Insert node at end of circular doubly linked list

The problem involves inserting a new node at the end of a circular doubly linked list. A circular doubly linked list is a data structure in which each node has pointers to both its previous and next nodes, and the last node's next pointer points back to the first node, creating a loop.

Problem Statement

Given a circular doubly linked list, the task is to insert a new node at the end of the list while maintaining the circular structure.

Example

Consider the circular doubly linked list: 1 <-> 2 <-> 3 <-> 4 <-> 5. After inserting a new node with value 6 at the end, the list will become: 1 <-> 2 <-> 3 <-> 4 <-> 5 <-> 6.

Idea to Solve the Problem

To insert a new node at the end of a circular doubly linked list, we need to follow these steps:

1. Create the new node with the given value.
2. If the list is empty, make the new node both the head and the tail. Update the next and previous pointers of the new node to point to itself.
3. If the list is not empty, update the pointers of the new node and the existing nodes to insert the new node at the end.
4. Update the next pointer of the current tail node to point to the new node and the prev pointer of the new node to point to the current tail node.
5. Update the prev pointer of the head node to point to the new node and the next pointer of the new node to point to the head node.
6. Finally, update the tail pointer to point to the new node.

Pseudocode

Here's the pseudocode to insert a node at the end of a circular doubly linked list:

function insert(value):
    // Create a new node
    new_node = createNode(value)
    if head is NULL:
        // List is empty
        head = new_node
        tail = new_node
        new_node.next = new_node
        new_node.prev = new_node
    else:
        new_node.next = head
        new_node.prev = tail
        tail.next = new_node
        head.prev = new_node
        tail = new_node

Algorithm Explanation

1. Create a new node with the given value using the createNode function.
2. Check if the linked list is empty. If it is, make the new node both the head and the tail. Update the next and prev pointers of the new node to point to itself.
3. If the list is not empty, update the next and prev pointers of the new node and the existing nodes to insert the new node at the end.
4. Update the next pointer of the current tail node to point to the new node and the prev pointer of the new node to point to the current tail node.
5. Update the prev pointer of the head node to point to the new node and the next pointer of the new node to point to the head node.
6. Finally, update the tail pointer to point to the new node.

Code Solution

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Time Complexity

The time complexity of inserting a node at the end of a circular doubly linked list is O(1), as it involves a constant number of pointer updates.