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 <iostream>using namespace std;// function to check if two numbers are equal // after bit rotationbool 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 functionint 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 Codeif __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 Codepublic 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 rotationfunction 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 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) { // 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 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> |
yes
Time Complexity: O(logn)
Auxiliary Space: O(1)
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