Check if bits in range L to R of two numbers are complement of each other or not

Given two non-negative numbers a and b and two values l and r. The problem is to check whether all bits at corresponding positions in the range l to r in both the given numbers are complement of each other or not. 
The bits are numbered from right to left, i.e., the least significant bit is considered to be at first position.
Examples: 

Input: a = 10, b = 5
       l = 1, r = 3
Output: Yes
(10)10 = (1010)2
(5)10 = (101)2 = (0101)2
All the bits in the range 1 to 3 are complement of each other.

Input: a = 21, b = 13
       l = 2, r = 4
Output: No
(21)10 = (10101)2
(13)10 = (1101)2 = (1101)2
All the bits in the range 2 to 4 are not complement of each other.

Approach: Below are the steps to solve the problem

• Calculate xor_value = a ^ b.
• Check whether all the bits are set or not in the range l to r in xor_value. Refer this post.

Below is the implementation of the above approach. 

C++

// C++ implementation to check
// whether all the bits in the given range
// of two numbers are complement of each other
#include <bits/stdc++.h>
using namespace std;

// function to check whether all the bits
// are set in the given range or not
bool allBitsSetInTheGivenRange(unsigned int n,
                               unsigned int l,
                               unsigned int r)
{
    // calculating a number 'num' having 'r'
    // number of bits and bits in the range l
    // to r are the only set bits
    int num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);

    // new number which will only have one or more
    // set bits in the range l to r and nowhere else
    int new_num = n & num;

    // if both are equal, then all bits are set
    // in the given range
    if (num == new_num)
        return true;

    // else all bits are not set
    return false;
}

// function to check whether all the bits in the given range
// of two numbers are complement of each other
bool bitsAreComplement(unsigned int a, unsigned int b,
                       unsigned int l, unsigned int r)
{
    unsigned int xor_value = a ^ b;
    return allBitsSetInTheGivenRange(xor_value, l, r);
}

// Driver Code
int main()
{
    unsigned int a = 10, b = 5;
    unsigned int l = 1, r = 3;

    if (bitsAreComplement(a, b, l, r))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

Java

// Java implementation to check
// whether all the bits in the
// given range of two numbers
// are complement of each other
class GFG
{
// function to check whether
// all the bits are set in
// the given range or not
static boolean allBitsSetInTheGivenRange(int n,
                                         int l, int r)
{
    // calculating a number 'num'
    // having 'r' number of bits
    // and bits in the range l
    // to r are the only set bits
    int num = ((1 << r) - 1) ^
              ((1 << (l - 1)) - 1);

    // new number which will only
    // have one or more set bits
    // in the range l to r and
    // nowhere else
    int new_num = n & num;

    // if both are equal,
    // then all bits are set
    // in the given range
    if (num == new_num)
        return true;

    // else all bits are not set
    return false;
}

// function to check whether all
// the bits in the given range
// of two numbers are complement
// of each other
static boolean bitsAreComplement(int a, int b,
                                 int l, int r)
{
    int xor_value = a ^ b;
    return allBitsSetInTheGivenRange(xor_value, l, r);
}

// Driver Code
public static void main(String []args)
{
    int a = 10, b = 5;
    int l = 1, r = 3;

    if (bitsAreComplement(a, b, l, r))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}

// This code is contributed by Smitha

Python 3

# Python 3 implementation to check whether
# all the bits in the given range of two
# numbers are complement of each other

# function to check whether all the bits
# are set in the given range or not
def allBitsSetInTheGivenRange(n, l, r):

    # calculating a number 'num' having 'r'
    # number of bits and bits in the range l
    # to r are the only set bits
    num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1)

    # new number which will only have one
    # or more set bits in the range l to r
    # and nowhere else
    new_num = n & num

    # if both are equal, then all bits
    # are set in the given range
    if (num == new_num):
        return True

    # else all bits are not set
    return False

# function to check whether all the bits
# in the given range of two numbers are
# complement of each other
def bitsAreComplement(a, b, l, r):
    xor_value = a ^ b
    return allBitsSetInTheGivenRange(xor_value, l, r)

