time equals another's start time are considered overlapping (typically they are not). Confirm the output format — column index (0-based) and total columns for the group — and whether events are guaranteed to be within a single day.
Sort Events by Start Time
Sort all events by their start time (break ties by end time) to enable a single left-to-right sweep. This O(n log n) step is the foundation for the greedy assignment.
Greedy Column Assignment
Maintain a list of columns, each tracking the latest end time of the event placed there. For each event, assign it to the first column whose latest end time is ≤ the event's start time; if none exists, open a new column. Record each event's assigned column index.
Identify Overlap Groups & Compute Total Columns
Group events into clusters of mutually overlapping intervals (connected components): sweep through sorted events and merge an event into the current cluster if it starts before the cluster's running max end time, otherwise start a new cluster. The total columns for every event in a cluster equals the maximum column index used within that cluster plus one.
Return Results & Analyze Complexity
Construct and return the result array with each event's column index and total columns. State the overall time complexity as O(n log n) due to sorting, and O(n) space for the column tracking structures.
Key Points to Mention
Part A was fine, pretty mechanical.
Suggested Approach
Break the problem into two clearly defined parts: Part A establishes the feasibility check (greedy placement into any valid row), while Part B adds an optimization layer using a priority queue or sorted selection to always pick the row with maximum remaining capacity. Implement Part A first to validate correctness, then extend it with the tie-breaking selection logic for Part B.
Clarify Constraints and Examples
Confirm that there are always exactly 3 rows, each with a fixed but potentially different max width, and ask for an example input/output to align on edge cases like strings that exceed all row capacities or empty string lists.
Model the State
Represent each row as a tuple or object tracking its index, max width, and remaining capacity. Initialize remaining capacity equal to max width for all three rows before processing begins.
Implement Part A — First-Fit Feasibility
Iterate through strings in order; for each string, scan the three rows and place it into the first row with sufficient remaining capacity, updating that row's remaining space. If no row can fit the string, report failure immediately.
Implement Part B — Best-Fit with Tie-Breaking
Extend Part A by selecting the row with the maximum remaining capacity before placement; use a max-heap keyed on remaining space (negated for Python's min-heap) with row index as the tie-breaker to efficiently find the optimal row in O(log 3) = O(1) time.
Return Results and Validate
After processing all strings, return the placement mapping (string → row index) and the final remaining capacity per row. Walk through your example to verify correctness, and discuss time complexity: O(n) for Part A and O(n log 3) ≈ O(n) for Part B.
Key Points to Mention
Discussion(2)
Sign in to join the discussion.
The grouping step is where this problem actually lives, and you're right that pairwise overlap checks aren't enough. The key insight I'd push on is that a 'group' here is really a connected component: if event A overlaps B, and B overlaps C, all three are in the same group even if A and C don't touch each other. So before you even think about column assignment, you want to build an adjacency structure and do a union-find or BFS pass to identify those components. Once you have clean component boundaries, the column assignment within each component is exactly greedy interval graph coloring: sort by start time, maintain a list of columns and what their last end time was, and for each event grab the first column whose last end time is at or before the current event's start. The total columns for that component is just the max column index you ended up using. The thing that makes this feel harder than it is at an onsite is that 'total columns needed for its overlap group' has to be computed per component and then stamped back onto every event in that component, so you need a second pass after you've processed everything. I made the mistake once of trying to emit the column count on the fly and got inconsistent answers for events processed early in a component before I knew how wide the component would get. Separate the two concerns: first assign columns greedily, then sweep back through each component to find its max column and annotate. The Robinhood version of this is essentially what Google Calendar does under the hood, so framing it that way in the interview can help you talk through the design intent while you're coding.
Part B is basically just a sorted insertion with a custom comparator. Read the tie-breaking rule twice before writing a single line.