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Sort a k sorted doubly linked list
• Difficulty Level : Medium
• Last Updated : 14 Apr, 2021

Given a doubly linked list containing n nodes, where each node is at most k away from its target position in the list. The problem is to sort the given doubly linked list.
For example, let us consider k is 2, a node at position 7 in the sorted doubly linked list, can be at positions 5, 6, 7, 8, 9 in the given doubly linked list.
Examples: Naive Approach: Sort the given doubly linked list using the insertion sort technique. While inserting each element in the sorted part of the list, there will be at most k swaps to place the element to its correct position since it is at most k steps away from its correct position.

## Java

 `// Java implementation to sort a k sorted doubly``import` `java.util.*;``class` `DoublyLinkedList``{``static` `Node head;``static` `class` `Node``{``    ``int` `data;``    ``Node next, prev;``    ``Node(``int` `d)``    ``{``    ``data = d;``    ``next = prev = ``null``;``    ``}``}` `// function to sort a k sorted doubly linked list``// Using Insertion Sort``// Time Complexity: O(n*k)``// Space Complexity: O(1)``Node sortAKSortedDLL( Node head, ``int` `k) {``      ``if``(head == ``null` `|| head.next == ``null``)``        ``return` `head;` `    ``// perform on all the nodes in list``    ``for``(Node i = head.next; i != ``null``; i = i.next) {``        ``Node j = i;``          ``// There will be atmost k swaps for each element in the list``        ``// since each node is k steps away from its correct position``        ``while``(j.prev != ``null` `&& j.data < j.prev.data) {``              ``// swap j and j.prev node``            ``Node temp = j.prev.prev;``            ``Node temp2 = j.prev;``            ``Node temp3 = j.next;``            ``j.prev.next = temp3;``            ``j.prev.prev = j;``            ``j.prev = temp;``            ``j.next = temp2;``            ``if``(temp != ``null``)``                ``temp.next = j;``            ``if``(temp3 != ``null``)``                ``temp3.prev = temp2;``        ``}``          ``// if j is now the new head``       ``// then reset head``        ``if``(j.prev == ``null``)``            ``head = j;``    ``}``    ``return` `head;``}` `/* UTILITY FUNCTIONS */``/* Function to insert a node at the beginning of the``    ``* Doubly Linked List */``void` `push(``int` `new_data)``{``    ``/* allocate node */``    ``Node new_node = ``new` `Node(new_data);` `    ``/* since we are adding at the beginning,``        ``prev is always NULL */``    ``new_node.prev = ``null``;` `    ``/* link the old list off the new node */``    ``new_node.next = head;` `    ``/* change prev of head node to new node */``    ``if` `(head != ``null``)``    ``{``    ``head.prev = new_node;``    ``}` `    ``/* move the head to point to the new node */``    ``head = new_node;``}` `/* Function to print nodes in a given doubly linked list``    ``This function is same as printList() of singly linked``    ``list */``void` `printList(Node node)``{``    ``while` `(node != ``null``)``    ``{``    ``System.out.print(node.data + ``" "``);``    ``node = node.next;``    ``}``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``DoublyLinkedList list = ``new` `DoublyLinkedList();` `    ``/* Let us create a k sorted doubly linked list to test the``        ``functions Created doubly linked list will be 3<->6<->2<->12<->56<->8``    ``*/``    ``list.push(``8``);``    ``list.push(``56``);``    ``list.push(``12``);``    ``list.push(``2``);``    ``list.push(``6``);``    ``list.push(``3``);` `    ``int` `k = ``2``;` `    ``System.out.println(``"Original Doubly linked list:"``);``    ``list.printList(head);` `    ``Node sortedDLL = list.sortAKSortedDLL(head, k);``    ``System.out.println(``""``);``    ``System.out.println(``"Doubly Linked List after sorting:"``);``    ``list.printList(sortedDLL);``}``}` `// This code is contributed by Mittul Mandhan(@mittulmandhan)`
Output

```Original Doubly linked list:
3 6 2 12 56 8
Doubly Linked List after sorting:
2 3 6 8 12 56 ```

Time Complexity: O(n*k)

Auxiliary Space: O(1)

