Given two positive integers x and y, check if one integer is obtained by rotating bits of other.

Input constraint:0 < x, y < 2^32

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

More information on bit rotation can be found here**Example 1 :**

Input : a = 8, b = 1 Output : yesExplanation :Represntation of a = 8 : 0000 0000 0000 0000 0000 0000 0000 1000 Represntation 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

**Example 2 :**

Input : a = 122, b = 2147483678 Output : yesExplanation :Represntation of a = 122 : 0000 0000 0000 0000 0000 0000 0111 1010 Represntation 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

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 it 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 concatenation of x to x ie..

x64 has first 32 bits same as bits of x and last 32 bits are also same as bits of x64.

Then we keep on shifting x64 by 1 on 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 combination due to rotation.

Here is implementation of above algorithm.

## C++

`// C++ program to check if two numbers are bit rotations` `// of each other.` `#include <iostream>` `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)` ` ` `{` ` ` `// comapring 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) {` ` ` `// 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` ` ` `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) :` ` ` ` ` `# comapring 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)` ` ` `{` ` ` `// comapring 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

`<?php` `// PHP 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.` ` ` `$x64` `= ` `$x` `| (` `$x` `<< 32);` ` ` `while` `(` `$x64` `>= ` `$y` `)` ` ` `{` ` ` `// comapring only last 32 bits` ` ` `if` `((` `$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

`<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

This article is contributed by **Pratik Chhajer**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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