Two Pointers on graph
Last updated: January 18, 2026
Quick Overview
Given a graph represented as an adjacency list, implement a two-pointer technique to find all pairs of vertices that are connected by a path of exactly two edges. The function should return a list of these vertex pairs.
DE Shaw
January 18, 202653
3
2,985 solved
Given a graph represented as an adjacency list, implement a two-pointer technique to find all pairs of vertices that are connected by a path of exactly two edges. The function should return a list of these vertex pairs.
This coding problem is frequently asked during Take-home Project at DE Shaw. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. DE Shaw expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Identify the correct data structure and algorithm for the problem
- Write clean, bug-free code with proper variable naming
- Analyze time and space complexity correctly
- Handle basic edge cases (empty input, single element)
- Communicate your thought process while coding
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- What is the worst-case input for your solution?
- Can you solve this in a single pass?
- Can you optimize the space complexity of your solution?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem requires finding pairs of vertices in a graph that are connected by exactly two edges. The two-pointer technique is applicable here because we can leverage the adjacency list representati...
Approach
- Initialize an empty list to store the pairs of vertices connected by two edges.
- Loop through each vertex in the graph. For each vertex 'u':
- Retrieve its neighbors from the adjacency lis...
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