Compruebe si todos los bits están establecidos en el rango dado

Dado un número no negativo n y dos valores l y r . El problema es verificar si todos los bits están establecidos o no en el rango de l a r en la representación binaria de n . 
Restricción: 1 <= l <= r <= número de bits en la representación binaria de n .
Ejemplos: 
 

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.

Enfoque: Los siguientes son los pasos:
 

1. Calcular num = ((1 << r) – 1) ^ ((1 << (l-1)) – 1). Esto producirá un número num que tiene un número r de bits y los bits en el rango de l a r son los únicos bits establecidos.
2. Calcula new_num = n & num.
3. Si num == new_num, devuelve «Sí» (todos los bits se establecen en el rango dado).
4. De lo contrario, devuelve «No» (no todos los bits están establecidos en el rango dado).

// 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;
}

// 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.

# 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.

// 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.

<?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
?>

<script>
 
// javascript 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
    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 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
var n = 22;
var l = 2, r = 3;
 
document.write(allBitsSetInTheGivenRange(
                                   n, l, r));
 
// This code contributed by Princi Singh
 
</script>

Producción: 
 

Yes

Complejidad del tiempo – O(1)

Complejidad espacial – O(1)

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