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++

// 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

Time Complexity : O(1) 

Auxiliary Space: O(1)