# Rearrange an array in maximum minimum form (O(1) extra space)

Hello Everyone,

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 max_element = arr[max_index] + 1 //can be any element which is more than the maximum value in array For i = 0 to n-1 If ‘i’ is even arr[i] += arr[max_index] % max_element * max_element max_index-- ELSE // if ‘i’ is odd 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:

`// C++ program to rearrange an array in minimum`

`// maximum form`

`#include <bits/stdc++.h>`

`using` `namespace` `std;`

`// Prints max at first position, min at second position`

`// second max at third position, second min at fourth`

`// position and so on.`

`void` `rearrange(` `int` `arr[], ` `int` `n)`

`{`

` ` `// initialize index of first minimum and first`

` ` `// maximum element`

` ` `int` `max_idx = n - 1, min_idx = 0;`

` ` `// store maximum element of array`

` ` `int` `max_elem = arr[n - 1] + 1;`

` ` `// traverse array elements`

` ` `for` `(` `int` `i = 0; i < n; i++) {`

` ` `// at even index : we have to put maximum element`

` ` `if` `(i % 2 == 0) {`

` ` `arr[i] += (arr[max_idx] % max_elem) * max_elem;`

` ` `max_idx--;`

` ` `}`

` ` `// at odd index : we have to put minimum element`

` ` `else` `{`

` ` `arr[i] += (arr[min_idx] % max_elem) * max_elem;`

` ` `min_idx++;`

` ` `}`

` ` `}`

` ` `// array elements back to it's original form`

` ` `for` `(` `int` `i = 0; i < n; i++)`

` ` `arr[i] = arr[i] / max_elem;`

`}`

`// Driver program to test above function`

`int` `main()`

`{`

` ` `int` `arr[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };`

` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr);`

` ` `cout << ` `"Original Arrayn"` `;`

` ` `for` `(` `int` `i = 0; i < n; i++)`

` ` `cout << arr[i] << ` `" "` `;`

` ` `rearrange(arr, n);`

` ` `cout << ` `"\nModified Array\n"` `;`

` ` `for` `(` `int` `i = 0; i < n; i++)`

` ` `cout << arr[i] << ` `" "` `;`

` ` `return` `0;`

`}`

Output :

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