How do you remove a loop in a linked list?

Removing a loop in a linked list is a crucial operation in managing linked lists, especially in scenarios where loops can lead to infinite traversals and crashes. Here’s a detailed explanation of how to detect and remove a loop from a linked list, including examples and code in various programming languages.

Understanding the Problem

A loop in a linked list occurs when a node’s next pointer points back to a previous node, creating a cycle. Detecting and removing such loops ensures that the linked list behaves correctly and can be traversed without getting stuck.

Steps to Remove a Loop

1. Detect the Loop:

• Floyd’s Cycle-Finding Algorithm (Tortoise and Hare): Use two pointers, one moving slow (one step at a time) and the other moving fast (two steps at a time). If they meet, a loop exists.

1. Find the Starting Node of the Loop:

• After detecting the loop, reset one pointer to the head of the list. Move both pointers (one from the head and one from the meeting point) one step at a time until they meet again. The meeting point is the start of the loop.

1. Remove the Loop:

• Traverse the loop from the starting node until you find the node that points back to the starting node and set its next to null.

Example

Consider a linked list with the following structure:
[ \text{Head} \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow \text{(back to 2)} ]

1. Detect the Loop:

• Slow pointer at 1, Fast pointer at 2.
• Move fast pointer twice as fast. They meet at node 2.

1. Find the Starting Node of the Loop:

• Move one pointer from the head and one from the meeting point. They meet again at node 2.

1. Remove the Loop:

• Traverse from node 2 to find the node pointing back to node 2 and set its next to null.

Code Examples

1. Python

class ListNode:
    def __init__(self, value=0, next=None):
        self.value = value
        self.next = next

def remove_loop(head):
    if head is None:
        return

    slow = fast = head

    # Detect loop
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
        if slow == fast:
            break
    else:
        # No loop detected
        return

    # Find the start of the loop
    slow = head
    while slow != fast:
        slow = slow.next
        fast = fast.next

    # Remove the loop
    while fast.next != slow:
        fast = fast.next
    fast.next = None

# Helper function to create a linked list with a loop for testing
def create_list_with_loop():
    head = ListNode(1)
    second = ListNode(2)
    third = ListNode(3)
    fourth = ListNode(4)
    fifth = ListNode(5)

    head.next = second
    second.next = third
    third.next = fourth
    fourth.next = fifth
    fifth.next = second  # Create loop here

    return head

# Example usage
head = create_list_with_loop()
remove_loop(head)

2. JavaScript

class ListNode {
    constructor(value = 0, next = null) {
        this.value = value;
        this.next = next;
    }
}

function removeLoop(head) {
    if (!head) return;

    let slow = head;
    let fast = head;

    // Detect loop
    while (fast && fast.next) {
        slow = slow.next;
        fast = fast.next.next;
        if (slow === fast) {
            break;
        }
    }
    if (!fast || !fast.next) {
        // No loop detected
        return;
    }

    // Find the start of the loop
    slow = head;
    while (slow !== fast) {
        slow = slow.next;
        fast = fast.next;
    }

    // Remove the loop
    while (fast.next !== slow) {
        fast = fast.next;
    }
    fast.next = null;
}

// Helper function to create a linked list with a loop for testing
function createListWithLoop() {
    const head = new ListNode(1);
    const second = new ListNode(2);
    const third = new ListNode(3);
    const fourth = new ListNode(4);
    const fifth = new ListNode(5);

    head.next = second;
    second.next = third;
    third.next = fourth;
    fourth.next = fifth;
    fifth.next = second;  // Create loop here

    return head;
}

// Example usage
const head = createListWithLoop();
removeLoop(head);

3. Java

class ListNode {
    int value;
    ListNode next;
    ListNode(int value) {
        this.value = value;
        this.next = null;
    }
}

public class Main {
    public static void removeLoop(ListNode head) {
        if (head == null) return;

        ListNode slow = head;
        ListNode fast = head;

        // Detect loop
        while (fast != null && fast.next != null) {
            slow = slow.next;
            fast = fast.next.next;
            if (slow == fast) {
                break;
            }
        }
        if (fast == null || fast.next == null) {
            // No loop detected
            return;
        }

