Given two non-negative integers a and b. The problem is to check if one of the two numbers is 1’s complement of the other.
The ones’ complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).
Examples:
Input : a = 10, b = 5 Output : Yes (10)10 = (1010)2 1's complement of 10 is = (0101)2 = (101)2 = (5)10 Input : a = 1, b = 14 Output : Yes (14)10 = (1110)2 1's complement of 14 is = (0001)2 = (1)2 = (1)10
Approach: Following are the steps:
- Calculate n = a ^ b.
- Check whether all bits are set in the binary representation of n. Refer to this post.
CPP
// C++ implementation to check if one of the two // numbers is one's complement of the other #include <bits/stdc++.h> using namespace std;
// function to check if all the bits are set // or not in the binary representation of 'n' bool areAllBitsSet(unsigned int n)
{ // all bits are not set
if (n == 0)
return false ;
// if true, then all bits are set
if (((n + 1) & n) == 0)
return true ;
// else all bits are not set
return false ;
} // function to check if one of the two numbers // is one's complement of the other bool isOnesComplementOfOther(unsigned int a,
unsigned int b)
{ return areAllBitsSet(a ^ b);
} // Driver program to test above int main()
{ unsigned int a = 10, b = 5;
if (isOnesComplementOfOther(a,b))
cout << "Yes" ;
else
cout << "No" ;
return 0;
} |
Java
// Java implementation to // check if one of the two // numbers is one's complement // of the other import java.util.*;
import java.lang.*;
public class GfG{
// function to check
// if all the bits are set
// or not in the binary
// representation of 'n'
public static boolean areAllBitsSet( long n)
{
// all bits are not set
if (n == 0 )
return false ;
// if true, then all bits are set
if (((n + 1 ) & n) == 0 )
return true ;
// else all bits are not set
return false ;
}
// function to check if
// one of the two numbers
// is one's complement
// of the other
public static boolean isOnesComplementOfOther( long a,
long b)
{
return areAllBitsSet(a ^ b);
}
// Driver function
public static void main(String argc[]){
long a = 10 , b = 5 ;
if (isOnesComplementOfOther(a,b))
System.out.println( "Yes" );
else
System.out.println( "No" );
}
} // This code is contributed by Sagar Shukla |
Python3
# Python3 implementation to # check if one of the two # numbers is one's complement # of the other # function to check if # all the bits are set # or not in the binary # representation of 'n' def areAllBitsSet(n):
# all bits are not set
if (n = = 0 ):
return False ;
# if True, then all bits are set
if (((n + 1 ) & n) = = 0 ):
return True ;
# else all bits are not set
return False ;
# function to check if one # of the two numbers is # one's complement of the other def isOnesComplementOfOther(a, b):
return areAllBitsSet(a ^ b)
# Driver program a = 1
b = 14
if (isOnesComplementOfOther(a, b)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by # Saloni Gupta 4 |
C#
// C# implementation to check // if one of the two numbers is // one's complement of the other using System;
class GFG {
// function to check
// if all the bits are set
// or not in the binary
// representation of 'n'
public static bool areAllBitsSet( long n)
{
// all bits are not set
if (n == 0)
return false ;
// if true, then all bits are set
if (((n + 1) & n) == 0)
return true ;
// else all bits are not set
return false ;
}
// function to check if
// one of the two numbers
// is one's complement
// of the other
public static bool isOnesComplementOfOther( long a,
long b)
{
return areAllBitsSet(a ^ b);
}
// Driver function
public static void Main()
{
long a = 10, b = 5;
if (isOnesComplementOfOther(a, b))
Console.Write( "Yes" );
else
Console.Write( "No" );
}
} // This code is contributed by Sam007 |
PHP
<?php // PHP implementation to // check if one of the two // numbers is one's complement // of the other // function to check if // all the bits are set // or not in the binary // representation of 'n' function areAllBitsSet( $n )
{ // all bits are not set
if ( $n == 0)
return false;
// if true, then all
// bits are set
if ((( $n + 1) & $n ) == 0)
return true;
// else all bits
// are not set
return false;
} // function to check if // one of the two numbers // is one's complement of // the other function isOnesComplementOfOther( $a ,
$b )
{ return areAllBitsSet( $a ^ $b );
} // Driver Code
$a = 10; $b = 5;
if (isOnesComplementOfOther( $a , $b ))
echo "Yes" ;
else
echo "No" ;
// This code is contributed by anuj_67. ?> |
Javascript
<script> // Javascript implementation to
// check if one of the two // numbers is one's complement // of the other // function to check
// if all the bits are set
// or not in the binary
// representation of 'n'
function areAllBitsSet(n)
{
// all bits are not set
if (n == 0)
return false ;
// if true, then all bits are set
if (((n + 1) & n) == 0)
return true ;
// else all bits are not set
return false ;
}
// function to check if
// one of the two numbers
// is one's complement
// of the other
function isOnesComplementOfOther(a, b)
{
return areAllBitsSet(a ^ b);
}
// Driver code
let a = 10, b = 5;
if (isOnesComplementOfOther(a,b))
document.write( "Yes" );
else
document.write( "No" );
</script> |
Output:
Yes
Time Complexity : O(1)
Auxiliary Space : O(1)