<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>

#include <vector>
using namespace std;

class Solution {
public:
    int countPrimes(int n) {
        if (n <= 2) return 0; // No primes less than 2
        
        vector<int> nums(n, 1);  // Create a vector of size n and initialize all elements to 1
        nums[0] = nums[1] = 0;   // 0 and 1 are not prime numbers

        int count = 0;

        // Start from the first prime number 2
        for (int i = 2; i * i < n; i++) {
            if (nums[i] == 1) {  // If `i` is prime
                for (int j = i * i; j < n; j += i) {  // Mark all multiples of `i` as non-prime
                    nums[j] = 0;
                }
            }
        }

        // Count all primes less than `n`
        for (int i = 2; i < n; i++) {
            if (nums[i] == 1) count++;
        }

        return count;
    }
};

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