PHP Program For Rearranging An Array In Maximum Minimum Form - Set 2 (O(1) extra space)

Given a sorted array of positive integers, this PHP program rearranges the array alternately: the first element is the maximum value, the second is the minimum value, the third is the second maximum, the fourth is the second minimum, and so on.

Examples:

Input: Arr = [ 1, 2, 3, 4, 5, 6, 7 ] 
Output: [ 7, 1, 6, 2, 5, 3, 4 ]

Input: Arr = [ 1, 2, 3, 4, 5, 6 ]
Output: [ 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
// PHP program to rearrange an 
// array in minimum-maximum form

// Prints max at first position, min 
// at second position second max at 
// third position, second min at fourth
// position and so on.
function rearrange(&$arr, $n) {
    // Initialize index of first
    // minimum and first maximum element
    $max_idx = $n - 1; $min_idx = 0;

    // Store maximum element of array
    $max_elem = $arr[$n - 1] + 1;

    // Traverse array elements
    for ($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 ($i = 0; $i < $n; $i++)
        $arr[$i] = (int)($arr[$i] / $max_elem);
}

// Driver Code
$arr = array(1, 2, 3, 4, 5, 6, 7, 8, 9);
$n = sizeof($arr);

echo "Original Array" . "";
for ($i = 0; $i < $n; $i++)
    echo $arr[$i] . " ";

rearrange($arr, $n);

echo "\nModified Array";
for ($i = 0; $i < $n; $i++)
    echo $arr[$i] . " ";

?>

Original Array1 2 3 4 5 6 7 8 9 
Modified Array9 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!

kartik

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Article Tags :

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• Web Technologies
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• DSA
• Arrays
• Zoho
• Modular Arithmetic
• array-rearrange

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