Design dynamic connectivity with alive nodes
Company: DoorDash
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: Medium
Interview Round: Onsite
Design a data structure to maintain an undirected graph of N nodes, where each node has a boolean 'alive' flag. Support the following operations efficiently for up to 100,000 operations:
(
1) activate(i) / deactivate(i) to toggle a node's alive status;
(
2) connect(u, v) that adds an edge only if both endpoints are currently alive;
(
3) disconnect(u, v) to remove an existing edge;
(
4) isConnected(u, v) that returns whether u and v are in the same connected component considering only alive nodes; and
(
5) countComponents() over alive nodes. Describe data structures, time/space complexities, and how you would handle deletions and node deactivations (e.g., lazy deletion vs. fully dynamic connectivity). Discuss any concurrency considerations if these operations are called from multiple threads.
Quick Answer: This question evaluates understanding of dynamic graph data structures, connectivity algorithms, state management for node activation/deactivation, complexity analysis, and concurrent operation considerations.
Simulate alive-node graph operations and return outputs for connectivity/count queries.
Constraints
- Inputs are Python literals matching the function signature.
- Return a deterministic exact-match value.
Examples
Input: (4, [['activate',0],['activate',1],['connect',0,1],['isConnected',0,1],['countComponents'],['deactivate',1],['isConnected',0,1],['countComponents']])
Expected Output: [None, None, None, True, 1, None, False, 1]
Explanation: Alive filtering.
Input: (3, [['connect',0,1],['activate',0],['activate',1],['isConnected',0,1]])
Expected Output: [None, None, None, False]
Explanation: Connect ignored while endpoints dead.
Hints
- Use deterministic tie-breaking for prompts with multiple valid outputs.
- For design-style APIs, simulate operations with explicit inputs.