# Driver Code
if __name__ == "__main__":

    a = 10
    b = 5
    l = 1
    r = 3

    if (bitsAreComplement(a, b, l, r)):
        print("Yes")
    else:
        print("No")

# This code is contributed by ita_c

C#

// C# implementation to check
// whether all the bits in the
// given range of two numbers
// are complement of each other
using System;

class GFG
{
// function to check whether
// all the bits are set in
// the given range or not
static bool allBitsSetInTheGivenRange(int n, int l,
                                      int r)
{
    // calculating a number 'num'
    // having 'r' number of bits
    // and bits in the range l
    // to r are the only set bits
    int num = ((1 << r) - 1) ^
              ((1 << (l - 1)) - 1);

    // new number which will only
    // have one or more set bits
    // in the range l to r and
    // nowhere else
    int new_num = n & num;

    // if both are equal,
    // then all bits are set
    // in the given range
    if (num == new_num)
        return true;

    // else all bits are not set
    return false;
}

// function to check whether all
// the bits in the given range
// of two numbers are complement
// of each other
static bool bitsAreComplement(int a, int b,
                              int l, int r)
{
    int xor_value = a ^ b;
    return allBitsSetInTheGivenRange(xor_value, l, r);
}

// Driver Code
static public void Main ()
{
    int a = 10, b = 5;
    int l = 1, r = 3;

    if (bitsAreComplement(a, b, l, r))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}

// This code is contributed
// by Ajit Deshpal.

PHP

<?php
// PHP implementation to check
// whether all the bits in the
// given range of two numbers
// are complement of each other

// function to check whether
// all the bits are set in
// the given range or not
function allBitsSetInTheGivenRange($n, $l ,$r)
{

    // calculating a number
    // 'num' having 'r' number
    // of bits and bits in
    // the range l to r are
    // the only set bits
    $num = ((1 << $r) - 1) ^
       ((1 << ($l - 1)) - 1);

    // new number which will
    // only have one or more
    // set bits in the range
    // l to r and nowhere else
    $new_num = ($n & $num);

    // if both are equal,
    // then all bits are set
    // in the given range
    if ($num == $new_num)
        return true;

    // else all bits
    // are not set
    return false;
}

// function to check whether
// all the bits in the given range
// of two numbers are complement
// of each other
function bitsAreComplement($a, $b,$l, $r)
{
    $xor_value = $a ^ $b;
    return allBitsSetInTheGivenRange($xor_value, $l, $r);
}

// Driver Code
$a = 10;
$b = 5;
$l = 1;
$r = 3;
if (bitsAreComplement($a, $b, $l, $r))
    echo "Yes";
else
    echo "No";

// This Code is Contributed by ajit
?>

Javascript

<script>
// javascript implementation to check
// whether all the bits in the
// given range of two numbers
// are complement of each other

// function to check whether
// all the bits are set in
// the given range or not
function allBitsSetInTheGivenRange(n, l , r)
{
    // calculating a number 'num'
    // having 'r' number of bits
    // and bits in the range l
    // to r are the only set bits
    var num = ((1 << r) - 1) ^
              ((1 << (l - 1)) - 1);

    // new number which will only
    // have one or more set bits
    // in the range l to r and
    // nowhere else
    var new_num = n & num;

    // if both are equal,
    // then all bits are set
    // in the given range
    if (num == new_num)
        return true;

    // else all bits are not set
    return false;
}

// function to check whether all
// the bits in the given range
// of two numbers are complement
// of each other
function bitsAreComplement(a , b,l , r)
{
    var xor_value = a ^ b;
    return allBitsSetInTheGivenRange(xor_value, l, r);
}

// Driver Code
var a = 10, b = 5;
var l = 1, r = 3;

if (bitsAreComplement(a, b, l, r))
    document.write("Yes");
else
    document.write("No");

// This code is contributed by Princi Singh
</script>

Output:

Yes

Time complexity: O(1) as it is performing constant operations
Auxiliary space: O(1)