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Check if binary representations of two numbers are anagram

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  • Difficulty Level : Easy
  • Last Updated : 22 Jul, 2022
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Given two numbers you are required to check whether they are anagrams of each other or not in binary representation.
Examples: 

Input : a = 8, b = 4 
Output : Yes
Binary representations of both
numbers have same 0s and 1s.

Input : a = 4, b = 5
Output : No

Simple Approach: 

  1. Find the Binary Representation of ‘a’ and ‘b’ using a simple decimal to binary representation technique.
  2. Check if two binary representations are an anagram

Below is the implementation of the above approach:

C++




// A simple C++ program to check if binary
// representations of two numbers are anagram.
#include <bits/stdc++.h>
#define ull unsigned long long int
using namespace std;
 
const int SIZE = 8 * sizeof(ull);
 
bool bit_anagram_check(ull a, ull b)
{
    // Find reverse binary representation of a
    // and store it in binary_a[]
    int i = 0, binary_a[SIZE] = { 0 };
    while (a > 0) {
        binary_a[i] = a % 2;
        a /= 2;
        i++;
    }
 
    // Find reverse binary representation of b
    // and store it in binary_a[]
    int j = 0, binary_b[SIZE] = { 0 };
    while (b > 0) {
        binary_b[j] = b % 2;
        b /= 2;
        j++;
    }
 
    // Sort two binary representations
    sort(binary_a, binary_a + SIZE);
    sort(binary_b, binary_b + SIZE);
 
    // Compare two sorted binary representations
    for (int i = 0; i < SIZE; i++)
        if (binary_a[i] != binary_b[i])
            return false;
 
    return true;
}
 
// Driver code
int main()
{
    ull a = 8, b = 4;
    cout << bit_anagram_check(a, b) << endl;
    return 0;
}


Java




// A simple Java program to check if binary
// representations of two numbers are anagram
import java.io.*;
import java.util.*;
 
class GFG
{
    public static int SIZE = 8;
     
    // Function to check if binary representation
    // of two numbers are anagram
    static int bit_anagram_check(long a, long b)
    {
        // Find reverse binary representation of a
        // and store it in binary_a[]
        int i = 0;
        long[] binary_a = new long[SIZE];
        Arrays.fill(binary_a, 0);
        while (a > 0)
        {
            binary_a[i] = a%2;
            a /= 2;
            i++;
        }
  
        // Find reverse binary representation of b
        // and store it in binary_a[]
        int j = 0;
        long[] binary_b = new long[SIZE];
        Arrays.fill(binary_b, 0);
        while (b > 0)
        {
            binary_b[j] = b%2;
            b /= 2;
            j++;
        }
  
        // Sort two binary representations
        Arrays.sort(binary_a);
        Arrays.sort(binary_b);
  
        // Compare two sorted binary representations
        for (i = 0; i < SIZE; i++)
            if (binary_a[i] != binary_b[i])
                return 0;
  
        return 1;
    }
 
    // driver program
    public static void main (String[] args)
    {
        long a = 8, b = 4;
        System.out.println(bit_anagram_check(a, b));
    }
}
 
// Contributed by Pramod Kumar


Python3




# A simple Python program to check if binary
# representations of two numbers are anagram.
SIZE = 8
def bit_anagram_check(a, b):
 
    # Find reverse binary representation of a
    # and store it in binary_a[]
    global size
 
    i = 0
    binary_a = [0] * SIZE
    while (a > 0):
        binary_a[i] = a % 2
        a //= 2
        i += 1
 
    # Find reverse binary representation of b
    # and store it in binary_a[]
    j = 0
    binary_b = [0] * SIZE
    while (b > 0):
        binary_b[j] = b % 2
        b //= 2
        j += 1
 
    # Sort two binary representations
    binary_a.sort()
    binary_b.sort()
 
    # Compare two sorted binary representations
    for i in range(SIZE):
        if (binary_a[i] != binary_b[i]):
            return 0
    return 1
 
# Driver code
if __name__ == "__main__":
 
    a = 8
    b = 4
    print(bit_anagram_check(a, b))
 
    # This code is contributed by ukasp.


C#




// A simple C# program to check if
// binary representations of two
// numbers are anagram
using System;
 
class GFG
{
public static int SIZE = 8;
 
// Function to check if binary
// representation of two numbers
// are anagram
public static int bit_anagram_check(long a,
                                    long b)
{
    // Find reverse binary representation
    // of a and store it in binary_a[]
    int i = 0;
    long[] binary_a = new long[SIZE];
    Arrays.Fill(binary_a, 0);
    while (a > 0)
    {
        binary_a[i] = a % 2;
        a /= 2;
        i++;
    }
 
    // Find reverse binary representation 
    // of b and store it in binary_a[]
    int j = 0;
    long[] binary_b = new long[SIZE];
    Arrays.Fill(binary_b, 0);
    while (b > 0)
    {
        binary_b[j] = b % 2;
        b /= 2;
        j++;
    }
 
    // Sort two binary representations
    Array.Sort(binary_a);
    Array.Sort(binary_b);
 
