Sort a Linked List in wave form

Given an unsorted Linked List of integers. The task is to sort the Linked List into a wave like Line. A Linked List is said to be sorted in Wave Form if the list after sorting is in the form: 

list[0] >= list[1] <= list[2] >= …..

Where list[i] denotes the data at i-th node of the Linked List.

Examples:  

Input : List = 2 -> 4 -> 6 -> 8 -> 10 -> 20
Output : 4 -> 2 -> 8 -> 6 -> 20 -> 10

Input : List = 3 -> 6 -> 5 -> 10 -> 7 -> 20
Output : 6 -> 3 -> 10 -> 5 -> 20 -> 7

A Simple Solution is to use sorting. First sort the input linked list, then swap all adjacent elements.

For example, let the input list be 3 -> 6 -> 5 -> 10 -> 7 -> 20. After sorting, we get 3 -> 5 -> 6 -> 7 -> 10 -> 20. After swapping adjacent elements, we get 5 -> 3 -> 7 -> 6 -> 20 -> 10 which is the required list in wave form.

Time Complexity: O(N*logN), where N is the number nodes in the list.

Efficient Solution: This can be done in O(n) time by doing a single traversal of the given list. The idea is based on the fact that if we make sure that all even positioned (at index 0, 2, 4, ..) elements are greater than their adjacent odd elements, we don’t need to worry about oddly positioned element. Following are simple steps.

Note: Assuming indexes in list starts from zero. That is, list[0] represents the first elements of the linked list.

Traverse all even positioned elements of input linked list, and do following. 

• If current element is smaller than previous odd element, swap previous and current.
• If current element is smaller than next odd element, swap next and current.

Below is the implementation of above approach:  

C++

// C++ program to sort linked list
// in wave form
#include <climits>
#include <iostream>

using namespace std;

// A linked list node
struct Node {
    int data;
    struct Node* next;
};

// Function to add a node at the
// beginning of 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;

    /* link the old list of the new node */
    new_node->next = (*head_ref);

    /* move the head to point to the new node */
    (*head_ref) = new_node;
}

// Function get size of the list
int listSize(struct Node* node)
{
    int c = 0;

    while (node != NULL) {
        c++;

        node = node->next;
    }

    return c;
}

// Function to print the list
void printList(struct Node* node)
{
    while (node != NULL) {
        cout << node->data << " ";

        node = node->next;
    }
}

/* UTILITY FUNCTIONS */
/* Function to swap two integers */
void swap(int* a, int* b)
{
    int temp;
    temp = *a;
    *a = *b;
    *b = temp;
}

// Function to sort linked list in
// wave form
void sortInWave(struct Node* head)
{
    struct Node* current = head;
    struct Node* prev = NULL;

    // Variable to track even position
    int i = 0;

    // Size of list
    int n = listSize(head);

    // Traverse all even positioned nodes
    while (i < n) {

        if (i % 2 == 0) {
            // If current even element is
            // smaller than previous
            if (i > 0 && (prev->data > current->data))
                swap(&(current->data), &(prev->data));

            // If current even element is
            // smaller than next
            if (i < n - 1 && (current->data < current->next->data))
                swap(&(current->data), &(current->next->data));
        }

        i++;

        prev = current;
        current = current->next;
    }
}

// Driver program to test above function
int main()
{
    struct Node* start = NULL;

    /* The constructed linked list is:
    10, 90, 49, 2, 1, 5, 23*/
    push(&start, 23);
    push(&start, 5);
    push(&start, 1);
    push(&start, 2);
    push(&start, 49);
    push(&start, 90);
    push(&start, 10);

    sortInWave(start);

    printList(start);

    return 0;
}

Java

// Java program to sort linked list
// in wave form
class GFG
{

// A linked list node
static class Node
{
    int data;
    Node next;
};

// Function to add a node at the
// beginning of 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;

    /* link the old list of the new node */
    new_node.next = (head_ref);

    /* move the head to point to the new node */
    (head_ref) = new_node;
    return head_ref;
}

// Function get size of the list
static int listSize( Node node)
{
    int c = 0;
    while (node != null)
    {
        c++;
        node = node.next;
    }
    return c;
}

// Function to print the list
static void printList( Node node)
{
    while (node != null)
    {
        System.out.print(node.data + " ");
        node = node.next;
    }
}

// Function to sort linked list in
// wave form
static Node sortInWave( Node head)
{
    Node current = head;
    Node prev = null;

    // Variable to track even position
    int i = 0;

    // Size of list
    int n = listSize(head);

    // Traverse all even positioned nodes
    while (i < n)
    {
        if (i % 2 == 0)
        {
            // If current even element is
            // smaller than previous
            if (i > 0 && (prev.data > current.data))
            {
                int t = prev.data;
                prev.data = current.data;
                current.data = t;
            }

            // If current even element is
            // smaller than next
            if (i < n - 1 && (current.data <
                              current.next.data))
            {
                int t = current.next.data;
                current.next.data = current.data;
                current.data = t;
            }
        }
        i++;

        prev = current;
        current = current.next;
    }
    return head;
}

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

    /* The constructed linked list is:
    10, 90, 49, 2, 1, 5, 23*/
    start = push(start, 23);
    start = push(start, 5);
    start = push(start, 1);
    start = push(start, 2);
    start = push(start, 49);
    start = push(start, 90);
    start = push(start, 10);

    start = sortInWave(start);

    printList(start);
}
}

// This code is contributed by Arnab Kundu

Python3

# Python3 program to sort linked list
# in wave form

# A linked list node
class Node:

    def __init__(self):

        self.data = 0
        self.next = None

# Function to add a node at the
# beginning of Linked List
def push( head_ref, new_data):

    ''' allocate node '''
    new_node = Node()

