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 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!