MathWorks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

MathWorks SWE interview with a graph problem that looks straightforward until you actually sit with it. One question, but it had enough depth to keep me busy for the whole session.

Questions Asked (1)

You have a weighted directed graph with n nodes. You can add any number of directed edges, each with weight 1, between any nodes you choose. After adding edges optimally, what is the minimum possible shortest-path distance from node 1 to node n?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was just Dijkstra and call it a day, which was wrong.

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AI HintsAI Generated

Suggested Approach

Model the problem as finding the minimum number of weight-1 edges to add so that the shortest path from 1 to n is minimized. Use a modified Dijkstra where the cost to reach a node is the minimum over all paths of (original path weight + number of added edges), and the answer is the minimum cost to reach n. Alternatively, binary search on the answer and check if there exists a path with original weight ≤ answer and length ≤ answer.

Pro tip: Clarify with the interviewer whether added edges can be used multiple times and whether they can be placed between any nodes, including already connected ones. This shows attention to problem constraints and avoids incorrect assumptions.

1. Understand the problem and constraints

Restate the problem: we can add any number of directed edges of weight 1 between any nodes. We want to minimize the shortest path distance from node 1 to node n after optimal additions. Ask clarifying questions about edge multiplicity and usage.

2. Formulate the objective

Realize that adding edges can only decrease or keep the shortest path distance. The goal is to find the minimum possible distance d such that there exists a path from 1 to n using original edges and at most d added edges, with total weight ≤ d.

3. Design an algorithm

Use a modified Dijkstra where the state is the node and the cost is the minimum number of added edges needed to reach that node with a given total path weight. Alternatively, binary search on the answer d and check feasibility using BFS on a transformed graph.

4. Analyze complexity and trade-offs

Discuss the time and space complexity of your approach. Compare with alternative methods like dynamic programming or binary search, and explain why your chosen method is efficient for large n.

5. Test with examples and edge cases

Walk through small examples, including cases where node 1 and n are already connected, disconnected, or have multiple paths. Verify that your algorithm handles these correctly.

Key Points to Mention

The problem reduces to finding the minimum d such that there is a path from 1 to n with original weight ≤ d and number of edges ≤ d.
Added edges can be used to bypass long original edges, effectively reducing the distance to the number of added edges plus original edges used.
A modified Dijkstra can track the minimum number of added edges needed to reach each node with a given total weight.
Binary search on the answer d is feasible because if a distance d is achievable, any larger distance is also achievable by adding extra edges.
The optimal strategy often involves adding edges to create a direct shortcut or to connect components efficiently.
Edge cases: n=1 (distance 0), no path exists even with added edges (but since we can add edges between any nodes, we can always connect 1 to n directly, so answer is at most 1).

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