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.
1function ListNode(val) {
2 this.val = val;
3 this.next = null;
4}
5
6var hasCycle = function(head) {
7 let slow = head, fast = head;
8 while (fast && fast.next) {
9 slow = slow.next;
10 fast = fast.next.next;
11 if (slow === fast) return true;
12 }
13 return false;
14};The JavaScript function leverages the same logic of two pointers. Different speeds of traversal will determine if a cycle exists when the pointers align.
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).
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 visited = set()
9 while head:
10 if head in visited:
11 return True
12 visited.add(head)
13 head = head.next
14 return FalseIn Python, a set is used to implement the logic similar to Java's HashSet. The cycle is detected by checking if a node has been seen before.