You are given a 1D array where each element is 0 (empty), 1 (person), or 2 (cake).
Part 1 (base): Find the minimum distance between any person and any cake in the array. Some variants ask: given a specific person's index, find the nearest cake to that person.
Part 2 (follow-up / global assignment): Assign each person to exactly one cake so that the total (or maximum) distance is globally minimized — a bijective matching. Specifically, if multiple people are closest to the same cake, the cake is assigned to the person with the smallest distance; other people must find their next-best cake. The problem guarantees no two people are equidistant from the same cake and no two cakes are equidistant from the same person (so the assignment is unique). Given a specific person's index, determine which cake that person ends up eating under this globally optimal assignment.
Constraints discussed: O(n) time for Part 1. The array is 1D (some reports initially describe 2D but clarify it is 1D). Ties in distance are broken by smallest distance; no ties guaranteed in some problem variants.
What are all the edge cases you need to handle?
Now consider global assignment: if multiple people want the same cake, it goes to the closest person. Given a specific person's index, which cake do they get under this globally optimal assignment? (when: Candidate solves Part 1 (minimum distance, single person to nearest cake))
Can you solve this in O(n) time? (when: Candidate solves with a simple approach (e.g., O(n log n) priority queue))
Can you optimize space complexity? Interviewer specifically mentioned DP approach.
How would you implement this if elements arrive as a stream (online/streaming variant)?
| Approach | Notes |
|---|---|
| Priority Queue / Min-Heap for global assignment | Enumerate all person-cake distances, insert into a min-heap, then greedily pop and assign while skipping already-matched persons/cakes. Correct but O(P*C * log(P*C)) — worse than the sorted greedy O(n log n) approach. |
| DP + sliding window | One report mentions interviewer pushed for DP optimization of the single-person closest-cake query, achieving O(n) space with DP + sliding window. Overkill for the base problem but may satisfy interviewers who specifically ask for DP framing. |
| Two-pass linear scan (left-to-right + right-to-left) | For the per-person closest-cake query: scan left and right from person index, return the first cake found in either direction. Simple and O(n) but only solves Part 1, not global assignment. |
| BFS (for 2D variant) | If the grid is 2D, multi-source BFS from all cakes simultaneously gives minimum distance to nearest cake for every cell. Correct for 2D but not the primary variant (which is 1D). |
Common mistakes: Returning the naively closest cake to the given person without checking if another person has an even shorter distance to that same cake — this misses the global assignment requirement and was the reported reason candidates failed the follow-up.; Using a priority queue for the global assignment, which runs O(n log n) and fails the O(n) bar the interviewer asked for.; Spending too long debugging the base problem, leaving no time to attempt the global assignment follow-up.
Interviewer hints: When a candidate was explaining their approach, the interviewer directly interrupted to ask whether space complexity could be optimized using DP, steering toward a DP plus sliding window solution.; The problem statement guarantees no two people are equidistant from the same cake and no two cakes are equidistant from the same person, meaning the assignment is unique — interviewers stated this constraint explicitly to remove ambiguity.
What passers do: Candidates who passed recognized that even when given a single person's index, the global assignment must be solved for all people first before answering which cake that person gets.; Solving the base problem with two linear passes (left-to-right and right-to-left) was the expected O(n) approach and candidates who presented this did well.; Candidates who proactively wrote test cases and ran them in the provided IDE environment aligned with what the interviewer expected.
Why people fail: Failing the follow-up (global assignment) after passing Part 1 — this was explicitly cited as a reason for failure; Implementing naive greedy (nearest available cake per person) without recognizing it is suboptimal; Debugging too long on Part 1, running out of time for follow-ups; Unable to produce a correct solution even after extended discussion / 30-minute 'brainstorming' session with interviewer
Edge cases probed: Multiple people equidistant to the same cake — who gets it? (Problem statement guarantees this won't happen, but interviewer probed candidate's awareness); Array like {1, 1, 2, 2}: second person is closer to first cake, so first cake goes to second person; first person gets second cake — naive greedy fails; No people or no cakes in array; Person at boundary (index 0 or last index); Adjacent person and cake (distance = 1); All positions are the same type (all people, no cakes, or vice versa)
What you just read — canonical solution, follow-up arc, what passing candidates actually did — exists for all 103 Snowflake questions, refreshed monthly from new candidate reports.