Sort a k sorted doubly linked list

03 Jul, 2022
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++
Java
Python3
Javascript
// C++ implementation to sort a k sorted doubly// linked list#include<bits/stdc++.h>using namespace std;  // a node of the doubly linked liststruct Node {    int data;    struct Node* next;    struct Node* prev;};    // function to sort a k sorted doubly linked liststruct 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 Listvoid 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 listvoid 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 aboveint 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 implementation to sort a k sorted doublyimport 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 codepublic 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)
# Python implementation to sort a k sorted doublyclass DoublyLinkedList {head = None  class Node:    def __init__(self, val):        self.data = val        self.prev = None        self.next = None  # function to sort a k sorted doubly linked list# Using Insertion Sort# Time Complexity: O(n*k)# Space Complexity: O(1)def sortAKSortedDLL(head , k):    if (head == None or head.next == None):        return head      # perform on all the nodes in list    i = head.next    while(i != None):        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 != None and j.data < j.prev.data):                        # swap j and j.prev node            temp = j.prev.prev            temp2 = j.prev            temp3 = j.next            j.prev.next = temp3            j.prev.prev = j            j.prev = temp            j.next = temp2            if (temp != None):                temp.next = j            if (temp3 != None):                temp3.prev = temp2                              # if j is now the new head            # then reset head        if (j.prev == None):            head = j        i = i.next      return head  # UTILITY FUNCTIONS ## Function to insert a node at the beginning of the Doubly Linked Listdef push(new_data):      global head          # allocate node    new_node = Node(new_data)      #    # since we are adding at the beginning, prev is always NULL    #    new_node.prev = None      # link the old list off the new node     new_node.next = head      # change prev of head node to new node    if (head != None):        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 listdef printList(node):    while (node != None):        print(node.data,end = " ")        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<->8push(8)push(56)push(12)push(2)push(6)push(3)  k = 2  print("Original Doubly linked list:")printList(head)  sortedDLL = sortAKSortedDLL(head, k)print("")print("Doubly Linked List after sorting:")printList(sortedDLL)  # This codeis contributed by shinjanpatra
<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 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     */    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>
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
Java
// C++ implementation to sort a k sorted doubly// linked list#include <bits/stdc++.h>using namespace std;  // a node of the doubly linked liststruct Node {    int data;    struct Node* next;    struct Node* prev;};  // 'compare' function used to build up the// priority queuestruct compare {    bool operator()(struct Node* p1, struct Node* p2)    {        return p1->data > p2->data;    }};  // function to sort a k sorted doubly linked liststruct 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 Listvoid 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 listvoid 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 aboveint 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 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
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)
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mittulmandhan
sachinjain74754
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shinjanpatra
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