Javascript Program to Count rotations divisible by 4

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. 

// Javascript program to count all
// rotation divisible by 4.

// Returns count of all
// rotations divisible
// by 4
function countRotations(n) {
    let len = n.length;

    // For single digit number
    if (len == 1) {
        let oneDigit = n[0] - '0';

        if (oneDigit % 4 == 0)
            return 1;

        return 0;
    }

    // At-least 2 digit
    // number (considering all
    // pairs)
    let twoDigit;
    let count = 0;

    for (let 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
let n = "4834";

console.log("Rotations: " + countRotations(n));

Rotations: 2

Complexity Analysis:

• 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!

kartik

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Article Tags :

• Strings
• Mathematical
• JavaScript
• Web Technologies
• DSA
• divisibility
• number-digits
• rotation
• large-numbers

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Practice Tags :

• Mathematical
• Strings