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Check whether all the bits are unset in the given range or not
  • Difficulty Level : Expert
  • Last Updated : 15 Apr, 2021

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:
 

  1. 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.
  2. Calculate new_num = n & num.
  3. If new_num == 0, return “Yes” (all bits are unset in the given range).
  4. 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#




// 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

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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