# https://leetcode.com/problems/linked-list-cycle-ii/description/
"""
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.

Example 1:
Input: head = [3,2,0,-4], pos = 1
Output: tail connects to node index 1
Explanation: There is a cycle in the linked list, where tail connects to the second node.

Example 2:
Input: head = [1,2], pos = 0
Output: tail connects to node index 0
Explanation: There is a cycle in the linked list, where tail connects to the first node.

Example 3:
Input: head = [1], pos = -1
Output: no cycle
Explanation: There is no cycle in the linked list.


Constraints:
The number of the nodes in the list is in the range [0, 104].
-105 <= Node.val <= 105
pos is -1 or a valid index in the linked-list.


Follow up: Can you solve it using O(1) (i.e. constant) memory?
"""
from typing import Optional

from puzzles.utils import ListNode


def detect_cycle(head: Optional[ListNode]) -> Optional[ListNode]:
    if not head:
        return
    slow, fast = head, head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
        if slow == fast:
            break
    if not fast or not fast.next:
        return

    fast = head
    while slow != fast:
        slow = slow.next
        fast = fast.next
    return fast
