Count longest subsequence in array
Last updated: May 5, 2026
Quick Overview
Given an array of integers, your task is to count the number of longest increasing subsequences within the array. An increasing subsequence is a sequence of numbers where each number is greater than the preceding one. The function should return an integer representing the count of distinct longest increasing subsequences.
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May 5, 202657
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Given an array of integers, your task is to count the number of longest increasing subsequences within the array. An increasing subsequence is a sequence of numbers where each number is greater than the preceding one. The function should return an integer representing the count of distinct longest increasing subsequences.
This coding problem is frequently asked during Onsite at ServiceNow. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. ServiceNow expects candidates to write production-quality code, not just solve the puzzle.
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 if the input doesn't fit in memory?
- How would your solution change if the input was sorted?
- What happens if the input contains duplicates?
- How would you modify your solution to handle streaming input?
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Problem Analysis
To solve the problem of counting the number of longest increasing subsequences (LIS) in an array, we can utilize a dynamic programming approach combined with a binary search method. The key pattern he...
Approach
- Initialization: Create two arrays,
dpandcount, both of the same length as the input array.dp[i]will store the length of the longest increasing subsequence ending at indexi, and `co...
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