<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:

    bool isPrime(int n){
        for(int i=2;i*i<=n;i++){
            if(n%i==0) return false;
        }
        return true;
    }

    int countPrimes(int n) {
        int cnt=0;
        // for(int i=2;i<n;i++){
        //     if(isPrime(i)) cnt++;
        // }
        int prime[n+1];
        //memset(prime,1,sizeof(prime));
        for(int i=0;i<=n;i++){
            prime[i]=1;
        }
        for(int i=2;i*i<=n;i++){
            if(prime[i]==1){
                for(int j=i*i;j<=n;j+=i){
                    prime[j]=0;
                }
            }
        }
        for(int x=2;x<n;x++){
            if(prime[x]) cnt++;
        }
        return cnt;
    }
};
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