Sorting a Bitonic Doubly Linked List

This set of vocabulary flashcards covers the concepts, steps, and technical complexities involved in sorting a bitonic doubly linked list as discussed in the lecture.

Bitonic Doubly Linked List

A linked list that exhibits a pattern of monotonically increasing elements followed by monotonically decreasing elements or vice versa.

Peak Node

The point in the sequence where the ascending order ends and the descending order begins.

Bitonic Point

The transition point where the list switches from an increasing sequence to a decreasing sequence.

Step 1: Identify the Peak Node

Traverse the doubly linked list from the beginning to locate the node where the ascending sequence ends.

Step 2: Split the List

Divide the original list into two parts: one containing the ascending sequence (from start to peak) and one containing the descending sequence (from after the peak to the end).

Step 3: Reverse the Second List

Perform an operation on the descending sublist to convert it into ascending order.

Step 4: Merge the Two Sorted Lists

Combine the first ascending part and the reversed second part to create a single, fully sorted doubly linked list.

Time Complexity

$O(n)$, where $n$ is the number of nodes, based on single traversal, reverse, and merge operations.

Space Complexity

$O(1)$ due to in-place pointer manipulation during the sorting process.

Space Complexity Optimization

Using an iterative approach for reversed sublists and rearranging existing pointers during merge to reduce auxiliary space from $O(n)$ to $O(1)$.

Node Class Structure

A static class containing integer data, a reference to the next node (next), and a reference to the previous node (prev).

reverse(Node head_ref)

A function that uses a current and temp node to swap the prev and next pointers of each node in the list.

merge(Node first, Node second)

A function that recursively compares node data to combine two sorted doubly linked lists into one.

push(Node head_ref, int new_data)

A function that adds a new node with specific data to the front of the doubly linked list.