Find kth largest element in graph
Last updated: October 28, 2025
Quick Overview
Given a directed or undirected graph represented as an adjacency list, write a function to find the k-th largest element among the nodes based on their values. The function should take the graph and an integer k as input and return the k-th largest value, or indicate if k is out of bounds.
Postmates
October 28, 202535
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Given a directed or undirected graph represented as an adjacency list, write a function to find the k-th largest element among the nodes based on their values. The function should take the graph and an integer k as input and return the k-th largest value, or indicate if k is out of bounds.
Postmates uses this problem in the Technical Screen to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
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 happens if the input contains duplicates?
- What is the worst-case input for your solution?
- How would you test this solution thoroughly?
- How would you parallelize this solution?
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Problem Analysis
This problem requires us to find the k-th largest element in a graph based on the node values. Given that the graph is represented as an adjacency list, we can view it as a collection of nodes with as...
Approach
- Initialize a min-heap to store the k largest elements.
- Start from a root node (or iterate through all nodes if the graph is disconnected).
- Use a DFS or BFS approach to traverse the graph....
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