142. linked list cycle ii

Given the head of a linked list, return the node where the cycle begins. If there is no cycle, return null.

There is a cycle in a linked list if there is some node in the list that can be reached again by continuously following the next pointer. Internally, pos is used to denote the index of the node that tail’s next pointer is connected to (0-indexed). It is -1 if there is no cycle. Note that pos is not passed as a parameter.

Do not modify the linked list.

solution

Use Floyd’s algorithm, but then move one of the nodes back to the front and move in lockstep.

def detectCycle(self, head: Optional[ListNode]):  
	# edge case for 0 and 1 node lists  
	if not head or not head.next:  
		return None  
	
	# floyd's algo  
	slow, fast = head, head  
	while fast and fast.next:  
		slow = slow.next  
		fast = fast.next.next  
	
	if slow == fast:  
		break  
	
	# if we broke before meeting, no cycle exists   
	if slow != fast:  
		return None  
	
	# reset slow to head and move lockstep  
	slow = head  
	while slow != fast:  
		slow = slow.next  
		fast = fast.next  
	
	return slow