# 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 ` ` `  `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(¤t); ` ` `  `    ``// 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 << ````" Doubly linked list after sorting:n"````; ` `    ``printList(head); ` ` `  `    ``return` `0; ` `} `

Output:

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

Time Complexity: O(n)