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Count Primes

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a JavaScript program to count the number of prime numbers less than a given non-negative integer n using the Sieve of Eratosthenes algorithm. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Example 1
    
      
  • Input: n = 10
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  • Output: 4
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  • Explanation: 
    • We need to find prime numbers less than 10: [2, 3, 5, 7]. 
    • Number 2 is prime, 3 is prime, 4 is not prime (2×2), 5 is prime. 
    • Number 6 is not prime (2×3), 7 is prime, 8 is not prime (2×4), 9 is not prime (3×3). 
    • Therefore, there are 4 prime numbers less than 10.
    •
Example 2
    
      
  • Input: n = 0
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  • Output: 0
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  • Explanation: 
    • There are no numbers less than 0. 
    • Therefore, the count of prime numbers is 0. 
    • The result is 0.
    •
Constraints
    
      
  • 0 ≤ n ≤ 5 × 10^6
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  • You must use the Sieve of Eratosthenes algorithm
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  • Time Complexity: O(n log log n)
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  • Space Complexity: O(n)
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Hint
Solution

Solution Hints

    
      
  • Create a boolean array of size n and initialize all values as true
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  • Start with the first prime number 2 and mark all its multiples as composite
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  • Find the next unmarked number and repeat the process
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  • Continue until you've processed all numbers up to √n
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  • Count all the numbers that remain marked as prime
    •

Steps to solve by this approach:

 Step 1: Create a boolean array of size n and initialize all values as true except indices 0 and 1
 Step 2: Start with the smallest prime number 2 and mark it as prime
 Step 3: Mark all multiples of 2 starting from 2² as composite (false)
 Step 4: Find the next unmarked number (next prime) and repeat the marking process
 Step 5: Continue this process until we've checked all numbers up to √n
 Step 6: Count all the indices that remain marked as true (prime)
 Step 7: Return the final count of prime numbers

Submitted Code :