# Sort an array in wave form

Posted: 9 Dec, 2020
Difficulty: Easy

## PROBLEM STATEMENT

#### Your task is to sort the array in such a way that the array looks like a wave array.

##### Example:
``````If the given sequence ‘ARR’ has ‘N’ elements then the sorted wave array looks like -
‘ARR >= ARR’ and ‘ARR <= ARR’
‘ARR >= ARR’ and ‘ARR <= ARR’
‘ARR >= ARR’ and ‘ARR <= ARR’  And so on.
``````
##### Note:
``````1. ‘ARR’ must be greater than or equal to ‘ARR’.

2. There can be multiple arrays that look like a wave array but you have to return only one.

3. We have an internal function that will check your solution and return 'True' in case your array is one of the solutions otherwise return 'False'.
``````

#### Explanation

``````The given array ‘ ARR = { 4, 3, 5, 2, 3, 1, 2 } ’
The below figure is a visual representation of the given ‘ARR’ and you can see we can express ‘ARR’ in a waveform array because
4>3 and 3<5
5>2 and 2<3
3>1 and 1<2
And it follows the condition of wave array.
`````` ``````Try to solve this problem in linear time complexity.
``````
##### Input format:
``````The first line of input contains an integer ‘T’ denoting the number of test cases.
The next ‘2*T’ lines represent the ‘T’ test cases.

The first line of each test case contains the single integer ‘N’ and ‘N’ is denoting the number elements in the given ‘ARR’.

The second line of each test case contains ‘N’ space-separated elements of ‘ARR’.
``````
##### Output Format:
``````For each test case, print in a single line space-separated integers that represent the elements of a wave array.
``````
##### Note:
``````You are not required to print the output explicitly, it has already been taken care of. Just implement the function.
``````
##### Constraints:
``````1 <= T <= 50
1 <= N<= 10^4
-10^9 <= ARR[i] <= 10^9

Time limit: 1 second
`````` Approach 1

The basic idea is that we try to make every even position to peak and every odd position to the valley.

• To implement this approach we place maximum value even indices and minimum value at odd indices if indices ‘0’ basis.
• Iterate a loop ‘i' which denotes the indices is odd or even
• If ‘i’ is odd then place maximum value of the array at position ‘i’, so iterate a loop ‘j’ which compare every element from ‘i’ to ‘N - 1’ if any elements are greater than the currently present element at ‘i’ then swap elements of position ‘i’ and ‘j’ and iterate for next ‘j’.
• If ‘i’ even then place minimum value of the array at position ‘i’, so iterate a loop ‘j’ which compare every element from ‘i’ to ‘N - 1’ if any element is less than currently present element at ‘i’ then swap elements of position ‘i’ and ‘j’ and iterate for next ‘j’.
• Iterate for next value of ‘i’.
• In the end, return ‘ARR’.