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
<?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, $n);echo "Modified Array";for ($i = 0; $i < $n; $i++) echo $arr[$i] . " ";// This code is contributed by Akanksha Rai(Abby_akku) |
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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