Check whether all the bits are unset in the given range

Last Updated : 30 Sep, 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. The bits are numbered from right to left, i.e., the least significant bit is considered to be at first position.
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 = 39, l = 4, r = 6
Output : No
(39)₁₀ = (100111)₂
The bits in the range 4 to 6 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
bool 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 could only have one or more
    // set bits in the range l to r and nowhere else
    int new_num = n & num;

    // if true, then all bits are unset
    // in the given range
    if (new_num == 0)
        return true;

    // else all bits are not unset
    // in the given range
    return false;
}

// Driver program to test above
int main()
{
    unsigned int n = 17;
    unsigned int l = 2, r = 4;
    if (allBitsSetInTheGivenRange(n, l, r))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Java implementation to check 
// whether all the bits are 
// unset in the given range or not
class GFG
{
    
// function to check whether 
// all the bits are unset in
// the given range or not
static boolean 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 could only 
    // have one or more set bits in
    // the range l to r and nowhere else
    int new_num = n & num;

    // if true, then all bits are 
    // unset in the given range
    if (new_num == 0)
        return true;

    // else all bits are not 
    // unset in the given range
    return false;
}

// Driver Code
public static void main(String[] args)
{
    int n = 17;
    int l = 2, r = 4;
    if (allBitsSetInTheGivenRange(n, l, r))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}

// This code is contributed
// by Smitha

Python3

# Python3 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 could only 
    # have one or more set bits in 
    # the range l to r and nowhere else
    new_num = n & num

    # if true, then all bits are 
    # unset in the given range
    if (new_num == 0):
        return True

    # else all bits are not 
    # unset in the given range
    return false

# Driver Code
n = 17
l = 2
r = 4
if (allBitsSetInTheGivenRange(n, l, r)):
    print("Yes")
else:
    print("No")

# This code is contributed 
# by Smitha

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

class GFG
{
    
// function to check whether 
// all the bits are unset in
// the given range or not
static bool 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 could  
    // only have one or more 
    // set bits in the range 
    // l to r and nowhere else
    int new_num = n & num;

    // if true, then all 
    // bits are unset
    // in the given range
    if (new_num == 0)
        return true;

    // else all bits are not 
    // unset in the given range
    return false;
}

// Driver Code
public static void Main()
{
    int n = 17;
    int l = 2, r = 4;
    if (allBitsSetInTheGivenRange(n, l, r))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}

// This code is contributed 
// by Smitha

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 could only 
    // have one or more set bits in
    // the range l to r and nowhere else
    $new_num = $n & $num;

    // if true, then all bits are 
    // unset in the given range
    if ($new_num == 0)
        return true;

    // else all bits are not unset
    // in the given range
    return false;
}

// Driver Code
$n = 17;
$l = 2;
$r = 4;
if (allBitsSetInTheGivenRange($n, $l, $r))
    echo "Yes";
else
    echo "No";
    
// This code is contributed by Smitha
?>

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
    let num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);

    // new number which could only have one or more
    // set bits in the range l to r and nowhere else
    let new_num = n & num;

    // if true, then all bits are unset
    // in the given range
    if (new_num == 0)
        return true;

    // else all bits are not unset
    // in the given range
    return false;
}

// Driver program to test above
    let n = 17;
    let l = 2, r = 4;
    if (allBitsSetInTheGivenRange(n, l, r))
        document.write("Yes");
    else
        document.write("No");

</script>

Output:

Yes

Time complexity: O(1) since constant bit operations are done
Auxiliary space: O(1)

Check whether bits are in alternate pattern in the given range

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Bit Magic

Check whether all the bits are unset in the given range

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