The Floyd's Tortoise and Hare algorithm is a two-pointer technique that is used to detect cycles in a linked list. The approach involves using two pointers, one moving twice as fast as the other. If there's a cycle, the fast pointer will eventually meet the slow pointer. This method works in O(n) time with O(1) space.
Time Complexity: O(n), where n is the number of nodes in the list.
Space Complexity: O(1), constant space usage.
1class ListNode:
2 def __init__(self, x):
3 self.val = x
4 self.next = None
5
6class Solution:
7 def hasCycle(self, head: ListNode) -> bool:
8 slow, fast = head, head
9 while fast and fast.next:
10 slow = slow.next
11 fast = fast.next.next
12 if slow == fast:
13 return True
14 return FalseIn Python, we utilize a two-pointer approach with the slow and fast pointers. The detection of a cycle is determined by whether the pointers meet during traversal.
This approach uses a HashSet to track the nodes visited during the traversal. If a node is encountered twice, there is a cycle. This method requires O(n) space but is simpler to understand.
Time Complexity: O(n^2) because of nested loops (non-optimal use of memory).
Space Complexity: O(n), where n is the number of nodes (uses additional storage).
1using System.Collections.Generic;
2
3public class ListNode {
4 public int val;
5 public ListNode next;
6 public ListNode(int x) {
7 val = x;
8 next = null;
9 }
10}
11
12public class Solution {
13 public bool HasCycle(ListNode head) {
14 HashSet<ListNode> visited = new HashSet<ListNode>();
15 while (head != null) {
16 if (visited.Contains(head)) return true;
17 visited.Add(head);
18 head = head.next;
19 }
20 return false;
21 }
22}The C# solution follows a logical pattern applying HashSet to track all encountered nodes. Cycle detection occurs when a node reappears in the set.