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reevo·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Interviewed for a software engineer role at reevo and got hit with a graph traversal problem that was trickier than it looked on the surface. The DFS angle was expected but the lexicographic ordering twist plus the multi-component handling caught me a bit off guard.

Questions Asked (1)

Q1

Given an undirected graph with nodes labeled 1 through n, return the lexicographically largest DFS traversal sequence. Start DFS from node 1 for its connected component, then handle remaining components by visiting each from its largest node, ordering the components themselves by their max node value descending.

Algorithms & Data Structures
Author's notes

I got the basic DFS part quickly but the multi-component ordering tripped me up for a bit.

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AI HintsAI Generated

Suggested Approach

Clarify that the goal is to produce the lexicographically largest DFS order by always visiting the largest available neighbor first, and that disconnected components are processed in descending order of their maximum node. Then outline a modified iterative DFS that uses a max-heap or sorted adjacency lists to enforce this ordering, while tracking visited nodes and component maxima.

Pro tip: Mention that using an explicit stack with neighbors pushed in ascending order (so the largest is popped first) avoids recursion depth issues and naturally yields the lexicographically largest order. Also note that pre-sorting adjacency lists once gives O(V+E) after sorting, which is optimal for this problem.

1. Clarify the problem and edge cases

Confirm that the graph is undirected, nodes are 1..n, and the output is a sequence of nodes. Discuss edge cases: n=0, isolated nodes, and multiple components.

2. Preprocess the graph

Sort each adjacency list in descending order so that when iterating neighbors, the largest is considered first. Optionally compute the maximum node in each connected component for component ordering.

3. Design the DFS traversal

Use an iterative DFS with a stack. Start at node 1 for its component. For each node, push unvisited neighbors in ascending order so the largest is popped next. Record nodes as visited when popped.

4. Handle remaining components

After finishing the component containing node 1, find all unvisited nodes. Group them into components, compute each component's maximum node, and process components in descending order of that maximum. For each component, start DFS from its largest node.

5. Analyze complexity and test

State time complexity: O(V + E log E) due to sorting adjacency lists, or O(V + E) if using a max-heap per node (but sorting is simpler). Space: O(V + E). Walk through a small example to verify correctness.

Key Points to Mention

  • Lexicographically largest DFS requires visiting the largest possible neighbor at each step.
  • Iterative DFS with a stack and reversed neighbor order avoids recursion limits and ensures correct order.
  • Disconnected components must be processed in descending order of their maximum node value.
  • Pre-sorting adjacency lists in descending order simplifies neighbor selection.
  • Time complexity: O(V + E log E) with sorting, or O(V + E) with a max-heap per node; space O(V + E).
  • Edge cases: empty graph, single node, isolated nodes, and multiple components with the same maximum.

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