BFS on interval list

Last updated: March 14, 2026

Quick Overview

Given a list of intervals, implement a Breadth-First Search (BFS) algorithm to determine if there exists a continuous range of numbers that can be covered by merging overlapping intervals. The input will be a list of intervals represented as pairs of integers, and the output should be a boolean indicating whether such a range exists.

Postmates
Coding & Algorithms
Machine Learning Engineer
Postmates
March 14, 2026
Machine Learning Engineer
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Coding & Algorithms
Easy

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Given a list of intervals, implement a Breadth-First Search (BFS) algorithm to determine if there exists a continuous range of numbers that can be covered by merging overlapping intervals. The input will be a list of intervals represented as pairs of integers, and the output should be a boolean indicating whether such a range exists.

Coding interviews at Postmates focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.

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
Graph algorithms and traversal
Dynamic programming and memoization
Binary search and divide and conquer
Hash maps and frequency counting
Tree structures and recursion
How to Approach This
  1. Clarify input constraints and edge cases before writing code.
  2. Walk through your approach verbally and confirm with the interviewer before coding.
  3. Start with a brute force solution, then optimize. Mention time and space complexity.
  4. Test your solution with examples, including edge cases like empty input or duplicates.
  5. Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
  • Can you solve this iteratively instead of recursively (or vice versa)?
  • Can you optimize the space complexity of your solution?
  • How would you test this solution thoroughly?
  • Can you solve this in a single pass?
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Problem Analysis

The problem requires us to determine if we can cover a continuous range of numbers by merging overlapping intervals from a given list. The key observation is that we can use a Breadth-First Search (BF...

Approach
  1. Sort the Intervals: Start by sorting the intervals based on their starting values. For example, given intervals [[1,3],[2,4],[5,7]][[1, 3], [2, 4], [5, 7]], sorting results in the same order since they are ...
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