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# Delete last n nodes from end of doubly linked list

The problem at hand involves deleting the last n nodes from a doubly linked list. In a doubly linked list, each node contains a data element and two pointers, one pointing to the next node and another pointing to the previous node. The task is to remove the last n nodes from the end of the list.

## Problem Statement

Given a doubly linked list and an integer n, the objective is to delete the last n nodes from the end of the list.

## Example

Consider the following doubly linked list:

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

If we want to delete the last 5 nodes from the end of the list, the resulting list should be:

1 <-> 2 <-> 3

## Idea to Solve

To solve this problem, you need to traverse the list while keeping track of the number of nodes you have visited. Once you have visited n nodes, you can manipulate the pointers of the nodes to remove them from the list.

## Pseudocode

function deleteLastN(n):
if head is null or n is less than or equal to 0:
return

counter = 0
auxiliary = null

// Check if n nodes exist in the list
while temp is not null and counter < n:
increment counter by 1
move temp to the next node

if counter is greater than or equal to n:
temp = tail
counter = n
// Traverse and delete last n nodes
while tail is not null and counter > 0:
move tail to the previous node
set temp's pointers to null
decrement counter by 1

if tail is not null:
set tail's next pointer to null
else:
print "Deleted " + n + " nodes are missing"

## Algorithm Explanation

1. Start by initializing temp to the head, counter to 0, and auxiliary to null.
2. Traverse the doubly linked list using the temp pointer:
• Increment the counter by 1.
• Move temp to the next node.
3. After traversing, check if counter is greater than or equal to n:
• If it is, you have visited at least n nodes.
• Initialize temp to the tail and counter to n.
• Loop through n times and delete nodes from the end:
• Move tail to the previous node.
• Set temp's pointers to null.
• If the node being deleted is the head, update head to null.
• Set tail's next pointer to null after deletion.
4. If counter is less than n, print a message indicating that the nodes to be deleted don't exist.

## Time Complexity

The time complexity of this algorithm is O(n), where n is the number of nodes in the doubly linked list. In the worst case, you might need to traverse the entire list to delete the last n nodes.

## Comment

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