How do you detect a loop in a linked list and find its start?

Medium

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This question asks candidates to implement an algorithm to identify cycles within a singly linked list structure. It specifically tests knowledge of pointer manipulation and Floyd's Cycle Detection Algorithm.

Why Interviewers Ask This

Interviewers ask this to evaluate a candidate's fundamental understanding of data structures, particularly how pointers work in memory. They want to see if the candidate can apply efficient algorithms like Floyd's Tortoise and Hare rather than using hash sets which consume extra space. This problem also assesses logical reasoning skills and the ability to handle edge cases where loops might be complex or non-existent.

How to Answer This Question

Start by explaining the two-pointer approach clearly, defining what slow and fast pointers represent. Discuss the mathematical intuition behind why they must meet if a cycle exists. Walk through the second phase of the algorithm where you reset one pointer to the head to find the exact entry point. Mention time complexity O(n) and space complexity O(1) as key differentiators for this optimal solution.

Key Points to Cover

Initialize slow and fast pointers at the head
Move pointers at different speeds to detect collision
Reset one pointer to head upon collision
Move both pointers one step to find start node

Sample Answer

I would use Floyd’s Cycle Detection Algorithm, often called the Tortoise and Hare method. First, I initialize two pointers, slow and fast, both starting at the head. The slow pointer moves one step while the fast moves two steps. If there is a cycle, they will eventually meet. Once they collide, I reset the slow pointer to the head and move both one step at a time until they meet again; that meeting point is the start of the loop. This approach ensures we solve the problem in linear time with constant space.

Common Mistakes to Avoid

Using a HashSet which increases space complexity to O(n)
Failing to handle the case where no cycle exists
Incorrectly calculating the start node after detection

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How do you detect a loop in a linked list and find its start?

Why Interviewers Ask This

How to Answer This Question

Key Points to Cover

Sample Answer

Common Mistakes to Avoid

Practice This Question with AI

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