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

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++

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// 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;

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Java

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// 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

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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 [tabby title="C#"]

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// 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

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PHP

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<?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
?>

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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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Improved By : jit_t, Sach_Code, Ita_c



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