Find the Starting Node of a Linked List Cycle

Given the head of a singly linked list, determine if the linked list has a cycle. If it does, return the node where the cycle begins. If there is no cycle, return null. This problem is crucial for understanding how to detect and locate circular data structures, which can arise in various scenarios like memory management or certain graph representations.

Problem Description

You are given the head of a singly linked list. Your task is to implement a function that detects if a cycle exists within the linked list. If a cycle is found, you must return the node that is the starting point of that cycle. If no cycle is present, you should return null.

Key Requirements:

You must be able to correctly identify the presence of a cycle.
If a cycle exists, you must pinpoint and return the exact node where the cycle begins.
If no cycle exists, you must return null.

Expected Behavior:

The function should traverse the linked list.
If it encounters a node that has already been visited during the current traversal, it has found a cycle.
The function should return the first node that is part of the cycle.

Edge Cases to Consider:

An empty linked list (head is null).
A linked list with only one node, which does not form a cycle.
A linked list with multiple nodes, but no cycle.
A linked list where the cycle starts at the head node.
A linked list where the cycle starts at the last node (forming a self-loop).

Examples

Example 1:

Input: head = [3, 2, 0, -4], pos = 1
(The linked list is 3 -> 2 -> 0 -> -4, and the tail connects to the node at index 1, which is 2)
Output: Node with value 2
Explanation: There is a cycle in the linked list, and the cycle begins at the node with value 2.

Example 2:

Input: head = [1, 2], pos = 0
(The linked list is 1 -> 2, and the tail connects to the node at index 0, which is 1)
Output: Node with value 1
Explanation: There is a cycle in the linked list, and the cycle begins at the node with value 1.

Example 3:

Input: head = [1], pos = -1
(The linked list is 1, and the tail does not connect to any node)
Output: null
Explanation: There is no cycle in the linked list.

Constraints

The number of nodes in the list is between 0 and 10^4.
The value of each node is between -10^5 and 10^5.
pos is the index of the node that the tail's next pointer is connected to. If pos is -1, there is no cycle.

Notes

You will be provided with a ListNode structure that has a val (value) and a next pointer.
Consider algorithms that do not require significant extra space.
A common approach for this problem involves using two pointers, often referred to as the "tortoise and hare" method. Think about how these pointers can detect a cycle and then how they can be used to find its starting point.

Find the Starting Node of a Linked List Cycle

Problem Description

Key Requirements:

You must be able to correctly identify the presence of a cycle.

If a cycle exists, you must pinpoint and return the exact node where the cycle begins.

If no cycle exists, you must return null.

Expected Behavior:

The function should traverse the linked list.

If it encounters a node that has already been visited during the current traversal, it has found a cycle.

The function should return the first node that is part of the cycle.

Edge Cases to Consider:

An empty linked list (head is null).

A linked list with only one node, which does not form a cycle.

A linked list with multiple nodes, but no cycle.

A linked list where the cycle starts at the head node.

A linked list where the cycle starts at the last node (forming a self-loop).

Examples

Example 1:

Input: head = [3, 2, 0, -4], pos = 1 (The linked list is 3 -> 2 -> 0 -> -4, and the tail connects to the node at index 1, which is 2) Output: Node with value 2 Explanation: There is a cycle in the linked list, and the cycle begins at the node with value 2.

Example 2:

Input: head = [1, 2], pos = 0 (The linked list is 1 -> 2, and the tail connects to the node at index 0, which is 1) Output: Node with value 1 Explanation: There is a cycle in the linked list, and the cycle begins at the node with value 1.

Example 3:

Input: head = [1], pos = -1 (The linked list is 1, and the tail does not connect to any node) Output: null Explanation: There is no cycle in the linked list.

Notes

You will be provided with a ListNode structure that has a val (value) and a next pointer.

Consider algorithms that do not require significant extra space.

A common approach for this problem involves using two pointers, often referred to as the "tortoise and hare" method. Think about how these pointers can detect a cycle and then how they can be used to find its starting point.