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:

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// 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 off 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;
}

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Output:

90 10 49 1 5 2 23


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Improved By : Akanksha_Rai