Starting node of cycle in Linked List

Starting node of cycle in Linked List

Problem Statement

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?

Hashing Technique

Complexity

  • Time Complexity: O(n).
  • Space Complexity: O(n).
/**
 * Definition for singly-linked list.
 * type ListNode struct {
 *     Val int
 *     Next *ListNode
 * }
 */
func detectCycle(head *ListNode) *ListNode {

	if head == nil || head.Next == nil {
		return nil
	}

	temp := head
	// define map 
	seen := map[*ListNode]bool{}

	for temp != nil {
		// we found the cycle and this is the first node in cycle
		if seen[temp] == true {
			return temp
		}
		seen[temp] = true

		// move to next position
		temp = temp.Next
	}

	return nil
}

Floyd’s Cycle Detection Algorithm

Fast and Slow Pointer Technique

Complexity

  • Time Complexity: O(n).
  • Space Complexity: O(1).
/**
 * Definition for singly-linked list.
 * type ListNode struct {
 *     Val int
 *     Next *ListNode
 * }
 */
func detectCycle(head *ListNode) *ListNode {
	if head == nil || head.Next == nil {
		return nil
	}

	slow, fast := head, head

	for fast != nil && fast.Next != nil {
		slow = slow.Next
        // This is critical condition to move fast by 2 positions
		fast = fast.Next.Next

		// we have detected a cycle
		if slow == fast {
			// now find the first node of a cycle
			slow = head

			for slow != fast {
				fast = fast.Next
				slow = slow.Next
			}
			return slow
		}
	}
	return nil
}

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