Java Program For Sorting A Linked List That Is Sorted Alternating Ascending And Descending Orders

Given a Linked List. The Linked List is in alternating ascending and descending orders. Sort the list efficiently. 

Example:

Input List: 10 -> 40 -> 53 -> 30 -> 67 -> 12 -> 89 -> NULL
Output List: 10 -> 12 -> 30 -> 40 -> 53 -> 67 -> 89 -> NULL

Input List: 1 -> 4 -> 3 -> 2 -> 5 -> NULL
Output List: 1 -> 2 -> 3 -> 4 -> 5 -> NULL

Simple Solution:
Approach: The basic idea is to apply to merge sort on the linked list. 
The implementation is discussed in this article: Merge Sort for linked List.
Complexity Analysis:

• Time Complexity: The merge sort of linked list takes O(n log n) time. In the merge sort tree, the height is log n. Sorting each level will take O(n) time. So time complexity is O(n log n).
• Auxiliary Space: O(n log n), In the merge sort tree the height is log n. Storing each level will take O(n) space. So space complexity is O(n log n).

Efficient Solution:
Approach:

1. Separate two lists.
2. Reverse the one in descending order
3. Merge both lists.

Diagram:

Below are the implementations of the above algorithm: 

Java

// Java program to sort a linked list
// that is alternatively sorted in
// increasing and decreasing order
import java.io.*;

public class LinkedList {
    // head of list
    Node head;

    // Linked list Node
    class Node {
        int data;
        Node next;
        Node(int d)
        {
            data = d;
            next = null;
        }
    }

    Node newNode(int key) { return new Node(key); }

    /* This is the main function that sorts
       the linked list.*/
    void sort()
    {
        /* Create 2 dummy nodes and initialise
           as heads of linked lists */
        Node Ahead = new Node(0), Dhead = new Node(0);

        // Split the list into lists
        splitList(Ahead, Dhead);

        Ahead = Ahead.next;
        Dhead = Dhead.next;

        // Reverse the descending list
        Dhead = reverseList(Dhead);

        // Merge the 2 linked lists
        head = mergeList(Ahead, Dhead);
    }

    // Function to reverse the linked list
    Node reverseList(Node Dhead)
    {
        Node current = Dhead;
        Node prev = null;
        Node next;
        while (current != null) {
            next = current.next;
            current.next = prev;
            prev = current;
            current = next;
        }
        Dhead = prev;
        return Dhead;
    }

    // Function to print linked list
    void printList()
    {
        Node temp = head;
        while (temp != null) {
            System.out.print(temp.data + " ");
            temp = temp.next;
        }
        System.out.println();
    }

    // A utility function to merge
    // two sorted linked lists
    Node mergeList(Node head1, Node head2)
    {
        // Base cases
        if (head1 == null)
            return head2;
        if (head2 == null)
            return head1;

        Node temp = null;
        if (head1.data < head2.data) {
            temp = head1;
            head1.next = mergeList(head1.next, head2);
        }
        else {
            temp = head2;
            head2.next = mergeList(head1, head2.next);
        }
        return temp;
    }

    // This function alternatively splits
    // a linked list with head as head into two:
    // For example, 10->20->30->15->40->7 is
    // splitted into 10->30->40 and 20->15->7
    // "Ahead" is reference to head of ascending
    // linked list
    // "Dhead" is reference to head of descending
    // linked list
    void splitList(Node Ahead, Node Dhead)
    {
        Node ascn = Ahead;
        Node dscn = Dhead;
        Node curr = head;

        // Link alternate nodes

        while (curr != null) {
            // Link alternate nodes in
            // ascending order
            ascn.next = curr;
            ascn = ascn.next;
            curr = curr.next;

            if (curr != null) {
                dscn.next = curr;
                dscn = dscn.next;
                curr = curr.next;
            }
        }

        ascn.next = null;
        dscn.next = null;
    }

    // Driver code
    public static void main(String args[])
    {
        LinkedList llist = new LinkedList();
        llist.head = llist.newNode(10);
        llist.head.next = llist.newNode(40);
        llist.head.next.next = llist.newNode(53);
        llist.head.next.next.next = llist.newNode(30);
        llist.head.next.next.next.next = llist.newNode(67);
        llist.head.next.next.next.next.next
            = llist.newNode(12);
        llist.head.next.next.next.next.next.next
            = llist.newNode(89);

        System.out.println("Given linked list");
        llist.printList();

        llist.sort();

        System.out.println("Sorted linked list");
        llist.printList();
    }
}
// This code is contributed by Rajat Mishra

Output

Given linked list
10 40 53 30 67 12 89 
Sorted linked list
10 12 30 40 53 67 89 

Complexity Analysis:

• Time Complexity: O(n). 
  One traversal is needed to separate the list and reverse them. The merging of sorted lists takes O(n) time.
• Auxiliary Space: O(1). 
  No extra space is required.

Please refer complete article on Sort a linked list that is sorted alternating ascending and descending orders? for more details!