    // Compare two sorted binary
    // representations
    for (i = 0; i < SIZE; i++)
    {
        if (binary_a[i] != binary_b[i])
        {
            return 0;
        }
    }
 
    return 1;
}
 
public static class Arrays
{
public static T[] CopyOf<T>(T[] original,
                            int newLength)
{
    T[] dest = new T[newLength];
    System.Array.Copy(original, dest, newLength);
    return dest;
}
 
public static T[] CopyOfRange<T>(T[] original,
                                 int fromIndex,
                                 int toIndex)
{
    int length = toIndex - fromIndex;
    T[] dest = new T[length];
    System.Array.Copy(original, fromIndex,
                         dest, 0, length);
    return dest;
}
 
public static void Fill<T>(T[] array, T value)
{
    for (int i = 0; i < array.Length; i++)
    {
        array[i] = value;
    }
}
 
public static void Fill<T>(T[] array, int fromIndex,
                           int toIndex, T value)
{
    for (int i = fromIndex; i < toIndex; i++)
    {
        array[i] = value;
    }
}
}
 
 
// Driver Code
public static void Main(string[] args)
{
    long a = 8, b = 4;
    Console.WriteLine(bit_anagram_check(a, b));
}
}
 
// This code is contributed by Shrikant13


Javascript




<script>
// A simple Javascript program to check if binary
// representations of two numbers are anagram
     
    let SIZE = 8;
     
    // Function to check if binary representation
    // of two numbers are anagram
    function bit_anagram_check(a,b)
    {
        // Find reverse binary representation of a
        // and store it in binary_a[]
        let i = 0;
        let binary_a = new Array(SIZE);
        for(let i=0;i<SIZE;i++)
        {
            binary_a[i]=0;
        }
        while (a > 0)
        {
            binary_a[i] = a%2;
            a = Math.floor(a/2);
            i++;
        }
   
        // Find reverse binary representation of b
        // and store it in binary_a[]
        let j = 0;
        let binary_b = new Array(SIZE);
        for(let i=0;i<SIZE;i++)
        {
            binary_b[i]=0;
        }
        while (b > 0)
        {
            binary_b[j] = b%2;
            b = Math.floor(b/2);
            j++;
        }
   
        // Sort two binary representations
        binary_a.sort(function(a,b){return a-b;});
        binary_b.sort(function(a,b){return a-b;});
   
        // Compare two sorted binary representations
        for (i = 0; i < SIZE; i++)
            if (binary_a[i] != binary_b[i])
                return 0;
   
        return 1;
    }
     
    // driver program
    let a = 8, b = 4;
    document.write(bit_anagram_check(a, b));
     
    //This code is contributed by rag2127
     
</script>


Output

1

Note that the above code uses GCC-specific functions. If we wish to write code for other compilers, we may use Count set bits in an integer.
Time Complexity: O (1) 
Auxiliary Space: O (1) No extra space is getting used.

Another Approach: If the number of set bits in two numbers is equal, then their binary representations are anagrams.
Below is the implementation of the above approach:

C++




// C++ program to check if binary
// representations of two numbers are anagrams.
#include <bits/stdc++.h>
 
using namespace std;
 
// Check each bit in a number is set or not
// and return the total count of the set bits.
int countSetBits(int n)
{
    int count = 0;
    while (n) {
        count += n & 1;
        n >>= 1;
    }
    return count;
}
 
bool areAnagrams(int A, int B)
{
    return countSetBits(A) == countSetBits(B);
}
 
// Driver code
int main()
{
    int a = 8, b = 4;
    cout << areAnagrams(a, b) << endl;
    return 0;
}
 
// This code is contributed by phasing17


Java




// Java program to check if binary
// representations of two numbers are anagrams.
 
import java.util.*;
 
class GFG {
 
    // Check each bit in a number is set or not
    // and return the total count of the set bits.
    public static int countSetBits(int n)
    {
        int count = 0;
        while (n != 0) {
            count += n & 1;
            n >>= 1;
        }
        return count;
    }
 
    public static boolean areAnagrams(int A, int B)
    {
        return countSetBits(A) == countSetBits(B);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int a = 8;
        int b = 4;
        System.out.println(areAnagrams(a, b));
    }
}
 
// This code is contributed by phasing17


Python3




# Python3 program to check if binary
# representations of two numbers are anagrams.
   
# Check each bit in a number is set or not
# and return the total count of the set bits.
def countSetBits(n) :
     
    count = 0
    while n>0 :
        count += n & 1
        n >>= 1
    return count
 
def areAnagrams(A, B) :
    return countSetBits(A) == countSetBits(B)
     
# Driver code
if __name__ == "__main__" :
     
    a,b = 8,4
    if areAnagrams(a, b) :
        print("1")
    else :
        print("0")
 
# this code is contributed by aditya942003patil


C#




// C# program to check if binary
// representations of two numbers are anagrams.
using System;
 
public static class GFG {
 
  // Check each bit in a number is set or not
  // and return the total count of the set bits.
  public static int countSetBits(int n)
  {
    int count = 0;
    while (n != 0) {
      count += n & 1;
      n >>= 1;
    }
    return count;
  }
 
  public static bool areAnagrams(int A, int B)
  {
    return countSetBits(A) == countSetBits(B);
  }
 
  // Driver code
  public static void Main()
  {
    int a = 8;
    int b = 4;
    Console.Write(areAnagrams(a, b));
    Console.Write("\n");
  }
}
 
// This code is contributed by Aarti_Rathi


Output

1

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

This article is contributed by Aarti_Rathi and Aditya Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 


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