How do you detect a cycle in a linked list and what is the time/space complexity?

• A. Using a hash table of visited nodes with O(n) space.
• B. Only possible with doubly linked lists.
• C. Cycle detection is not possible in singly linked lists.
• D. Floyd's cycle-finding; slow and fast pointers; O(n) time, O(1) space.

Answer: (D)

Cycle detection in a linked list can be done efficiently by using two pointers moving at different speeds. This approach, Floyd's cycle-finding algorithm, uses a slow pointer that advances one node per step and a fast pointer that advances two nodes per step. If there is a cycle, the fast pointer will eventually catch up to the slow pointer inside the loop; if there is no cycle, the fast pointer will reach the end of the list.

The time complexity is O(n) because, in the worst case, both pointers traverse the list in linear time and the meeting (or end) occurs after a number of steps proportional to n. The space complexity is O(1) since only a few pointers are stored, regardless of list size.

Another common approach is to use a hash table to record visited nodes, which can detect a cycle but requires O(n) extra space. A cycle can occur in singly linked lists; it is not limited to doubly linked lists.