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Php Program to Count rotations divisible by 4

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  • Last Updated : 02 Jun, 2022
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Given a large positive number as string, count all rotations of the given number which are divisible by 4. 

Examples: 

Input: 8
Output: 1

Input: 20
Output: 1
Rotation: 20 is divisible by 4
          02 is not divisible by 4

Input : 13502
Output : 0
No rotation is divisible by 4

Input : 43292816
Output : 5
5 rotations are : 43292816, 16432928, 81643292
                  92816432, 32928164 

For large numbers it is difficult to rotate and divide each number by 4. Therefore, ‘divisibility by 4’ property is used which says that a number is divisible by 4 if the last 2 digits of the number is divisible by 4. Here we do not actually rotate the number and check last 2 digits for divisibility, instead we count consecutive pairs (in circular way) which are divisible by 4. 

Illustration:  

Consider a number 928160
Its rotations are 928160, 092816, 609281, 160928, 
    816092, 281609.
Now form pairs from the original number 928160
as mentioned in the approach.
Pairs: (9,2), (2,8), (8,1), (1,6), 
         (6,0), (0,9)
We can observe that the 2-digit number formed by the these 
pairs, i.e., 92, 28, 81, 16, 60, 09, are present in the last
2 digits of some rotation.
Thus, checking divisibility of these pairs gives the required
number of rotations. 

Note: A single digit number can directly
be checked for divisibility.

Below is the implementation of the approach. 

PHP




<?php
// PHP program to count all
// rotation divisible by 4.
 
// Returns count of all
// rotations divisible
// by 4
function countRotations($n)
{
    $len = strlen($n);
 
    // For single digit number
    if ($len == 1)
    {
        $oneDigit = $n[0] - '0';
 
        if ($oneDigit % 4 == 0)
            return 1;
 
        return 0;
    }
 
    // At-least 2 digit
    // number (considering all
    // pairs)
    $twoDigit;$count = 0;
    for ($i = 0; $i < ($len - 1); $i++)
    {
        $twoDigit = ($n[$i] - '0') * 10 +
                    ($n[$i + 1] - '0');
 
        if ($twoDigit % 4 == 0)
            $count++;
    }
 
    // Considering the number
    // formed by the pair of
    // last digit and 1st digit
    $twoDigit = ($n[$len - 1] - '0') * 10 +
                ($n[0] - '0');
 
    if ($twoDigit % 4 == 0)
        $count++;
 
    return $count;
}
 
// Driver Code
$n = "4834";
echo "Rotations: " ,
      countRotations($n);
 
// This code is contributed by ajit
?>


Output: 

Rotations: 2

Time Complexity : O(n) where n is number of digits in input number.

Auxiliary Space: O(1)

Please refer complete article on Count rotations divisible by 4 for more details!


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