Check whether all the bits are set in the given range

Given a non-negative number n and two values l and r. The problem is to check whether all the bits are set 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 = 22, l = 2, r = 3
Output : Yes
(22)10 = (10110)2
The bits in the range 2 to 3 are all set.

Input : n = 47, l = 2, r = 5 
Output : No
(47)10 = (101111)2
The bits in the range 2 to 5 are all not set.



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 num == new_num, return “Yes” (all bits are set in the given range).
  4. Else return “No” (all bits are not set in the given range).

C++

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// C++ implementation to check whether all the bits
// are set in the given range or not
#include <bits/stdc++.h>
  
using namespace std;
  
// function to check whether all the bits
// are set 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 both are equal, then all bits are set
    // in the given range
    if (num == new_num)
        return "Yes";
          
    // else all bits are not set    
    return "No";    
}
  
// Driver program to test above
int main()
{
    unsigned int n = 22;
    unsigned int l = 2, r = 3;
    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 set in the given range or not 


class GFG { 


          


    // function to check whether all the bits 


    // are set 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 both are equal, then all bits are 


        // set in the given range 


        if (num == new_num) 


            return "Yes"; 


              


        // else all bits are not set  


        return "No";  


    } 


      


    //Driver code 


    public static void main (String[] args) 


    { 


        int n = 22; 


        int l = 2, r = 3; 


          


        System.out.print(allBitsSetInTheGivenRange( 


                                           n, l, r)); 


    } 


} 


  


// This code is contributed by Anant Agarwal. 



















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Python3














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# Python3 implementation to check 


# whether all the bits are set in 


# the given range or not 


  


# 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 "Yes"


          


    # else all bits are not set  


    return "No"


  


# Driver code 


n, l, r = 22, 2, 3


print(allBitsSetInTheGivenRange(n, l, r)) 


  


# This code is contributed by Anant Agarwal. 



















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C#














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// C# implementation to check whether all the bits 


// are set in the given range or not 


using System; 


  


class GFG 


{ 


    // function to check whether all the bits 


    // are set 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 both are equal, then all bits are set 


        // in the given range 


        if (num == new_num) 


            return "Yes"; 


               


        // else all bits are not set     


        return "No";     


    } 


      


    //Driver code 


    public static void Main () 


    { 


        int n = 22; 


        int l = 2, r = 3; 


        Console.Write(allBitsSetInTheGivenRange(n, l, r)); 


    } 


} 


  


// This code is contributed by Anant Agarwal. 



















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PHP














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<?php 


// PHP implementation to check 


// whether all the bits are set 


// in the given range or not 


  


// 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 "Yes"; 


          


    // else all bits 


    // are not set  


    return "No";  


} 


  


    // Driver Code 


    $n = 22; 


    $l = 2; 


    $r = 3; 


    echo allBitsSetInTheGivenRange($n, $l, $r); 


      


// This code is contributed by Ajit 


?> 



















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Output:


Yes



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