# Check if binary representations of two numbers are anagram

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:**

- Find the Binary Representation of ‘a’ and ‘b’ using a simple decimal to binary representation technique.
- 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)

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