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
    
    temp = head
    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
            if temp equals head:
                set head 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.

Program List

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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.