        // Find the start of the loop
        slow = head;
        while (slow != fast) {
            slow = slow.next;
            fast = fast.next;
        }

        // Remove the loop
        while (fast.next != slow) {
            fast = fast.next;
        }
        fast.next = null;
    }

    // Helper function to create a linked list with a loop for testing
    public static ListNode createListWithLoop() {
        ListNode head = new ListNode(1);
        ListNode second = new ListNode(2);
        ListNode third = new ListNode(3);
        ListNode fourth = new ListNode(4);
        ListNode fifth = new ListNode(5);

        head.next = second;
        second.next = third;
        third.next = fourth;
        fourth.next = fifth;
        fifth.next = second;  // Create loop here

        return head;
    }

    public static void main(String[] args) {
        ListNode head = createListWithLoop();
        removeLoop(head);
    }
}

4. C++

#include <iostream>

struct ListNode {
    int value;
    ListNode* next;
    ListNode(int val) : value(val), next(nullptr) {}
};

void removeLoop(ListNode* head) {
    if (head == nullptr) return;

    ListNode* slow = head;
    ListNode* fast = head;

    // Detect loop
    while (fast != nullptr && fast->next != nullptr) {
        slow = slow->next;
        fast = fast->next->next;
        if (slow == fast) {
            break;
        }
    }
    if (fast == nullptr || fast->next == nullptr) {
        // No loop detected
        return;
    }

    // Find the start of the loop
    slow = head;
    while (slow != fast) {
        slow = slow->next;
        fast = fast->next;
    }

    // Remove the loop
    while (fast->next != slow) {
        fast = fast->next;
    }
    fast->next = nullptr;
}

// Helper function to create a linked list with a loop for testing
ListNode* createListWithLoop() {
    ListNode* head = new ListNode(1);
    ListNode* second = new ListNode(2);
    ListNode* third = new ListNode(3);
    ListNode* fourth = new ListNode(4);
    ListNode* fifth = new ListNode(5);

    head->next = second;
    second->next = third;
    third->next = fourth;
    fourth->next = fifth;
    fifth->next = second;  // Create loop here

    return head;
}

int main() {
    ListNode* head = createListWithLoop();
    removeLoop(head);

    // Clean up memory
    while (head) {
        ListNode* temp = head;
        head = head->next;
        delete temp;
    }

    return 0;
}

5. C

using System;

class ListNode {
    public int Value;
    public ListNode Next;
    public ListNode(int value) {
        Value = value;
        Next = null;
    }
}

class Program {
    public static void RemoveLoop(ListNode head) {
        if (head == null) return;

        ListNode slow = head;
        ListNode fast = head;

        // Detect loop
        while (fast != null && fast.Next != null) {
            slow = slow.Next;
            fast = fast.Next.Next;
            if (slow == fast) {
                break;
            }
        }
        if (fast == null || fast.Next == null) {
            // No loop detected
            return;
        }

        // Find the start of the loop
        slow = head;
        while (slow != fast) {
            slow = slow.Next;
            fast = fast.Next;
        }

        // Remove the loop
        while (fast.Next != slow) {
            fast

 = fast.Next;
        }
        fast.Next = null;
    }

    // Helper function to create a linked list with a loop for testing
    public static ListNode CreateListWithLoop() {
        ListNode head = new ListNode(1);
        ListNode second = new ListNode(2);
        ListNode third = new ListNode(3);
        ListNode fourth = new ListNode(4);
        ListNode fifth = new ListNode(5);

        head.Next = second;
        second.Next = third;
        third.Next = fourth;
        fourth.Next = fifth;
        fifth.Next = second;  // Create loop here

        return head;
    }

    static void Main() {
        ListNode head = CreateListWithLoop();
        RemoveLoop(head);
    }
}

Removing a loop in a linked list involves three main steps:

1. Detecting the Loop: Use Floyd’s Cycle-Finding Algorithm (Tortoise and Hare).
2. Finding the Start of the Loop: Reset one pointer to the head and move both pointers one step at a time until they meet.
3. Removing the Loop: Traverse the loop to find the node pointing to the start and set its next to null.