<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) {
        //Create an list of integers with 5, 7, 11, 13, 17, ... equal to 5 and 7 plus multiples of 6
        //plus multiples of 6

        int possiblePrimeCount = 0;
        if (n > 5)
        {
            possiblePrimeCount = 2 * (n / 6) + ((n % 6) > 1 ? 1 : 0) - 1;
        }

        std::vector<bool> possiblePrimes(possiblePrimeCount, true);

        int result = 0;
        if (n > 2) ++result;
        if (n > 3) ++result;

        for (int i = 0; i < possiblePrimeCount; ++i)
        {
            if (!possiblePrimes[i])
            {
                continue;
            }

            ++result;

            //This is a prime
            //Multiples of the prime, i.e. 5p, 7p, 11p, 13p, etc. should be eliminated
            int jump1 = 4 * i + (i & 1 ? 5 : 7);
            int jump2 = 2 * i + 3;

            for (int j = i;;)
            {
                j += jump1;
                if (j >= possiblePrimeCount) break;
                possiblePrimes[j] = false;

                j += jump2;
                if (j >= possiblePrimeCount) break;
                possiblePrimes[j] = false;
            }
        }

        return result;
    }
};
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