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.
// 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 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 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# 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 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.
?>
<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)