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Sort a k sorted doubly linked list
  • Difficulty Level : Medium
  • Last Updated : 23 May, 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.

C++




// C++ implementation to sort a k sorted doubly
// linked list
#include<bits/stdc++.h>
using namespace std;
 
// a node of the doubly linked list
struct Node {
    int data;
    struct Node* next;
    struct Node* prev;
};
 
 
// function to sort a k sorted doubly linked list
struct Node* sortAKSortedDLL(struct 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;
}
 
// 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;
}
 
// This code is contributed by sachinejain74754.

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)

Javascript




<script>
// javascript implementation to sort a k sorted doublyclass DoublyLinkedList {
    var head;
 
     class Node {
            constructor(val) {
                this.data = val;
                this.prev = null;
                this.next = null;
            }
        }
 
    // function to sort a k sorted doubly linked list
    // Using Insertion Sort
    // Time Complexity: O(n*k)
    // Space Complexity: O(1)
    function sortAKSortedDLL(head , k) {
        if (head == null || head.next == null)
            return head;
 
        // perform on all the nodes in list
        for (i = head.next; i != null; i = i.next) {
    var 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
        var temp = j.prev.prev;
        var temp2 = j.prev;
        var 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
     */
    function push(new_data) {
        /* allocate node */
var 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 povar to the new node */
        head = new_node;
    }
 
    /*
     * Function to prvar nodes in a given doubly linked list This function is same
     * as printList() of singly linked list
     */
    function printList(node) {
        while (node != null) {
            document.write(node.data + " ");
            node = node.next;
        }
    }
 
    // Driver code
     
            /*
         * 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
         */
        push(8);
        push(56);
        push(12);
        push(2);
        push(6);
        push(3);
 
        var k = 2;
 
        document.write("Original Doubly linked list:<br/>");
        printList(head);
 
var sortedDLL = sortAKSortedDLL(head, k);
        document.write("");
        document.write("<br/>Doubly Linked List after sorting:<br/>");
        printList(sortedDLL);
 
// This code contributed by aashish1995
</script>
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 <bits/stdc++.h>
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<Node*, vector<Node*>, 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<Node>
  {
    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<Node> pq = new PriorityQueue<Node>(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 write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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