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Find valid split-stay listing combinations

Q: Find valid split-stay listing combinations

This question evaluates a candidate's ability to manipulate intervals and set-based availability data, reason about contiguous date ranges, and enumerate valid single-listing and ordered two-listing split combinations.

Company: Airbnb

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: hard

Interview Round: Technical Screen

You are building a feature that suggests a **split stay**: a guest stays in one home for the first part of a trip, then switches to a second home for the remainder. You are given: - A map `availability` from **listing name** (e.g., "A", "B") to a list of **available day numbers** (integers). - A requested **date range** `[startDay, endDay]` inclusive. Return **all valid split-stay options**: 1) **Single-listing stay**: any listing that is available for **every day** in `[startDay, endDay]`. 2) **Two-listing split stay**: any ordered pair `(L1, L2)` for which there exists a split day `k` with `startDay <= k < endDay` such that: - `L1` is available for every day in `[startDay, k]`, and - `L2` is available for every day in `[k+1, endDay]`. Notes / clarifications: - Availability is per-day; treat it as a set (duplicates don’t matter). - A listing may appear in at most one position within a split option (i.e., `L1 != L2`). - Output can be in any order; avoid duplicates. Example: - `A = [1,2,3,6,7,10,11]` - `B = [3,4,5,6,8,9,10,13]` - `C = [7,8,9,10,11]` - Query range: `[3, 11]` Determine which single listings and/or two-listing split stays satisfy the rules above.

Quick Answer: This question evaluates a candidate's ability to manipulate intervals and set-based availability data, reason about contiguous date ranges, and enumerate valid single-listing and ordered two-listing split combinations.

You are given a dictionary `availability` where each key is a listing name and each value is a list of available day numbers. You are also given `startDay` and `endDay` for a requested trip, inclusive. Return all valid stay options in the form `{'single_stays': [...], 'split_stays': [...]}`. A single stay is any listing available for every day in `[startDay, endDay]`. A split stay is any ordered pair `[L1, L2]` with `L1 != L2` such that there exists a split day `k` where `startDay <= k < endDay`, `L1` is available for every day in `[startDay, k]`, and `L2` is available for every day in `[k + 1, endDay]`. Treat each availability list as a set, so duplicates do not matter. To make the output deterministic, return `single_stays` sorted lexicographically and `split_stays` sorted lexicographically by first listing name, then second listing name. For the example in the prompt, the correct result is `{'single_stays': [], 'split_stays': [['B', 'C']]}`.

Constraints

0 <= len(availability) <= 200
All day numbers, `startDay`, and `endDay` are integers, and `startDay <= endDay`
0 <= total number of availability entries across all listings <= 2 * 10^4
`endDay - startDay <= 365`
Availability lists may be unsorted and may contain duplicates

Examples

Input: ({'A': [1, 2, 3, 6, 7, 10, 11], 'B': [3, 4, 5, 6, 8, 9, 10, 13], 'C': [7, 8, 9, 10, 11]}, 3, 11)

Expected Output: {'single_stays': [], 'split_stays': [['B', 'C']]}

Explanation: No listing covers every day from 3 through 11. Listing B covers 3 through 6, and listing C covers 7 through 11, so splitting after day 6 gives the only valid ordered pair.

Input: ({'A': [1, 2, 3, 4], 'B': [3, 4], 'C': [1, 2], 'D': [1, 2, 3, 4, 4]}, 1, 4)

Expected Output: {'single_stays': ['A', 'D'], 'split_stays': [['A', 'B'], ['A', 'D'], ['C', 'A'], ['C', 'B'], ['C', 'D'], ['D', 'A'], ['D', 'B']]}

Explanation: A and D each cover the whole range alone. C can cover the first half and B the second half, and full-range listings A and D can also be used on one side of a split. Ordered pairs matter, so validity depends on which listing comes first.

Input: ({'Loft': [5, 5, 3], 'Cabin': [4, 5], 'Studio': []}, 5, 5)

Expected Output: {'single_stays': ['Cabin', 'Loft'], 'split_stays': []}

Explanation: The trip is only one day long, so there is no possible split day. Cabin and Loft are both available on day 5, so they are valid single stays.

Input: ({'X': [-2, -1], 'Y': [1, 2], 'Z': [-2, 0, 1]}, -2, 1)

Expected Output: {'single_stays': [], 'split_stays': [['X', 'Z']]}

Explanation: Negative day numbers are allowed. X covers days -2 and -1, while Z covers days 0 and 1, so splitting after day -1 makes `[X, Z]` valid. No single listing covers the whole range.

Input: ({}, 1, 3)

Expected Output: {'single_stays': [], 'split_stays': []}

Explanation: With no listings, there are no possible single stays or split stays.

Hints

For each listing, precompute how far it can continuously cover from `startDay` and how far it can continuously cover backward from `endDay`.
A pair `[L1, L2]` is valid if `L1`'s prefix coverage reaches at least one day before `L2`'s suffix coverage starts.

Quick Overview

This question evaluates a candidate's ability to manipulate intervals and set-based availability data, reason about contiguous date ranges, and enumerate valid single-listing and ordered two-listing split combinations.