Sort a k sorted doubly linked list

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.


Naive Approach: Sort the given doubly linked list using insertion sort technique.

Time Complexity: O(nk)
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.

// 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' implemeted 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'

        // 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 =;
            newHead->prev = NULL;

            // 'last' points to the last node
            // of the result sorted list so far
            last = newHead;

        else {
            last->next =;
  >prev = last;
            last =;

        // remove element from 'pq'

        // if there are more nodes left in the input list
        if (head != NULL) {
            // push the node on to 'pq'

            // 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 begining,
    // 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";

    // sort the biotonic DLL
    head = sortAKSortedDLL(head, k);

    cout << "\nDoubly linked list after sorting:n";

    return 0;


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

Time Complexity: O(nLogk)
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 or mail your article to See your article appearing on the GeeksforGeeks main page and help other Geeks.

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