Efficient Approach: We can sort the list using the MIN HEAP data structure. The approach has been explained in Sort a nearly sorted (or K sorted) array. We only have to be careful while traversing the input doubly linked list and adjusting the required next and previous links in the final sorted list.

## CPP

 `// C++ implementation to sort a k sorted doubly``// linked list``#include ``using` `namespace` `std;` `// a node of the doubly linked list``struct` `Node {``    ``int` `data;``    ``struct` `Node* next;``    ``struct` `Node* prev;``};` `// 'compare' function used to build up the``// priority queue``struct` `compare {``    ``bool` `operator()(``struct` `Node* p1, ``struct` `Node* p2)``    ``{``        ``return` `p1->data > p2->data;``    ``}``};` `// function to sort a k sorted doubly linked list``struct` `Node* sortAKSortedDLL(``struct` `Node* head, ``int` `k)``{``    ``// if list is empty``    ``if` `(head == NULL)``        ``return` `head;` `    ``// priority_queue 'pq' implemented as min heap with the``    ``// help of 'compare' function``    ``priority_queue, compare> pq;` `    ``struct` `Node* newHead = NULL, *last;` `    ``// Create a Min Heap of first (k+1) elements from``    ``// input doubly linked list``    ``for` `(``int` `i = 0; head != NULL && i <= k; i++) {``        ``// push the node on to 'pq'``        ``pq.push(head);` `        ``// move to the next node``        ``head = head->next;``    ``}` `    ``// loop till there are elements in 'pq'``    ``while` `(!pq.empty()) {` `        ``// place root or top of 'pq' at the end of the``        ``// result sorted list so far having the first node``        ``// pointed to by 'newHead'``        ``// and adjust the required links``        ``if` `(newHead == NULL) {``            ``newHead = pq.top();``            ``newHead->prev = NULL;` `            ``// 'last' points to the last node``            ``// of the result sorted list so far``            ``last = newHead;``        ``}` `        ``else` `{``            ``last->next = pq.top();``            ``pq.top()->prev = last;``            ``last = pq.top();``        ``}` `        ``// remove element from 'pq'``        ``pq.pop();` `        ``// if there are more nodes left in the input list``        ``if` `(head != NULL) {``            ``// push the node on to 'pq'``            ``pq.push(head);` `            ``// move to the next node``            ``head = head->next;``        ``}``    ``}` `    ``// making 'next' of last node point to NULL``    ``last->next = NULL;` `    ``// new head of the required sorted DLL``    ``return` `newHead;``}` `// Function to insert a node at the beginning``// of the Doubly Linked List``void` `push(``struct` `Node** head_ref, ``int` `new_data)``{``    ``// allocate node``    ``struct` `Node* new_node =``          ``(``struct` `Node*)``malloc``(``sizeof``(``struct` `Node));` `    ``// put in the data``    ``new_node->data = new_data;` `    ``// since we are adding at the beginning,``    ``// prev is always NULL``    ``new_node->prev = NULL;` `    ``// link the old list off the new node``    ``new_node->next = (*head_ref);` `    ``// change prev of head node to new node``    ``if` `((*head_ref) != NULL)``        ``(*head_ref)->prev = new_node;` `    ``// move the head to point to the new node``    ``(*head_ref) = new_node;``}` `// Function to print nodes in a given doubly linked list``void` `printList(``struct` `Node* head)``{``    ``// if list is empty``    ``if` `(head == NULL)``        ``cout << ``"Doubly Linked list empty"``;` `    ``while` `(head != NULL) {``        ``cout << head->data << ``" "``;``        ``head = head->next;``    ``}``}` `// Driver program to test above``int` `main()``{``    ``struct` `Node* head = NULL;` `    ``// Create the doubly linked list:``    ``// 3<->6<->2<->12<->56<->8``    ``push(&head, 8);``    ``push(&head, 56);``    ``push(&head, 12);``    ``push(&head, 2);``    ``push(&head, 6);``    ``push(&head, 3);` `    ``int` `k = 2;` `    ``cout << ``"Original Doubly linked list:\n"``;``    ``printList(head);` `    ``// sort the biotonic DLL``    ``head = sortAKSortedDLL(head, k);` `    ``cout << ``"\nDoubly linked list after sorting:\n"``;``    ``printList(head);` `    ``return` `0;``}`

