Meta·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Meta coding interview with a graph or greedy problem about minimizing water supply costs across a village. Not much context on how it went but the problem itself is a classic minimum spanning tree type setup.

Questions Asked (1)

Given a village with multiple houses, find the minimum total cost to supply water to all of them.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This is a minimum spanning tree problem in disguise, but the twist is usually that you can also build a well at any house, so you have to model that as a virtual node connected to every house.

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AI HintsAI Generated

Suggested Approach

Model the problem as a graph where houses are nodes and potential pipes are weighted edges, then find the Minimum Spanning Tree (MST) using Prim's or Kruskal's algorithm. Clarify whether wells are available (each house can have its own well with a cost) and if so, add a virtual node representing the water source connected to each house with the well cost. If no wells, the graph is complete with pipe costs between all pairs of houses.

Pro tip: Always discuss the trade-offs between Prim's and Kruskal's algorithms based on graph density and implementation complexity, and mention that using a priority queue (heap) can optimize Prim's to O(E log V). Also, proactively ask about constraints (e.g., number of houses, whether wells are allowed) to show thoroughness.

1. Clarify the problem

Ask clarifying questions: Are wells allowed? If so, what are their costs? Are pipe costs symmetric? What are the constraints on the number of houses? This ensures you understand the exact problem.

2. Model as a graph

Represent houses as nodes. If wells are allowed, add a virtual node representing the water source, with edges to each house weighted by the well cost. Add edges between houses weighted by pipe costs. If no wells, the graph is complete with pipe costs.

3. Choose MST algorithm

Decide between Prim's and Kruskal's based on graph density and constraints. Prim's with a priority queue is efficient for dense graphs; Kruskal's with union-find is good for sparse graphs. Explain your choice.

4. Implement and analyze

Outline the algorithm steps, including data structures (e.g., priority queue, union-find). Analyze time and space complexity, and discuss potential optimizations.

5. Test and validate

Walk through a small example to verify correctness. Discuss edge cases (e.g., single house, no wells, disconnected graph) and how to handle them.

Key Points to Mention

Minimum Spanning Tree (MST) concept and why it applies to this problem.
Prim's algorithm: start from any node, grow MST by adding cheapest edge connecting to a new node; use priority queue for efficiency.
Kruskal's algorithm: sort edges by weight, add if they don't form a cycle; use union-find for cycle detection.
Virtual node technique for incorporating well costs as edges from a super-source.
Time complexity: O(E log V) for Prim's with binary heap, O(E log E) for Kruskal's; space complexity O(V + E).
Trade-offs: Prim's better for dense graphs, Kruskal's better for sparse graphs; implementation complexity and memory considerations.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.