Given the head of a singly linked list that may contain a cycle, return the 0-indexed position of the node where the cycle begins, or -1 if there is no cycle. Since node values may repeat, the answer has to be a position, not a value — otherwise an earlier duplicate could be mistaken for the loop's actual start. The optimal solution runs Floyd's Cycle DetectionFloyd's Cycle DetectionThe "tortoise and hare" algorithm: slow and fast pointers moving at 1 and 2 steps per iteration. Once they meet inside a cycle, resetting one pointer to head and advancing both at equal speed makes them meet again exactly at the cycle's first node — a property that follows from the arithmetic of how far each pointer traveled to reach the meeting point. in two phases: first find where slow and fast meet, then reset one pointer to head and walk both one step at a time until they meet again — that second meeting point is the loop's start.