Lecture Notes: Rotating a Linked List

Introduction

• Welcome back to the channel!
• Today's problem: Rotate a given linked list by K times.
• Example: Rotate a linked list with K = 2.

Understanding Linked List Rotation

1. Rotation Process:

   • First Rotation:
     • Last element moves to the front.
     • Other elements shift right by one place.
   • Second Rotation:
     • Last element again moves to the front.
     • Elements shift right by one place again.

2. Final State After Two Rotations:

   • Updated linked list is shown.

Key Considerations

• Range of K:

  • K can be any non-negative integer.
  • For example, K can be 1, 5, 10, 100, etc.

• Edge Cases for Large K:

  • If K is equal to or greater than the length of the linked list, rotations may bring the list back to the original configuration.
  • If K equals length: return the original head.
  • If K is a multiple of length: return original head.
  • Example: K = 13 can be reduced to K = 3 (length = 5).

Algorithm Steps

1. Initial Setup:
   • Determine the length of the linked list.
   • Identify the tail node.
2. Handle Edge Cases:
   • If K is a multiple of the length, return original head.
3. Tail Node Adjustments:
   • Set the tail node's next pointer to the head.
4. Finding New Tail:
   • New tail is located at (length - K) position (after skipping last K nodes).
5. Update Head and Tail:
   • Update head to be the new head (next of the new tail).
   • Set the new tail's next pointer to null.
6. Return Updated Head.

Pseudocode Overview

• Initialize length and tail.
• Traverse to find length and tail node.
• Check if K is divisible by length: if yes, return head.
• Adjust pointers and update head and new tail.

Implementation Details

• Considerations for cases where list is empty or there are zero rotations.
• Implement a generic function to find the Nth node.

Complexity Analysis

• Time Complexity: O(N) due to traversals for length and finding the Nth node.
  • In the worst case, you may traverse the entire linked list twice.
• Space Complexity: O(1) as no additional space is used beyond a few variables.

Conclusion

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