Count Primes

Count the number of prime numbers less than a non-negative number, n.

Example:

Input: 10
Output: 4
Explanation: There are 4 prime numbers less than 10, they are 2, 3, 5, 7.

class Solution {
    public int countPrimes(int n) {
        // Create a boolean array "prime[0..n]" and initialize
        // all entries it as true. A value in prime[i] will
        // finally be false if i is Not a prime, else true.
        boolean prime[] = new boolean[n + 1];
        for (int i = 0; i < n; i++)
            prime[i] = true;
            
        for (int p = 2; p * p <= n; p++) {
            // If prime[p] is not changed, then it is a prime
            if (prime[p] == true)
                // Update all multiples of p
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
        }
        int count = 0;
        // Print all prime numbers
        for (int i = 2; i <= n; i++) {
            if (prime[i] == true)
                count++;
        }
        return count;
    }
}