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:

**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(¤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 << "\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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.