Prime Number of Set Bits in Binary Representation

Given two integers ‘L’ and ‘R’, write a program to find the total numbers that are having prime number of set bits in their binary representation in the range [L, R].
Examples:

Input  : l = 6, r = 10
Output : 4
Explanation  :
6  -> 110  (2 set bits, 2 is prime)
7  -> 111  (3 set bits, 3 is prime)
9  -> 1001 (2 set bits, 2 is prime)
10 -> 1010 (2 set bits, 2 is prime)
Hence count is 4

Input  : l = 10, r = 15
Output : 5
10 -> 1010 (2 set bits, 2 is prime)
11 -> 1011 (3 set bits, 3 is prime)
12 -> 1100 (2 set bits, 2 is prime)
13 -> 1101 (3 set bits, 3 is prime)
14 -> 1110 (3 set bits, 3 is prime)
Hence count is 5

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Explanation: In this program we find a total number, that’s having prime number of set bit. so we use a CPP predefined function __builtin_popcount() these functions provide a total set bit in number. as well as be check the total bit’s is prime or not if prime we increase the counter these process repeat till given range.

C++

// CPP program to count total prime  
// number of set bits in given range 
#include <bits/stdc++.h> 
using namespace std; 
  
bool isPrime(int n) 
{ 
    // Corner cases 
    if (n <= 1)  return false; 
    if (n <= 3)  return true; 
   
    // This is checked so that we can skip  
    // middle five numbers in below loop 
    if (n%2 == 0 || n%3 == 0) return false; 
   
    for (int i=5; i*i<=n; i=i+6) 
        if (n%i == 0 || n%(i+2) == 0) 
           return false; 
   
    return true; 
} 
  
// count number, that contains prime number of set bit 
int primeBitsInRange(int l, int r) 
{ 
    // tot_bit store number of bit in number 
    int tot_bit, count = 0; 
  
    // iterate loop from l to r 
    for (int i = l; i <= r; i++) { 
  
        // use predefined function for finding  
        // set bit it is return number of set bit 
        tot_bit = __builtin_popcount(i); 
  
        // check tot_bit prime or, not 
        if (isPrime(tot_bit)) 
            count++; 
    } 
    return count; 
} 
  
// Driven Program 
int main() 
{ 
    int l = 6, r = 10;     
    cout << primeBitsInRange(l, r); 
    return 0; 
} 

Java

// Java program to count total prime  
// number of set bits in given range 
import java.lang.*; 
  
class GFG{ 
static boolean isPrime(int n) 
{ 
    // Corner cases 
    if (n <= 1) return false; 
    if (n <= 3) return true; 
  
    // This is checked so that we can skip  
    // middle five numbers in below loop 
    if (n%2 == 0 || n%3 == 0) return false; 
  
    for (int i=5; i*i<=n; i=i+6) 
        if (n%i == 0 || n%(i+2) == 0) 
        return false; 
  
    return true; 
} 
  
// count number, that contains prime number of set bit 
static int primeBitsInRange(int l, int r) 
{ 
    // tot_bit store number of bit in number 
    int tot_bit, count = 0; 
  
    // iterate loop from l to r 
    for (int i = l; i <= r; i++) { 
  
        // use predefined function for finding  
        // set bit it is return number of set bit 
        tot_bit = Integer.bitCount(i); 
  
        // check tot_bit prime or, not 
        if (isPrime(tot_bit)) 
            count++; 
    } 
    return count; 
} 
  
// Driven Program 
public static void main(String[] args) 
{ 
    int l = 6, r = 10;  
    System.out.println(primeBitsInRange(l, r)); 
      
} 
} 
// This code is Contributed by mits 

Python3

# Python3 program to count total prime  
# number of set bits in given range 
def isPrime(n): 
  
    # Corner cases 
    if (n <= 1): return False; 
    if (n <= 3): return True; 
  
    # This is checked so that we can skip  
    # middle five numbers in below loop 
    if (n % 2 == 0 or n % 3 == 0): 
        return False; 
          
    i = 5; 
    while (i * i <= n): 
        if(n % i == 0 or n % (i + 2) == 0): 
            return False; 
        i = i + 6; 
  
    return True; 
  
