# Sort the biotonic doubly linked list

Sort the given biotonic doubly linked list. A biotonic doubly linked list is a doubly linked list which is first increasing and then decreasing. A strictly increasing or a strictly decreasing list is also a biotonic doubly linked list.

Examples:

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

Approach: Find the first node in the list which is smaller than its previous node. Let it be current. If no such node is present then list is already sorted. Else split the list into two lists, first starting from head node till the current’s previous node and second starting from current node till the end of the list. Reverse the second doubly linked list. Refer this post. Now merge the first and second sorted doubly linked list. Refer merge procedure of this post. The final merged list is the required sorted doubly linked list.

```// C++ implementation to sort the biotonic 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 reverse a Doubly Linked List
void reverse(struct Node** head_ref)
{
struct Node* temp = NULL;
struct Node* current = *head_ref;

// swap next and prev for all nodes
// of doubly linked list
while (current != NULL) {
temp = current->prev;
current->prev = current->next;
current->next = temp;
current = current->prev;
}

// Before changing head, check for the cases
// like empty list and list with only one node
if (temp != NULL)
*head_ref = temp->prev;
}

// Function to merge two sorted doubly linked lists
struct Node* merge(struct Node* first, struct Node* second)
{
// If first linked list is empty
if (!first)
return second;

// If second linked list is empty
if (!second)
return first;

// Pick the smaller value
if (first->data < second->data) {
first->next = merge(first->next, second);
first->next->prev = first;
first->prev = NULL;
return first;
} else {
second->next = merge(first, second->next);
second->next->prev = second;
second->prev = NULL;
return second;
}
}

// function to sort a biotonic doubly linked list
struct Node* sort(struct Node* head)
{
// if list is empty or if it contains a single
// node only
if (head == NULL || head->next == NULL)
return head;

struct Node* current = head->next;

while (current != NULL) {

// if true, then 'current' is the first node
// which is smaller than its previous node
if (current->data < current->prev->data)
break;

// move to the next node
current = current->next;
}

// if true, then list is already sorted
if (current == NULL)
return head;

// spilt into two lists, one starting with 'head'
// and other starting with 'current'
current->prev->next = NULL;
current->prev = NULL;

// reverse the list starting with 'current'
reverse(&current);

// merge the two lists and return the
// final merged doubly linked list
return merge(head, current);
}

// 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:
// 2<->5<->7<->12<->10<->6<->4<->1
push(&head, 1);
push(&head, 4);
push(&head, 6);
push(&head, 10);
push(&head, 12);
push(&head, 7);
push(&head, 5);
push(&head, 2);

cout << "Original Doubly linked list:n";
printList(head);

// sort the biotonic DLL
head = sort(head);

cout << "\nDoubly linked list after sorting:n";
printList(head);

return 0;
}
```

Output:

```Original Doubly linked list:
2 5 7 12 10 6 4 1
Doubly linked list after sorting:
1 2 4 5 6 7 10 12
```

Time Complexity: O(n)

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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