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Javascript Program to Sort an array in wave form

  • Last Updated : 27 Dec, 2021

Given an unsorted array of integers, sort the array into a wave like array. An array ‘arr[0..n-1]’ is sorted in wave form if arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4] >= …..

Examples: 

 Input:  arr[] = {10, 5, 6, 3, 2, 20, 100, 80}
 Output: arr[] = {10, 5, 6, 2, 20, 3, 100, 80} OR
                 {20, 5, 10, 2, 80, 6, 100, 3} OR
                 any other array that is in wave form

 Input:  arr[] = {20, 10, 8, 6, 4, 2}
 Output: arr[] = {20, 8, 10, 4, 6, 2} OR
                 {10, 8, 20, 2, 6, 4} OR
                 any other array that is in wave form

 Input:  arr[] = {2, 4, 6, 8, 10, 20}
 Output: arr[] = {4, 2, 8, 6, 20, 10} OR
                 any other array that is in wave form

 Input:  arr[] = {3, 6, 5, 10, 7, 20}
 Output: arr[] = {6, 3, 10, 5, 20, 7} OR
                 any other array that is in wave form
 

A Simple Solution is to use sorting. First sort the input array, then swap all adjacent elements.
For example, let the input array 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}. 

Below are implementations of this simple approach. 

Javascript




<script>
  
// A JavaScript program to sort an array 
// in wave form using a sorting function
  
// A utility method to swap two numbers.
function swap(arr, x, y)
{
    let temp = arr[x];
    arr[x] = arr[y];
    arr[y] = temp
}
  
// This function sorts arr[0..n-1] in 
// wave form, i.e.,
// arr[0] >= arr[1] <= arr[2] >= 
// arr[3] <= arr[4] >= arr[5]..
function sortInWave(arr, n)
{
      
    // Sort the input array
    arr.sort((a, b) => a - b);
  
    // Swap adjacent elements
    for(let i = 0; i < n - 1; i += 2)
        swap(arr, i, i + 1);
}
  
// Driver code
let arr = [ 10, 90, 49, 2, 1, 5, 23 ];
let n = arr.length;
  
sortInWave(arr, n);
  
for(let i = 0; i < n; i++)
    document.write(arr[i] + " ");
  
// This code is contributed by Surbhi Tyagi.
  
</script>

Output: 

2 1 10 5 49 23 90

The time complexity of the above solution is O(nLogn) if a O(nLogn) sorting algorithm like Merge Sort, Heap Sort, .. etc is used.
This can be done in O(n) time by doing a single traversal of given array. 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 odd positioned element. Following are simple steps. 
1) Traverse all even positioned elements of input array, and do following. 
….a) If current element is smaller than previous odd element, swap previous and current. 
….b) If current element is smaller than next odd element, swap next and current.

Below are implementations of above simple algorithm. 

Javascript




<script>
  
// A O(n) program to sort 
// an input array in wave form
  
// A utility method to swap two numbers.
function swap(arr, a, b)
    {
        let temp = arr[a];
        arr[a] = arr[b];
        arr[b] = temp;
    }
    
    // This function sorts arr[0..n-1] 
    // in wave form, i.e.,
    // arr[0] >= arr[1] <= arr[2] >= 
    // arr[3] <= arr[4]....
function sortInWave( arr, n)
    {
        // Traverse all even elements
        for (let i = 0; i < n; i+=2)
        {
            // If current even element 
            // is smaller than previous
            if (i>0 && arr[i-1] > arr[i] )
                swap(arr, i-1, i);
    
            // If current even element 
            // is smaller than next
            if (i<n-1 && arr[i] < arr[i+1] )
                swap(arr, i, i + 1);
        }
    }
  
    // driver code 
      
    let arr = [10, 90, 49, 2, 1, 5, 23];
    let n = arr.length;
    sortInWave(arr, n);
    for (let i=0; i<n; i++)
      document.write(arr[i] + " ");
      
</script>

Output: 

90 10 49 1 5 2 23
 

Please refer complete article on Sort an array in wave form for more details!


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