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.

Examples:

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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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