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Instacart·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Went through a technical phone screen for a software engineer role at Instacart. It was a graph problem dressed up as a math problem, which I thought was a clever framing.

Questions Asked (1)

Q1

You're given a list of equations like A / B = k, where each equation is a pair of variables and a numeric result. Given a set of queries asking for the value of C / D, evaluate each one using the known equations. Return -1.0 for any query that can't be determined.

Algorithms & Data Structures
Author's notes

My first instinct was to treat it as a pure math problem and I wasted probably two minutes going down that path before realizing the variables form a graph.

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AI HintsAI Generated

Suggested Approach

Model the equations as a directed graph where each variable is a node and each equation A / B = k creates edges A→B with weight k and B→A with weight 1/k. For each query C / D, perform a graph traversal (DFS or BFS) from C to D, multiplying edge weights along the path; if no path exists, return -1.0. Use memoization or union-find to optimize repeated queries.

Pro tip: Clarify edge cases upfront: variables not in the graph, self-queries (C/C = 1.0), and disconnected components. Mention that using union-find with component tracking can quickly reject impossible queries, but DFS with memoization is simpler and sufficient for most interview constraints.

1. Build the Graph

Create an adjacency list (e.g., HashMap<String, List<Pair<String, Double>>>) where each equation A/B=k adds A→B with weight k and B→A with weight 1/k.

2. Handle Edge Cases

Check if either variable in the query is missing from the graph; if so, return -1.0. Also handle self-queries (C/C) by returning 1.0 if C exists.

3. Traverse for Each Query

For each query C/D, perform DFS or BFS from C to D, multiplying edge weights along the path. If D is reached, return the product; otherwise, return -1.0.

4. Optimize with Memoization

Cache results for repeated queries or intermediate paths to avoid redundant traversals, especially if the number of queries is large.

5. Analyze Complexity

Discuss time complexity: O(E + Q*(V+E)) for DFS per query, or O(E + Q*α(V)) with union-find. Space complexity: O(V+E) for the graph.

Key Points to Mention

  • Graph representation: variables as nodes, equations as weighted directed edges.
  • DFS/BFS traversal with weight multiplication to compute ratios.
  • Handling disconnected components and missing variables.
  • Self-query (C/C) returns 1.0 if variable exists.
  • Time and space complexity trade-offs between DFS and union-find.
  • Memoization to optimize multiple queries.

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