# Sort an array in wave form

• Difficulty Level : Medium
• Last Updated : 26 Jul, 2022

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] >= …..

what is a wave array?

well, you have seen waves right? how do they look? if you will form a graph of them it would be some in some up-down fashion.

that is what you have to do here, you are supposed to arrange numbers in such a way that if we will form a graph it will be in an up-down fashion rather than a straight line.

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

here you can see {10, 5, 6, 2, 20, 3, 100, 80} first element is larger than the second and the same
thing is repeated again and again. large element - small element-large element -small element
and so on .
it can be small element-larger element - small element-large element -small element too.
all you need to maintain is the up-down fashion which represents a wave.

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
```
Recommended Practice

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 is implementation of the above idea.

## C++

 `// A C++ program to sort an array in wave form using``// a sorting function``#include``#include``using` `namespace` `std;` `// A utility method to swap two numbers.``void` `swap(``int` `*x, ``int` `*y)``{``    ``int` `temp = *x;``    ``*x = *y;``    ``*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]..``void` `sortInWave(``int` `arr[], ``int` `n)``{``    ``// Sort the input array``    ``sort(arr, arr+n);` `    ``// Swap adjacent elements``    ``for` `(``int` `i=0; i

## Java

 `// Java implementation of naive method for sorting``// an array in wave form.``import` `java.util.*;` `class` `SortWave``{``    ``// A utility method to swap two numbers.``    ``void` `swap(``int` `arr[], ``int` `a, ``int` `b)``    ``{``        ``int` `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]..``    ``void` `sortInWave(``int` `arr[], ``int` `n)``    ``{``        ``// Sort the input array``        ``Arrays.sort(arr);` `        ``// Swap adjacent elements``        ``for` `(``int` `i=``0``; i

## Python3

 `# Python function to sort the array arr[0..n-1] in wave form,``# i.e., arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4] >= arr[5]``def` `sortInWave(arr, n):``    ` `    ``#sort the array``    ``arr.sort()``   ` `    ``# Swap adjacent elements``    ``for` `i ``in` `range``(``0``,n``-``1``,``2``):``        ``arr[i], arr[i``+``1``] ``=` `arr[i``+``1``], arr[i]` `# Driver program``arr ``=` `[``10``, ``90``, ``49``, ``2``, ``1``, ``5``, ``23``]``sortInWave(arr, ``len``(arr))``for` `i ``in` `range``(``0``,``len``(arr)):``    ``print` `(arr[i],end``=``" "``)``    ` `# This code is contributed by __Devesh Agrawal__`

## C#

 `// C# implementation of naive method``// for sorting an array in wave form.``using` `System;` `class` `SortWave {``    ` `    ``// A utility method to swap two numbers.``    ``void` `swap(``int``[] arr, ``int` `a, ``int` `b)``    ``{``        ``int` `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]..``    ``void` `sortInWave(``int``[] arr, ``int` `n)``    ``{``        ``// Sort the input array``        ``Array.Sort(arr);` `        ``// Swap adjacent elements``        ``for` `(``int` `i = 0; i < n - 1; i += 2)``            ``swap(arr, i, i + 1);``    ``}` `    ``// Driver method``    ``public` `static` `void` `Main()``    ``{``        ``SortWave ob = ``new` `SortWave();``        ``int``[] arr = { 10, 90, 49, 2, 1, 5, 23 };``        ``int` `n = arr.Length;``        ` `        ``ob.sortInWave(arr, n);``        ``for` `(``int` `i = 0; i < n; i++)``        ``Console.Write(arr[i] + ``" "``);``    ``}``}` `// This code is contributed by vt_m.`

## Javascript

 ``

Output:

`2 1 10 5 49 23 90`

Time Complexity: O(nlogn)

Auxiliary Space: O(1)
The time complexity of the above solution is O(nLogn) if an O(nLogn) sorting algorithm like Merge Sort, Heap Sort, etc are used.
This can be done in O(n) time by doing a single traversal of the 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 oddly positioned elements.

