<p>Given an integer <code>n</code>, return <em>the number of prime numbers that are strictly less than</em> <code>n</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 4 prime numbers less than 10, they are 2, 3, 5, 7.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 0
<strong>Output:</strong> 0
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= n &lt;= 5 * 10<sup>6</sup></code></li>
</ul>

class Solution {
public:

    int countPrimes(int n) {
        if (n < 3) return 0;

        int sqrtn = sqrt(n-1);
        int smallPrimes[sqrtn];
        int smallPrimeSquares[sqrtn];
        int smallPrimeCount = 0;

        for(int i = 2; i <= sqrtn; i++) {
            bool isPrime = true;
            for(int j = 0; j < smallPrimeCount - 1 && smallPrimeSquares[j] <= i; j++) {
                if (i % smallPrimes[j] == 0) {
                    isPrime = false;
                    break;
                }
            }
            if (isPrime) {
                smallPrimes[smallPrimeCount] = i;
                smallPrimeSquares[smallPrimeCount] = i*i;
                smallPrimeCount++;
            }
        }
        int primeCount = (n - 2) + smallPrimeCount - adjust(smallPrimes, smallPrimeCount, n, 1, 0);
        return primeCount;
    }

private: 

    int adjust(int* primes, int numPrimes, int n, int base, int start) {
        int adj = 0;
        for (int i = start; i < numPrimes; i++) {
            int num = base * primes[i];
            if (num >= n) break;
            adj += ((n-1) / num);
            if (i + 1 < numPrimes && num <= n / primes[i+1]) {
                adj -= adjust(primes, numPrimes, n, num, i+1);
            }
        }
        return adj;
    }

};
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