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# Php Program For Rearranging An Array In Maximum Minimum Form – Set 2 (O(1) extra space)

Given a sorted array of positive integers, rearrange the array alternately i.e first element should be the maximum value, second minimum value, third-second max, fourth-second min and so on.
Examples:

Input: arr[] = {1, 2, 3, 4, 5, 6, 7}
Output: arr[] = {7, 1, 6, 2, 5, 3, 4}
Input: arr[] = {1, 2, 3, 4, 5, 6}
Output: arr[] = {6, 1, 5, 2, 4, 3}

We have discussed a solution in below post:
Rearrange an array in maximum minimum form | Set 1 : The solution discussed here requires extra space, how to solve this problem with O(1) extra space.

In this post a solution that requires O(n) time and O(1) extra space is discussed. The idea is to use multiplication and modular trick to store two elements at an index.

```even index : remaining maximum element.
odd index  : remaining minimum element.

max_index : Index of remaining maximum element
(Moves from right to left)
min_index : Index of remaining minimum element
(Moves from left to right)

Initialize: max_index = 'n-1'
min_index = 0

// Can be any element which is more than
// the maximum value in array
max_element = arr[max_index] + 1

For i = 0 to n-1
If 'i' is even
arr[i] += (arr[max_index] % max_element *
max_element)
max_index--

// if 'i' is odd
ELSE
arr[i] +=  (arr[min_index] % max_element *
max_element)
min_index++```

How does expression “arr[i] += arr[max_index] % max_element * max_element” work ?
The purpose of this expression is to store two elements at index arr[i]. arr[max_index] is stored as multiplier and “arr[i]” is stored as remainder. For example in {1 2 3 4 5 6 7 8 9}, max_element is 10 and we store 91 at index 0. With 91, we can get original element as 91%10 and new element as 91/10.
Below implementation of above idea:

## PHP

 `

Output :

```Original Array
1 2 3 4 5 6 7 8 9
Modified Array
9 1 8 2 7 3 6 4 5 ```

Time Complexity: O(N), as we are using a loop to traverse N times.

Auxiliary Space: O(1), as we are not using any extra space.

Please refer complete article on Rearrange an array in maximum minimum form | Set 2 (O(1) extra space) for more details!

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