Check whether all the bits are unset in the given range or not

Last Updated : 13 Jun, 2022

Given a non-negative number n and two values l and r. The problem is to check whether all the bits are unset or not in the range l to r in the binary representation of n.
Constraint: 1 <= l <= r <= number of bits in the binary representation of n.
Examples:

Input : n = 17, l = 2, r = 4
Output : Yes
(17)₁₀ = (10001)₂
The bits in the range 2 to 4 are all unset.

Input : n = 36, l = 3, r = 5
Output : No
(36)₁₀ = (100100)₂
The bits in the range 3 to 5 are all not unset.

Approach: Following are the steps:

Calculate num = ((1 << r) – 1) ^ ((1 << (l-1)) – 1). This will produce a number num having r number of bits and bits in the range l to r are the only set bits.
Calculate new_num = n & num.
If new_num == 0, return “Yes” (all bits are unset in the given range).
Else return “No” (all bits are not unset in the given range).

C++

// C++ implementation to check whether all 
// the bits are unset in the given range 
// or not
#include <bits/stdc++.h>
using namespace std;

// function to check whether all the bits
// are unset in the given range or not
string 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 new num is 0, then all bits 
    // are unset in the given range
    if (new_num == 0)
        return "Yes";
        
    // else all bits are not unset 
    return "No"; 
}

// Driver program to test above
int main()
{
    unsigned int n = 17;
    unsigned int l = 2, r = 4;
    cout << allBitsSetInTheGivenRange(n, l, r);
    return 0;
}

Java

// Java implementation to 
// check whether all the
// bits are unset in the 
// given range or not
import java.io.*;

class GFG 
{
    
// function to check whether 
// all the bits are unset in
// the given range or not
static String 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 new num is 0, then 
    // all bits are unset in
    // the given range
    if(new_num == 0)
        return "Yes";
        
    // else all bits
    // are not unset 
    return "No"; 
}

// Driver Code
public static void main (String[] args)
{
    int n = 17;
    int l = 2;
    int r = 4;
    System.out.println(
           allBitsSetInTheGivenRange(n, l, r));
}
}

// This code is contributed by akt_mit

Python 3

# Python 3 implementation to check whether  
# all the bits are unset in the given range 
# or not

# function to check whether all the bits
# are unset 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 new num is 0, then all bits 
    # are unset in the given range
    if (new_num == 0):
        return "Yes"
        
    # else all bits are not unset 
    return "No"

# Driver Code
if __name__ == "__main__":
    
    n = 17
    l = 2
    r = 4
    print(allBitsSetInTheGivenRange(n, l, r))

# This code is contributed by ita_c

// C#  implementation to 
// check whether all the 
// bits are unset in the 
// given range or not 
using System;

public class GFG{
            
// function to check whether 
// all the bits are unset in 
// the given range or not 
static String 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 new num is 0, then 
    // all bits are unset in 
    // the given range 
    if(new_num == 0) 
        return "Yes"; 
        
    // else all bits 
    // are not unset 
    return "No"; 
} 

// Driver Code 
    static public void Main (){
        int n = 17; 
        int l = 2; 
        int r = 4; 
        Console.WriteLine( 
            allBitsSetInTheGivenRange(n, l, r)); 
    } 
} 

// This code is contributed by k_mit

PHP

<?php
// PHP implementation to check
// whether all the bits are 
// unset in the given range 
// or not

// function to check whether 
// all the bits are unset 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 new num is 0, then 
    // all bits are unset in
    // the given range
    if ($new_num == 0)
        return "Yes";
        
    // else all bits
    // are not unset 
    return "No"; 
}

// Driver Code
$n = 17;
$l = 2; $r = 4;
echo allBitsSetInTheGivenRange($n, 
                               $l, $r);

// This code is contributed
// by ajit
?>

JavaScript

<script>

// Javascript implementation to check whether all 
// the bits are unset in the given range 
// or not

// function to check whether all the bits
// are unset 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 new num is 0, then all bits 
    // are unset in the given range
    if (new_num == 0)
        return "Yes";
        
    // else all bits are not unset 
    return "No"; 
}

// Driver program to test above
var n = 17;
var l = 2, r = 4;
document.write( allBitsSetInTheGivenRange(n, l, r));

</script>

Output:

Yes

Time Complexity : O(1)

Auxiliary Space: O(1)

Analysis of Algorithms

Ayush

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Bit Magic

Check whether all the bits are unset in the given range or not

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