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

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

    ''' move the head to point to the new node '''
    (head_ref) = new_node;

    return head_ref

# Function get size of the list
def listSize(node):

    c = 0;

    while (node != None):
        c += 1

        node = node.next;

    return c;

# Function to print the list
def printList(node):

    while (node != None):

        print(node.data, end = ' ')

        node = node.next;

# Function to sort linked list in
# wave form
def sortInWave(head):

    current = head;
    prev = None;

    # Variable to track even position
    i = 0;

    # Size of list
    n = listSize(head);

    # Traverse all even positioned nodes
    while (i < n):

        if (i % 2 == 0):

            # If current even element is
            # smaller than previous
            if (i > 0 and (prev.data > current.data)):
                (current.data), (prev.data) = (prev.data), (current.data)

            # If current even element is
            # smaller than next
            if (i < n - 1 and (current.data < current.next.data)):
                (current.data), (current.next.data) = (current.next.data), (current.data)

        i += 1

        prev = current;
        current = current.next;

# Driver program to test above function
if __name__=='__main__':

    start = None;

    ''' The constructed linked list is:
    10, 90, 49, 2, 1, 5, 23'''
    start = push(start, 23);
    start = push(start, 5);
    start = push(start, 1);
    start = push(start, 2);
    start = push(start, 49);
    start = push(start, 90);
    start = push(start, 10)

    sortInWave(start)

    printList(start);

# This code is contributed by pratham76

C#

// C# program to sort linked list
// in wave form
using System;

class GFG{

// A linked list node
class Node
{
    public int data;
    public Node next;
};

// Function to add a node at the
// beginning of 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;

    // Link the old list of the new node
    new_node.next = (head_ref);

    // Move the head to point to the new node
    (head_ref) = new_node;
    return head_ref;
}

// Function get size of the list
static int listSize( Node node)
{
    int c = 0;

    while (node != null)
    {
        c++;
        node = node.next;
    }
    return c;
}

// Function to print the list
static void printList( Node node)
{
    while (node != null)
    {
        Console.Write(node.data + " ");
        node = node.next;
    }
}

// Function to sort linked list in
// wave form
static Node sortInWave( Node head)
{
    Node current = head;
    Node prev = null;

    // Variable to track even position
    int i = 0;

    // Size of list
    int n = listSize(head);

    // Traverse all even positioned nodes
    while (i < n)
    {
        if (i % 2 == 0)
        {

            // If current even element is
            // smaller than previous
            if (i > 0 && (prev.data >
                          current.data))
            {
                int t = prev.data;
                prev.data = current.data;
                current.data = t;
            }

            // If current even element is
            // smaller than next
            if (i < n - 1 && (current.data <
                              current.next.data))
            {
                int t = current.next.data;
                current.next.data = current.data;
                current.data = t;
            }
        }
        i++;

        prev = current;
        current = current.next;
    }
    return head;
}

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

    // The constructed linked list is:
    // 10, 90, 49, 2, 1, 5, 23
    start = push(start, 23);
    start = push(start, 5);
    start = push(start, 1);
    start = push(start, 2);
    start = push(start, 49);
    start = push(start, 90);
    start = push(start, 10);

    start = sortInWave(start);

    printList(start);
}
}

// This code is contributed by rutvik_56

Javascript

<script>

      // JavaScript program to sort linked list
      // in wave form
      // A linked list node
      class Node {
        constructor() {
          this.data = 0;
          this.next = null;
        }
      }

      // Function to add a node at the
      // beginning of Linked List
      function push(head_ref, new_data) {
        // Allocate node
        var new_node = new Node();

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

        // Link the old list of the new node
        new_node.next = head_ref;

        // Move the head to point to the new node
        head_ref = new_node;
        return head_ref;
      }

      // Function get size of the list
      function listSize(node) {
        var c = 0;

        while (node != null) {
          c++;
          node = node.next;
        }
        return c;
      }

      // Function to print the list
      function printList(node) {
        while (node != null) {
          document.write(node.data + " ");
          node = node.next;
        }
      }

      // Function to sort linked list in
      // wave form
      function sortInWave(head) {
        var current = head;
        var prev = null;

        // Variable to track even position
        var i = 0;

        // Size of list
        var n = listSize(head);

        // Traverse all even positioned nodes
        while (i < n) {
          if (i % 2 == 0) {
            // If current even element is
            // smaller than previous
            if (i > 0 && prev.data > current.data) {
              var t = prev.data;
              prev.data = current.data;
              current.data = t;
            }

            // If current even element is
            // smaller than next
            if (i < n - 1 && current.data < current.next.data) {
              var t = current.next.data;
              current.next.data = current.data;
              current.data = t;
            }
          }
          i++;

          prev = current;
          current = current.next;
        }
        return head;
      }

      // Driver Code
      var start = null;

      // The constructed linked list is:
      // 10, 90, 49, 2, 1, 5, 23
      start = push(start, 23);
      start = push(start, 5);
      start = push(start, 1);
      start = push(start, 2);
      start = push(start, 49);
      start = push(start, 90);
      start = push(start, 10);

      start = sortInWave(start);

      printList(start);

</script>

Output

90 10 49 1 5 2 23