## Java

 `// Java implementation to sort a k sorted doubly``import` `java.util.*;``class` `DoublyLinkedList``{``  ``static` `Node head;``  ``static` `class` `Node``  ``{``    ``int` `data;``    ``Node next, prev;``    ``Node(``int` `d)``    ``{``      ``data = d;``      ``next = prev = ``null``;``    ``}``  ``}``  ``class` `compareNode ``implements` `Comparator``  ``{``    ``public` `int` `compare(Node n1, Node n2){``      ``return` `n1.data-n2.data;``    ``}``  ``}` `  ``// function to sort a k sorted doubly linked list``  ``Node sortAKSortedDLL( Node head, ``int` `k)``  ``{``    ` `    ``// if list is empty``    ``if` `(head == ``null``)``      ``return` `head;` `    ``// priority_queue 'pq' implemented as min heap with the``    ``// help of 'compare' function in compare Node class``    ``PriorityQueue pq = ``new` `PriorityQueue(``new` `compareNode());` `    ``Node newHead = ``null``, last = ``null``;` `    ``// Create a Min Heap of first (k+1) elements from``    ``// input doubly linked list``    ``for` `(``int` `i = ``0``; head != ``null` `&& i <= k; i++)``    ``{``      ` `      ``// push the node on to 'pq'``      ``pq.add(head);` `      ``// move to the next node``      ``head = head.next;``    ``}` `    ``// loop till there are elements in 'pq'``    ``while` `(!pq.isEmpty())``    ``{` `      ``// place root or top of 'pq' at the end of the``      ``// result sorted list so far having the first node``      ``// pointed to by 'newHead'``      ``// and adjust the required links``      ``if` `(newHead == ``null``)``      ``{``        ``newHead = pq.peek();``        ``newHead.prev = ``null``;` `        ``// 'last' points to the last node``        ``// of the result sorted list so far``        ``last = newHead;``      ``}` `      ``else``      ``{``        ``last.next = pq.peek();``        ``pq.peek().prev = last;``        ``last = pq.peek();``      ``}` `      ``// remove element from 'pq'``      ``pq.poll();` `      ``// if there are more nodes left in the input list``      ``if` `(head != ``null``)``      ``{``        ` `        ``// push the node on to 'pq'``        ``pq.add(head);` `        ``// move to the next node``        ``head = head.next;``      ``}``    ``}` `    ``// making 'next' of last node point to NULL``    ``last.next = ``null``;` `    ``// new head of the required sorted DLL``    ``return` `newHead;``  ``}` `  ``/* UTILITY FUNCTIONS */``  ``/* Function to insert a node at the beginning of the``     ``* Doubly Linked List */``  ``void` `push(``int` `new_data)``  ``{``    ``/* allocate node */``    ``Node new_node = ``new` `Node(new_data);` `    ``/* since we are adding at the beginning,``         ``prev is always NULL */``    ``new_node.prev = ``null``;` `    ``/* link the old list off the new node */``    ``new_node.next = head;` `    ``/* change prev of head node to new node */``    ``if` `(head != ``null``)``    ``{``      ``head.prev = new_node;``    ``}` `    ``/* move the head to point to the new node */``    ``head = new_node;``  ``}` `  ``/* Function to print nodes in a given doubly linked list``     ``This function is same as printList() of singly linked``     ``list */``  ``void` `printList(Node node)``  ``{``    ``while` `(node != ``null``)``    ``{``      ``System.out.print(node.data + ``" "``);``      ``node = node.next;``    ``}``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String[] args)``  ``{``    ``DoublyLinkedList list = ``new` `DoublyLinkedList();` `    ``/* Let us create a k sorted doubly linked list to test the``         ``functions Created doubly linked list will be 3<->6<->2<->12<->56<->8``       ``*/``    ``list.push(``8``);``    ``list.push(``56``);``    ``list.push(``12``);``    ``list.push(``2``);``    ``list.push(``6``);``    ``list.push(``3``);` `    ``int` `k = ``2``;` `    ``System.out.println(``"Original Doubly linked list:"``);``    ``list.printList(head);` `    ``Node sortedDLL = list.sortAKSortedDLL(head, k);``    ``System.out.println(``""``);``    ``System.out.println(``"Doubly Linked List after sorting:"``);``    ``list.printList(sortedDLL);``  ``}``}` `// This code is contributed by Kushagra Keserwani`
Output
```Original Doubly linked list:
3 6 2 12 56 8
Doubly linked list after sorting:
2 3 6 8 12 56 ```

Time Complexity: O(n*log k)
Auxiliary Space: O(k)

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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