Count shortest distance in graph
Last updated: March 20, 2026
Quick Overview
Given an undirected graph represented by an adjacency list, write a function to count the number of shortest paths from a starting node to a target node. The function should return the count of distinct shortest paths, considering all possible routes that yield the minimum distance. The input will be the adjacency list of the graph, the starting node, and the target node, and the output should be an integer representing the number of shortest paths.
ServiceNow
March 20, 2026132
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Given an undirected graph represented by an adjacency list, write a function to count the number of shortest paths from a starting node to a target node. The function should return the count of distinct shortest paths, considering all possible routes that yield the minimum distance. The input will be the adjacency list of the graph, the starting node, and the target node, and the output should be an integer representing the number of shortest paths.
Coding interviews at ServiceNow 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
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
- Can you optimize the space complexity of your solution?
- How would you parallelize this solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
- How would you modify your solution to handle streaming input?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem can be effectively solved using the Breadth-First Search (BFS) algorithm. BFS is particularly suitable here because it explores all neighbors at the present depth prior to moving on t...
Approach
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Initialize Data Structures: Use a queue for BFS, a dictionary to keep track of the number of paths to each node, and a set to track visited nodes at the current level.
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Start BFS: Enqueu...
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