How do you detect and measure the length of a cycle once detected in a linked list?

• A. After detection, traverse the cycle until returning to the start node and count steps to measure length.
• B. Return a fixed length equal to the number of nodes before the cycle.
• C. Traverse from the head to the end of the cycle and return the count.
• D. Length cannot be measured once a cycle is detected.

Answer: (A)

After detecting a cycle, the way to measure its length is to walk around the cycle itself starting from a node that lies inside the cycle and count how many steps it takes to return to that same node. With the typical detection method (such as Floyd’s), the meeting point is guaranteed to be inside the cycle, so you can start there. Move from that node to its next node repeatedly, incrementing a counter, until you arrive back at the starting node. The final count is the number of distinct nodes in the cycle. This works because you stay within the loop, and you will eventually come back to where you started, having touched every node in the cycle exactly once.

The other ideas don’t fit: the number of nodes before the cycle isn’t the cycle length, since that length only counts the nodes that form the loop itself. There isn’t an end to traverse to count the cycle length, so starting from the head or trying to count to an end isn’t meaningful. And the cycle length can indeed be measured once a cycle is detected, so stating otherwise isn’t correct.