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The Floyd's Cycle Detection Algorithm, also known as the tortoise and hare algorithm, is well-suited for detecting cycles in a linked list.
In this approach, two pointers (slow and fast) are initiated. The slow pointer moves one step at a time, while the fast pointer moves two steps. If a cycle is present, the fast pointer will meet the slow pointer within the cycle. Once a cycle is detected, reset one pointer to the head of the linked list and keep the other pointer at the meeting point. Move both pointers one step at a time; the node where they meet again is the cycle's start.
Time Complexity: O(n) - The list is traversed twice at most.
Space Complexity: O(1) - No additional space apart from pointers.
1class ListNode:
2 def __init__(self, x):
3 self.val = x
4 self.next = None
5
6class Solution:
7 def detectCycle(self, head: ListNode) -> ListNode:
8 if not head or not head.next:
9 return None
10
11 slow = fast = head
12 while fast and fast.next:
13 slow = slow.next
14 fast = fast.next.next
15 if slow == fast:
16 fast = head
17 while slow != fast:
18 slow = slow.next
19 fast = fast.next
20 return slow
21 return NoneIn Python, the detectCycle function is implemented within the Solution class, utilizing the same Floyd's Cycle Detection logic with slow and fast pointers to find and return the beginning of the cycle if present.
This approach involves using a hash table (or set) to record visited nodes. Traverse the linked list, and for each node, check if it has already been seen (exists in the hash set). If it has, a cycle is detected that starts at this node. If the end of the list is reached without seeing any node twice, the list does not contain a cycle.
Though this technique uses extra space for the data structure, it can be easier to implement and understand.
Time Complexity: O(n) - each node is visited once.
Space Complexity: O(n) - for the hash table.
1
This C solution creates a hash table, inserting each visited node with a hashed pointer as the key. If a node is found in the table during traversal, it's part of the cycle's start and returned. Otherwise, the list is acyclic.