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.
1#include <stdbool.h>
2
3struct ListNode {
4 int val;
5 struct ListNode *next;
6};
7
8bool hasCycle(struct ListNode *head) {
9 struct ListNode *slow = head, *fast = head;
10 while (fast != NULL && fast->next != NULL) {
11 slow = slow->next;
12 fast = fast->next->next;
13 if (slow == fast) {
14 return true;
15 }
16 }
17 return false;
18}In this solution, we create two pointers, slow and fast. The slow pointer moves one step at a time while the fast moves two steps. If the list contains a cycle, these pointers will eventually meet inside the cycle. If there's no cycle, fast or fast->next will become null.
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.