Javascript Program to Check if two numbers are bit rotations of each other or not

Given two positive integers x and y (0 < x, y < 2^32), check if one integer is obtained by rotating bits of the other.

Bit Rotation: A rotation (or circular shift) is an operation similar to a shift except that the bits that fall off at one end are put back to the other end.

Examples:

Input : a = 8, b = 1
Output : yes
Explanation : Representation of a = 8 : 0000 0000 0000 0000 0000 0000 0000 1000 ,Representation of b = 1 : 0000 0000 0000, 0000 0000 0000 0000 0001. If we rotate a by 3 units right we get b, hence answer is yes.

Input : a = 122, b = 2147483678
Output : yes
Explanation :Representation of a = 122        : 0000 0000 0000 0000 0000 0000 0111 1010,Representation of b = 2147483678 : 1000 0000 0000 0000 0000 0000 0001 1110, If we rotate a by 2 units right we get b, hence answer is yes.

Approach:

• Since total bits in which x or y can be represented is 32 since x, y > 0 and x, y < 2^32. 
• So we need to find all 32 possible rotations of x and compare them with y till x and y are not equal. 
• To do this we use a temporary variable x64 with 64 bits, which is result of the concatenation of x to x ie. x64 has the first 32 bits the same as bits of x and the last 32 bits are also the same as bits of x64.
• Then we keep on shifting x64 by 1 on the right side and compare the rightmost 32 bits of x64 with y. 
• In this way, we’ll be able to get all the possible bits combinations due to rotation.

Here is the implementation of the above algorithm.

Javascript

<script>

// javascript program to check if two numbers are bit rotations
// of each other.

// function to check if two numbers are equal
// after bit rotation
function isRotation(x, y)
{

    // x64 has concatenation of x with itself.
    var x64 = x | (x << 32);
    while (x64 >= y)
    {

        // comapring only last 32 bits
        if (x64 == y) {
            return true;
        }

        // right shift by 1 unit
        x64 >>= 1;
    }
    return false;
}

// driver code to test above function
var x = 122;
var y = 2147483678;

if (isRotation(x, y) == false) {
    document.write("Yes");
} else {
    document.write("No");
}

// This code is contributed by 29AjayKumar
</script>

Output:

yes

Time Complexity: O(log₂n), where n is the given number
Auxiliary Space: O(1)

Please refer complete article on Check if two numbers are bit rotations of each other or not for more details!