← Grammarly Interview Insights
The basic cycle detection part went fine, slow and fast pointer, they meet inside the cycle and you return true.
Use Floyd's cycle-finding algorithm (tortoise and hare) to detect a cycle in O(n) time and O(1) space. For the follow-up, after detection, reset one pointer to the head and move both pointers one step at a time until they meet; that meeting point is the start of the cycle. Explain the algorithm clearly, justify the time and space complexity, and handle edge cases.
Pro tip: Mention that you can also use Brent's algorithm for slightly better constant factors, but Floyd's is more commonly expected. Also, be prepared to prove why the two-pointer approach works, as interviewers often ask for the mathematical reasoning.
Restate the problem to ensure you understand: detect a cycle in a singly linked list with O(n) time and O(1) space, and if a cycle exists, return the node where it begins. Ask if the list can be modified (it shouldn't be) and if there are constraints on the number of nodes.
Describe using two pointers, slow and fast, both starting at the head. Slow moves one step at a time, fast moves two steps. If they meet, a cycle exists; if fast reaches null, no cycle.
After detecting a cycle, reset one pointer to the head and keep the other at the meeting point. Move both one step at a time; the node where they meet again is the start of the cycle.
State that time complexity is O(n) because each pointer traverses at most the length of the list plus cycle length, and space is O(1) since only two pointers are used. Discuss edge cases: empty list, single node, cycle at head, no cycle.
Write clean code for the detection and start-finding functions. Walk through a small example to verify correctness, and consider mentioning alternative algorithms like hashing (O(n) space) to contrast.
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