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:

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.

Implementation:

C++14

// 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;

    // split 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 beginning,
    // prev is always NULL
    new_node->prev = NULL;

    // link the old list of 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;
}

Java

// Java implementation to sort the
// biotonic doubly linked list
import java.io.*;
import java.util.*;

class GFG {

    // a node of the doubly linked list
    static class Node {
        int data;
        Node next;
        Node prev;
    }

    // Function to reverse a Doubly Linked List
    static Node reverse(Node head_ref)
    {
        Node temp = null;
        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;
        return head_ref;
    }

    // Function to merge two sorted doubly linked lists
    static Node merge(Node first, Node second)
    {
        // If first linked list is empty
        if (first == null)
            return second;

        // If second linked list is empty
        if (second == null)
            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
    static Node sort(Node head)
    {
        // if list is empty or if it contains
        // a single node only
        if (head == null || head.next == null)
            return head;

        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;

        // split 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'
        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
    static Node push(Node head_ref, int new_data)
    {
        // allocate node
        Node new_node = new Node();

        // put in the data
        new_node.data = new_data;

        // since we are adding at the beginning,
        // prev is always null
        new_node.prev = null;

        // link the old list of 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;
        return head_ref;
    }

    // Function to print nodes in a given doubly
    // linked list
    static void printList(Node head)
    {
        // if list is empty
        if (head == null)
            System.out.println("Doubly Linked list empty");

        while (head != null) {
            System.out.print(head.data + " ");
            head = head.next;
        }
    }

    // Driver Code
    public static void main(String args[])
    {
        Node head = null;

        // Create the doubly linked list:
        // 2<.5<.7<.12<.10<.6<.4<.1
        head = push(head, 1);
        head = push(head, 4);
        head = push(head, 6);
        head = push(head, 10);
        head = push(head, 12);
        head = push(head, 7);
        head = push(head, 5);
        head = push(head, 2);

        System.out.println("Original Doubly linked list:");
        printList(head);

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

        System.out.println(
            "\nDoubly linked list after sorting:");
        printList(head);
    }
}

// This code is contributed by Arnab Kundu

Python

# Python implementation to sort the
# biotonic doubly linked list

# Node of a doubly linked list
class Node:
    def __init__(self, next = None, prev = None,
                data = None):
        self.next = next
        self.prev = prev
        self.data = data

# Function to reverse a Doubly Linked List
def reverse( head_ref):

    temp = None
    current = head_ref

    # swap next and prev for all nodes
    # of doubly linked list
    while (current != None):

        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 != None):
        head_ref = temp.prev
        return head_ref

# Function to merge two sorted doubly linked lists
def merge( first, second):

    # If first linked list is empty
    if (first == None):
        return second

    # If second linked list is empty
    if (second == None):
        return first

    # Pick the smaller value
    if (first.data < second.data):

        first.next = merge(first.next, second)
        first.next.prev = first
        first.prev = None
        return first

    else:

        second.next = merge(first, second.next)
        second.next.prev = second
        second.prev = None
        return second

# function to sort a biotonic doubly linked list
def sort( head):

    # if list is empty or if it contains
    # a single node only
    if (head == None or head.next == None):
        return head

    current = head.next

    while (current != None) :

        # 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 == None):
        return head

    # split into two lists, one starting with 'head'
    # and other starting with 'current'
    current.prev.next = None
    current.prev = None

    # reverse the list starting with 'current'
    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
def push( head_ref, new_data):

    # allocate node
    new_node =Node()

    # put in the data
    new_node.data = new_data

    # since we are adding at the beginning,
    # prev is always None
    new_node.prev = None

    # link the old list of the new node
    new_node.next = (head_ref)

    # change prev of head node to new node
    if ((head_ref) != None):
        (head_ref).prev = new_node

    # move the head to point to the new node
    (head_ref) = new_node
    return head_ref


# Function to print nodes in a given doubly
# linked list
def printList( head):

    # if list is empty
    if (head == None):
        print("Doubly Linked list empty")

    while (head != None):

        print(head.data, end= " ")
        head = head.next

# Driver Code

head = None

# Create the doubly linked list:
# 2<.5<.7<.12<.10<.6<.4<.1
head = push(head, 1)
head = push(head, 4)
head = push(head, 6)
head = push(head, 10)
head = push(head, 12)
head = push(head, 7)
head = push(head, 5)
head = push(head, 2)

print("Original Doubly linked list:")
printList(head)