The following are simple steps.
1) Traverse all even positioned elements of the input array, and do the following.
….a) If the current element is smaller than the previous odd element, swap previous and current.
….b) If the current element is smaller than the next odd element, swap next and current.

Below is implementation of the above idea.

## C++14

 `// A O(n) program to sort an input array in wave form``#include``using` `namespace` `std;` `// A utility method to swap two numbers.``void` `swap(``int` `*x, ``int` `*y)``{``    ``int` `temp = *x;``    ``*x = *y;``    ``*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] ....``void` `sortInWave(``int` `arr[], ``int` `n)``{``    ``// Traverse all even elements``    ``for` `(``int` `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], &arr[i-1]);` `        ``// If current even element is smaller than next``        ``if` `(i

## Java

 `// A O(n) Java program to sort an input array in wave form``class` `SortWave``{``    ``// A utility method to swap two numbers.``    ``void` `swap(``int` `arr[], ``int` `a, ``int` `b)``    ``{``        ``int` `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]....``    ``void` `sortInWave(``int` `arr[], ``int` `n)``    ``{``        ``// Traverse all even elements``        ``for``(``int` `i = ``0``; i < n-``1``; i+=``2``){``            ``//swap odd and even positions``            ``if``(i > ``0` `&& arr[i - ``1``] > arr[i])``              ``swap(arr, i, i+``1``);``              ``if``(i < n-``1` `&& arr[i + ``1``] > arr[i])``              ``swap(arr, i, i+``1``);``        ``}``    ``}` `    ``// Driver program to test above function``    ``public` `static` `void` `main(String args[])``    ``{``        ``SortWave ob = ``new` `SortWave();``        ``int` `arr[] = {``10``, ``90``, ``49``, ``2``, ``1``, ``5``, ``23``};``        ``int` `n = arr.length;``        ``ob.sortInWave(arr, n);``        ``for` `(``int` `i : arr)``            ``System.out.print(i+``" "``);``    ``}``}``/*This code is contributed by Rajat Mishra*/`

## Python3

 `# Python function to sort the array arr[0..n-1] in wave form,``# i.e., arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4] >= arr[5]``def` `sortInWave(arr, n):``    ` `    ``# Traverse all even elements``    ``for` `i ``in` `range``(``0``, n, ``2``):``        ` `        ``# If current even element is smaller than previous``        ``if` `(i> ``0` `and` `arr[i] < arr[i``-``1``]):``            ``arr[i],arr[i``-``1``] ``=` `arr[i``-``1``],arr[i]``        ` `        ``# If current even element is smaller than next``        ``if` `(i < n``-``1` `and` `arr[i] < arr[i``+``1``]):``            ``arr[i],arr[i``+``1``] ``=` `arr[i``+``1``],arr[i]` `# Driver program``arr ``=` `[``10``, ``90``, ``49``, ``2``, ``1``, ``5``, ``23``]``sortInWave(arr, ``len``(arr))``for` `i ``in` `range``(``0``,``len``(arr)):``    ``print` `(arr[i],end``=``" "``)``    ` `# This code is contributed by __Devesh Agrawal__`

## C#

 `// A O(n) C# program to sort an``// input array in wave form``using` `System;` `class` `SortWave {``    ` `    ``// A utility method to swap two numbers.``    ``void` `swap(``int``[] arr, ``int` `a, ``int` `b)``    ``{``        ``int` `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]....``    ``void` `sortInWave(``int``[] arr, ``int` `n)``    ``{``        ``// Traverse all even elements``        ``for` `(``int` `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 program to test above function``    ``public` `static` `void` `Main()``    ``{``        ``SortWave ob = ``new` `SortWave();``        ``int``[] arr = { 10, 90, 49, 2, 1, 5, 23 };``        ``int` `n = arr.Length;``        ` `        ``ob.sortInWave(arr, n);``        ``for` `(``int` `i = 0; i < n; i++)``        ``Console.Write(arr[i] + ``" "``);``    ``}``}` `// This code is contributed by vt_m.`

## Javascript

 ``

Output:

`90 10 49 1 5 2 23`

Time Complexity: O(n)

Auxiliary Space: O(1)