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# 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 implementation of above algorithm.

## C++

 `// C++ program to check if two numbers are bit rotations``// of each other.``#include ``using` `namespace` `std;` `// function to check if  two numbers are equal``// after bit rotation``bool` `isRotation(unsigned ``int` `x, unsigned ``int` `y)``{``    ``// x64 has concatenation of x with itself.``    ``unsigned ``long` `long` `int` `x64 = x | ((unsigned ``long` `long` `int``)x << 32);` `    ``while` `(x64 >= y)``    ``{``        ``// comparing only last 32 bits``        ``if` `(unsigned(x64) == y)``            ``return` `true``;` `        ``// right shift by 1 unit``        ``x64 >>= 1;``    ``}``    ``return` `false``;``}` `// driver code to test above function``int` `main()``{``    ``unsigned ``int` `x = 122;``    ``unsigned ``int` `y = 2147483678;` `    ``if` `(isRotation(x, y))``        ``cout << ``"yes"` `<< endl;``    ``else``        ``cout << ``"no"` `<< endl;` `    ``return` `0;``}`

## Java

 `// Java program to check if two numbers are bit rotations``// of each other.``class` `GFG {` `// function to check if two numbers are equal``// after bit rotation``    ``static` `boolean` `isRotation(``long` `x, ``long` `y) {``        ``// x64 has concatenation of x with itself.``        ``long` `x64 = x | (x << ``32``);` `        ``while` `(x64 >= y) {``            ``// comparing only last 32 bits``            ``if` `(x64 == y) {``                ``return` `true``;``            ``}` `            ``// right shift by 1 unit``            ``x64 >>= ``1``;``        ``}``        ``return` `false``;``    ``}` `// driver code to test above function``    ``public` `static` `void` `main(String[] args) {``        ``long` `x = ``122``;``        ``long` `y = 2147483678L;` `        ``if` `(isRotation(x, y) == ``false``) {``            ``System.out.println(``"Yes"``);``        ``} ``else` `{``            ``System.out.println(``"No"``);``        ``}``    ``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to check if two``# numbers are bit rotations of each other.` `# function to check if two numbers``# are equal after bit rotation``def` `isRotation(x, y) :``    ` `    ``# x64 has concatenation of x``    ``# with itself.``    ``x64 ``=` `x | (x << ``32``)``    ` `    ``while` `(x64 >``=` `y) :``        ` `        ``# comparing only last 32 bits``        ``if` `((x64) ``=``=` `y) :``            ``return` `True` `        ``# right shift by 1 unit``        ``x64 >>``=` `1` `    ``return` `False` `# Driver Code``if` `__name__ ``=``=` `"__main__"` `:` `    ``x ``=` `122``    ``y ``=` `2147483678``    ` `    ``if` `(isRotation(x, y) ``=``=` `False``) :``        ``print``(``"yes"``)``    ``else` `:``        ``print``(``"no"``)` `# This code is contributed by Ryuga`

## C#

 `// C# program to check if two numbers``// are bit rotations of each other.``using` `System;` `class` `GFG``{` `// function to check if two numbers``// are equal after bit rotation``static` `bool` `isRotation(``long` `x, ``long` `y)``{``    ``// x64 has concatenation of``    ``// x with itself.``    ``long` `x64 = x | (x << 32);` `    ``while` `(x64 >= y)``    ``{``        ``// comparing only last 32 bits``        ``if` `(x64 == y)``        ``{``            ``return` `true``;``        ``}` `        ``// right shift by 1 unit``        ``x64 >>= 1;``    ``}``    ``return` `false``;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``long` `x = 122;``    ``long` `y = 2147483678L;` `    ``if` `(isRotation(x, y) == ``false``)``    ``{``        ``Console.Write(``"Yes"``);``    ``}``    ``else``    ``{``        ``Console.Write(``"No"``);``    ``}``}``}` `// This code is contributed``// by 29AjayKumar`

## PHP

 `= ``\$y``)``    ``{``        ``// comparing only last 32 bits``        ``if` `((``\$x64``) == ``\$y``)``            ``return` `1;` `        ``// right shift by 1 unit``        ``\$x64` `>>= 1;``    ``}``    ``return` `-1;``}` `// Driver Code``\$x` `= 122;``\$y` `= 2147483678;` `if` `(isRotation(``\$x``, ``\$y``))``    ``echo` `"yes"` `,``"\n"``;``else``    ``echo` `"no"` `,``"\n"``;` `// This code is contributed by aj_36``?>`

## Javascript

 ``

Output

```yes
```

Time Complexity: O(logn)
Auxiliary Space: O(1)

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