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 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' 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 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"; printList(head); // sort the biotonic DLL head = sortAKSortedDLL(head, k); cout << "\nDoubly linked list after sorting:n"; printList(head); return 0; }

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(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 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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