# sort the biotonic DLL
head = sort(head)

print("\nDoubly linked list after sorting:")
printList(head)

# This code is contributed by Arnab Kundu

C#

// C# implementation to sort the
// biotonic doubly linked list
using System;

class GFG
{

// a node of the doubly linked list
public class Node
{
    public int data;
    public Node next;
    public Node prev;
}

// Function to reverse a Doubly Linked List
static Node reverse( Node head_ref)
{
    Node temp = null;
    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;
        return head_ref;
}

// Function to merge two sorted doubly linked lists
static Node merge(Node first, Node second)
{
    // If first linked list is empty
    if (first == null)
        return second;

    // If second linked list is empty
    if (second == null)
        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
static Node sort(Node head)
{
    // if list is empty or if it contains
    // a single node only
    if (head == null || head.next == null)
        return head;

    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;

    // split 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'
    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
static Node push( Node head_ref, int new_data)
{
    // allocate node
    Node new_node = new Node();

    // put in the data
    new_node.data = new_data;

    // since we are adding at the beginning,
    // prev is always null
    new_node.prev = null;

    // link the old list of 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;
    return head_ref;
}

// Function to print nodes in a given doubly
// linked list
static void printList( Node head)
{
    // if list is empty
    if (head == null)
        Console.WriteLine("Doubly Linked list empty");

    while (head != null)
    {
        Console.Write(head.data + " ");
        head = head.next;
    }
}

// Driver Code
public static void Main(String []args)
{
    Node head = null;

    // Create the doubly linked list:
    // 2<.5<.7<.12<.10<.6<.4<.1
    head = push(head, 1);
    head = push(head, 4);
    head = push(head, 6);
    head = push(head, 10);
    head = push(head, 12);
    head = push(head, 7);
    head = push(head, 5);
    head = push(head, 2);

    Console.WriteLine("Original Doubly linked list:");
    printList(head);

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

    Console.WriteLine("\nDoubly linked list after sorting:");
    printList(head);
}
}

// This code is contributed by PrinciRaj1992

Javascript

<script>
// javascript implementation to sort the
// biotonic doubly linked list    // a node of the doubly linked list
 class Node {
        constructor() {
            this.data = 0;
            this.prev = null;
            this.next = null;
        }
    }

    // Function to reverse a Doubly Linked List
    function reverse(head_ref) {
var temp = null;
var 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;
        return head_ref;
    }

    // Function to merge two sorted doubly linked lists
    function merge(first,  second) {
        // If first linked list is empty
        if (first == null)
            return second;

        // If second linked list is empty
        if (second == null)
            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
    function sort(head) {
        // if list is empty or if it contains
        // a single node only
        if (head == null || head.next == null)
            return head;

var 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;

        // split 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'
        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
    function push(head_ref , new_data) {
        // allocate node
var new_node = new Node();

        // put in the data
        new_node.data = new_data;

        // since we are adding at the beginning,
        // prev is always null
        new_node.prev = null;

        // link the old list of 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;
        return head_ref;
    }

    // Function to print nodes in a given doubly
    // linked list
    function printList(head) {
        // if list is empty
        if (head == null)
            document.write("Doubly Linked list empty");

        while (head != null) {
            document.write(head.data + " ");
            head = head.next;
        }
    }

    // Driver Code

var head = null;

        // Create the doubly linked list:
        // 2<.5<.7<.12<.10<.6<.4<.1
        head = push(head, 1);
        head = push(head, 4);
        head = push(head, 6);
        head = push(head, 10);
        head = push(head, 12);
        head = push(head, 7);
        head = push(head, 5);
        head = push(head, 2);

        document.write("Original Doubly linked list:<br/>");
        printList(head);

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

        document.write("<br/>Doubly linked list after sorting:<br/>");
        printList(head);

// This code contributed by aashish1995
</script>

Output

Original Doubly linked list:n2 5 7 12 10 6 4 1 
Doubly linked list after sorting:n1 2 4 5 6 7 10 12 

Time Complexity: O(n)