# count number, that contains  
# prime number of set bit 
def primeBitsInRange(l, r): 
  
    # tot_bit store number of 
    # bit in number 
    count = 0; 
  
    # iterate loop from l to r 
    for i in range(l, r + 1): 
  
        # use predefined function for finding  
        # set bit it is return number of set bit 
        tot_bit = bin(i).count('1'); 
  
        # check tot_bit prime or, not 
        if (isPrime(tot_bit)): 
            count += 1; 
  
    return count; 
  
# Driver Code 
l = 6;  
r = 10;  
print(primeBitsInRange(l, r)); 
  
# This code is contributed by mits 

C#

// C# program to count total prime  
// number of set bits in given range  
  
class GFG{ 
      
    // To count the bits 
static int BitCount(int n) 
{ 
    int count = 0; 
    while (n != 0) 
    { 
        count++; 
        n &= (n - 1); 
    } 
      
    return count; 
} 
          
static bool isPrime(int n)  
{  
    // Corner cases  
    if (n <= 1) return false;  
    if (n <= 3) return true;  
  
    // This is checked so that we can skip  
    // middle five numbers in below loop  
    if (n%2 == 0 || n%3 == 0) return false;  
  
    for (int i=5; i*i<=n; i=i+6)  
        if (n%i == 0 || n%(i+2) == 0)  
        return false;  
  
    return true;  
}  
  
// count number, that contains prime number of set bit  
static int primeBitsInRange(int l, int r)  
{  
    // tot_bit store number of bit in number  
    int tot_bit, count = 0;  
  
    // iterate loop from l to r  
    for (int i = l; i <= r; i++) {  
  
        // use predefined function for finding  
        // set bit it is return number of set bit  
        tot_bit = BitCount(i);  
  
        // check tot_bit prime or, not  
        if (isPrime(tot_bit))  
            count++;  
    }  
    return count;  
}  
  
// Driven Program  
public static void Main()  
{  
    int l = 6, r = 10;  
    System.Console.WriteLine(primeBitsInRange(l, r));  
      
}  
}  
// This code is Contributed by mits  

PHP

<?php 
// PHP program to count total prime  
// number of set bits in given range 
function BitCount($n) 
{ 
    $count = 0; 
    while ($n != 0) 
    { 
        $count++; 
        $n &= ($n - 1); 
    } 
      
    return $count; 
} 
  
function isPrime($n) 
{ 
    // Corner cases 
    if ($n <= 1) return false; 
    if ($n <= 3) return true; 
  
    // This is checked so that we can skip  
    // middle five numbers in below loop 
    if ($n % 2 == 0 || $n % 3 == 0) 
        return false; 
  
    for ($i = 5; $i * $i <= $n; $i = $i + 6) 
        if ($n % $i == 0 ||  
            $n % ($i + 2) == 0) 
        return false; 
  
    return true; 
} 
  
// count number, that contains  
// prime number of set bit 
function primeBitsInRange($l, $r) 
{ 
    // tot_bit store number of 
    // bit in number 
    $count = 0; 
  
    // iterate loop from l to r 
    for ($i = $l; $i <= $r; $i++) 
    { 
  
        // use predefined function for finding  
        // set bit it is return number of set bit 
        $tot_bit = BitCount($i); 
  
        // check tot_bit prime or, not 
        if (isPrime($tot_bit)) 
            $count++; 
    } 
    return $count; 
} 
  
// Driver Code 
$l = 6;  
$r = 10;  
echo primeBitsInRange($l, $r); 
  
// This code is contributed by mits 
?> 

Output:

Time Complexity : Let’s n = (r-l)
so overall time complexity is N*sqrt(N)

We can optimize above solution using Sieve of Eratosthenes.

Prime Number of Set Bits in Binary Representation | Set 2

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My Personal Notes

Prime Number of Set Bits in Binary Representation | Set 1

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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