Identify members lacking specialty coverage
Company: DoorDash
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Onsite
# Identify members lacking specialty coverage
Oscar wants to ensure that every insurance member has adequate access to in-network healthcare providers within a reasonable travel distance.
You are given:
- A list of **providers**, where each provider has:
- `id`: an integer provider ID
- `specialty`: a string (e.g., `"Cardiology"`, `"Dermatology"`)
- `location`: a 2D coordinate `(x, y)` representing the provider’s location
- A list of **members**, where each member has:
- `id`: an integer member ID
- `location`: a 2D coordinate `(x, y)` representing the member’s location
- `required_specialties`: a list of strings indicating the specialties this member needs
- A number `max_distance` (float or integer), which is the maximum allowed travel distance.
Assume **Euclidean distance** between two points `(x1, y1)` and `(x2, y2)`:
\[
\text{distance} = \sqrt{(x1 - x2)^2 + (y1 - y2)^2}
\]
A member has **adequate coverage** if, for **every** specialty in their `required_specialties`, there exists **at least one provider** with that specialty whose distance from the member is **less than or equal to** `max_distance`.
A member **lacks adequate coverage** if there is **at least one required specialty** for which no such provider exists within `max_distance`.
**Task**:
Write a function that, given `providers`, `members`, and `max_distance`, returns a list of the IDs of all members who **lack adequate coverage**.
You may return the member IDs in any order.
---
**Example**
```python
providers = [
{"id": 1, "specialty": "Cardiology", "location": (1, 2)},
{"id": 2, "specialty": "Dermatology", "location": (3, 4)},
]
members = [
{"id": 101, "location": (2, 3), "required_specialties": ["Cardiology", "Dermatology"]},
{"id": 102, "location": (10, 10), "required_specialties": ["Cardiology"]},
]
max_distance = 5
```
Distances:
- Member 101 to provider 1 (Cardiology):
- distance = \(\sqrt{(2-1)^2 + (3-2)^2} = \sqrt{2} \approx 1.41\) ≤ 5
- Member 101 to provider 2 (Dermatology):
- distance = \(\sqrt{(2-3)^2 + (3-4)^2} = \sqrt{2} \approx 1.41\) ≤ 5
- Member 102 to provider 1 (Cardiology):
- distance = \(\sqrt{(10-1)^2 + (10-2)^2} = \sqrt{145} \approx 12.04\) > 5
So member 101 has adequate coverage for all required specialties, but member 102 does not.
**Expected output**:
```python
[102]
```
### Constraints & Assumptions
- Preserve the scope, facts, inputs, and requested outputs from the prompt above.
- If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
- Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.
### Clarifying Questions to Ask
- Clarify input sizes, value ranges, mutability, return format, and tie-breaking.
- State the target time and space complexity before coding.
- Call out edge cases such as empty inputs, duplicates, invalid values, overflow, and boundary sizes.
### What a Strong Answer Covers
- A clear algorithm with the right data structures and enough pseudocode or code-level detail to implement it.
- A correctness argument that explains why the algorithm covers all required cases.
- Time and space complexity, plus at least one alternative approach when relevant.
- Focused tests for normal cases, edge cases, and failure modes.
### Follow-up Questions
- How would the approach change if the input were streaming or too large for memory?
- What invariants would you assert in production code?
- Which tests would catch off-by-one, duplicate, or tie-breaking bugs?
Quick Answer: Identify members lacking specialty coverage evaluates algorithm design, data structures, correctness, complexity, edge cases, and implementation details in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.
Solution
# Solution Alignment
The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests.
## Problem Restatement
Oscar wants to ensure that every insurance member has adequate access to in-network healthcare providers within a reasonable travel distance. You are given: - A list of **providers**, where each provider has: - `id`: an integer provider ID - `specialty`: a string (e.g., `"Cardiology"`, `"Dermatology"`) - `location`: a 2D coordinate `(x, y)` representing the provider’s location - A list of **members**, where each member has: - `id`: an integer member ID - `location`: a 2D coordinate `(x, y)` representing the member’s location - `required_specialties`: a list of strings indicating the specialties this member needs - A number `max_distance` (float or integer), which is the maximum allowed trave...
## Recommended Approach
Use the string constraints to choose between two pointers, a stack, frequency counts, prefix/suffix state, or dynamic programming. Maintain the invariant that processed characters have already been normalized, counted, or matched according to the operation.
## Correctness
The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call.
## Complexity
Most direct string scans are O(n) time. Space ranges from O(1) for two pointers to O(n) for stacks, maps, or DP tables.
## Edge Cases and Tests
Empty string, length 1, repeated characters, invalid characters, case sensitivity, Unicode vs ASCII, and very long input.