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:  

90 10 49 1 5 2 23