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# Convert a doubly linked list into reversal anti clockwise spiral form

In this article, we will explore a fascinating algorithmic problem: converting a doubly linked list into a reversal anti-clockwise spiral form. We'll delve into the problem statement, walk through an illustrative example, outline the algorithmic approach, provide pseudocode, detail the algorithm's implementation, explain the resulting output, and analyze the time complexity of the solution.

## Problem Statement

Given a doubly linked list, we are tasked with transforming it into a specific arrangement known as the reversal anti-clockwise spiral form. This form involves altering the links between nodes in such a way that the order of nodes in the list forms an anti-clockwise spiral pattern. Additionally, the direction of the doubly linked list should be reversed. The problem presents a unique challenge that combines linked list manipulation and spiral pattern creation.

## Illustrative Example

Consider the following doubly linked list:

``1 <-> 2 <-> 3 <-> 4 <-> 5 <-> 6 <-> 7 <-> 8 <-> 9``

After converting the list into the reversal anti-clockwise spiral form, it will look like this:

``5 <-> 4 <-> 6 <-> 3 <-> 7 <-> 2 <-> 8 <-> 1 <-> 9``

This transformation involves reordering the nodes to create an anti-clockwise spiral pattern while reversing the direction of the list.

## Algorithmic Approach

1. Initialize pointers `current` and `last` to the head and tail of the linked list, respectively.
2. Set up auxiliary pointers to assist in link swapping.
3. Begin converting the list:
• Swap links between `current` and `last`, considering the anti-clockwise spiral pattern.
• Update pointers and auxiliary pointers as needed.
4. Reverse the entire linked list to complete the transformation.

## Pseudocode

``````reversalAntiSpiral():
return
Initialize last = tail, current = head, auxiliary = null
Set up temp and back pointers

Set head as tail to start the new configuration

Loop until current and last pointers meet or cross:
Handle edge cases when current and last are adjacent
Swap links considering the anti-clockwise spiral
Update pointers and auxiliary pointers

Reverse the entire linked list using reverseNode()

reverseNode():
return
Initialize temp = head, back = null

Traverse the list and modify links to reverse nodes

Main():
Initialize a doubly linked list (dll)
Insert nodes into the linked list

Display the list before the transformation
Convert the list to reversal anti-clockwise spiral form
Display the transformed list``````

## Time Complexity Analysis

• The `reversalAntiSpiral` function iterates through the linked list once, performing constant-time operations per iteration. Therefore, its time complexity is O(n), where n is the number of nodes in the linked list.
• The `reverseNode` function also traverses the entire linked list once, resulting in a time complexity of O(n).

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