Count cycle in array
Last updated: April 3, 2026
Quick Overview
Given an array of integers, write a function to count the number of distinct cycles present in the array. A cycle is defined as a sequence of indices where each index points to the next index in the cycle, and the last index points back to the first. The function should return the count of such cycles found in the array.
Two Sigma
April 3, 2026169
7
4,647 solved
Given an array of integers, write a function to count the number of distinct cycles present in the array. A cycle is defined as a sequence of indices where each index points to the next index in the cycle, and the last index points back to the first. The function should return the count of such cycles found in the array.
Two Sigma uses this problem in the Take-home Project 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 is the worst-case input for your solution?
- How would you modify your solution to handle streaming input?
- How would you test this solution thoroughly?
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Problem Analysis
To solve the problem of counting distinct cycles in an array of integers, we can view the array as a directed graph where each index points to another index based on the value at that index. This mean...
Approach
- Initialize a
visitedarray of the same size as the input array to track which indices have been processed. - Loop through each index of the array:
- If the index has not been visited, initiat...
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