Overview

Detecting a loop in a linked list is a fundamental problem in computer science, focusing on identifying if a linked list contains a cycle. This means that a node in the list points back to a previous node, creating a loop. It is crucial because loops in linked lists can lead to infinite loops in algorithms, causing programs to crash or run indefinitely. Various approaches, from simple iterative methods to more complex algorithms like Floyd's Tortoise and Hare, are used to solve this problem.

Key Concepts

1. Floyd's Cycle Finding Algorithm: Also known as the Tortoise and Hare algorithm, it uses two pointers moving at different speeds to detect a loop.
2. Hashing: Keeping track of visited nodes by storing them in a hash set. If a node is revisited, a loop exists.
3. Pointer Analysis: Analyzing the next pointers of nodes. If a node's next pointer points to a previously visited node, a loop is detected.

Common Interview Questions

Basic Level

1. How can you use Floyd's Cycle Finding Algorithm to detect a loop in a linked list?
2. Explain the concept of using hashing to detect a loop in a linked list.

Intermediate Level

3. How does the space complexity of Floyd's Cycle Finding Algorithm compare to using hashing for loop detection?

Advanced Level

4. Can you implement a function to detect a loop in a linked list and return the node where the loop begins?

Detailed Answers

1. How can you use Floyd's Cycle Finding Algorithm to detect a loop in a linked list?

Answer: Floyd's Cycle Finding Algorithm, also known as the Tortoise and Hare algorithm, involves two pointers that traverse the list at different speeds (one moves two steps at a time, the other just one). If the linked list has a loop, the two pointers will eventually meet inside the loop. If they never meet, the list does not contain a loop.

Key Points:
- The slow pointer moves one node at a time.
- The fast pointer moves two nodes at a time.
- If there's a loop, the fast and slow pointers will eventually meet.

Example:

public class ListNode {
    public int Value { get; set; }
    public ListNode Next { get; set; }
}

public bool HasCycle(ListNode head) {
    if (head == null) return false;

    ListNode slow = head, fast = head;

    while (fast != null && fast.Next != null) {
        slow = slow.Next;
        fast = fast.Next.Next;

        if (slow == fast) {
            return true; // Cycle detected
        }
    }

    return false; // No cycle
}

2. Explain the concept of using hashing to detect a loop in a linked list.

Answer: The hashing approach involves traversing the linked list and storing the address/reference of each node in a hash set. For each node, we check if its reference is already in the hash set. If it is, a loop exists because we are revisiting a node. Otherwise, we add the node's reference to the hash set and move on.

Key Points:
- Use a hash set to store node references.
- Check for the presence of a node in the hash set to detect loops.
- This method has a higher space complexity due to the use of a hash set.

Example:

public bool HasCycleWithHashing(ListNode head) {
    HashSet<ListNode> nodesSeen = new HashSet<ListNode>();

    while (head != null) {
        if (nodesSeen.Contains(head)) {
            return true; // Cycle detected
        }
        nodesSeen.Add(head);
        head = head.Next;
    }

    return false; // No cycle
}

3. How does the space complexity of Floyd's Cycle Finding Algorithm compare to using hashing for loop detection?

Answer: Floyd's Cycle Finding Algorithm has a space complexity of O(1) because it only uses two pointers, regardless of the size of the linked list. On the other hand, using hashing for loop detection has a space complexity of O(n), where n is the number of nodes in the linked list, due to the need to store each node's reference in a hash set.

Key Points:
- Floyd's algorithm is more space-efficient (O(1) space).
- Hashing requires storing references for all visited nodes (O(n) space).
- Choosing an algorithm depends on space and time complexity constraints.

Example: Refer to the examples in questions 1 and 2 for code implementations of each method.

4. Can you implement a function to detect a loop in a linked list and return the node where the loop begins?

Answer: To find the entry point of the loop, we can use Floyd's Cycle Finding Algorithm to first detect if a loop exists. Once a loop is detected, one pointer is moved to the head of the list while the other stays at the meeting point. Both pointers then move one step at a time. The point at which they meet again is the start of the loop.

Key Points:
- Detect loop using Floyd's Cycle Finding Algorithm.
- To find the loop's start, move one pointer to the list's head after detection.
- The meeting point of the two pointers, when moved one step at a time, is the loop's start.

Example:

public ListNode DetectCycleStart(ListNode head) {
    if (head == null) return null;

    ListNode slow = head, fast = head;
    bool hasCycle = false;

    // First step: Determine if a cycle exists
    while (fast != null && fast.Next != null) {
        slow = slow.Next;
        fast = fast.Next.Next;
        if (slow == fast) {
            hasCycle = true;
            break;
        }
    }

    // If a cycle exists, find the entry point
    if (hasCycle) {
        slow = head;
        while (slow != fast) {
            slow = slow.Next;
            fast = fast.Next;
        }
        return slow; // The start of the loop
    }

    return null; // No cycle found
}