Which algorithm detects cycles in a linked list with O(1) extra space?

• A. Floyd’s cycle-finding algorithm (tortoise and hare); O(n) time, O(1) space.
• B. Brent’s algorithm; O(n) time, O(1) space.
• C. Using a hash set to track visited nodes; O(n) space.
• D. Counting nodes until a repeat; O(n^2) time.

Answer: (A)

Detecting a cycle in a linked list with no extra storage relies on using two pointers that move at different speeds. The slow pointer advances one node at a time, while the fast pointer moves two nodes at a time. If a cycle exists, the fast pointer will eventually lap the slow pointer and they will meet inside the cycle. This meeting confirms a cycle using only the two pointers, so the extra space is constant.

The time to detect the cycle remains linear in the length of the list, because the pointers progress through the nodes in a way that scales with n, even after entering the cycle. In contrast, methods that track visited nodes with a hash set use additional space, and approaches that count nodes until a repeat tend to be less efficient.

Floyd’s cycle-finding algorithm is the classic approach for this task, celebrated for its straightforward logic and guaranteed O(1) extra space. Brent’s variation achieves the same space bound as well, but Floyd’s method is the standard example that demonstrates the concept.