<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>

//if N donot have any factor between 2 to rootN then N is a Prime number
// class Solution {
// public:
//     int countPrimes(int n) {
//        //Sieve of Eratosthenis 
//        int count = 0;
//        vector<bool> prime(n+1,true);

//        prime[0] = prime[1] = false;

//        for(int i = 2;i<n;i++){
//         if(prime[i]){
//             count++;
//             for(int j = 2*i; j<n;j += i ){
//                 prime[j] = 0;
//             }
//         }
//        }
//        return count; 
//     }
// };
// Segmented Sieve 
// class Solution {
// public:
//     int countPrimes(int n) {
        
//         int a[n+1];
//         for(int i =0; i<=n; i++){
//             a[i] =0;
//         }
//         for(int i =2; i*i<=n; i++){
//             for(int j =i+i; j<=n; j+=i){
//                 a[j] =1;
//             }
//         }
//         int cnt =0;
//         for(int i =2; i<n; i++){
//             if(a[i]==0){
//                 cnt++;
//             }
//         }
        
//         return cnt;
//     }
// };
class Solution {
private:
    vector<long long> Sieve(int n){
        vector<bool> prime(n+1,true);
        vector<long long> Nprime;
        prime[0] = prime[1] = false;
        for(int i = 2; i <= sqrt(n); i++){
            if(prime[i] == true){
                for(int j = i*i; j <= n; j += i){
                    prime[j] = false;
                }
            }
        }
        for(int i = 0; i <= n; i++){
            if(prime[i])
                Nprime.push_back(i);
        }
        return Nprime;
    }
public:
    int countPrimes(int n) {
        if (n <= 2) return 0;  // no primes less than 2
        
        int l = 2; // start from 2 since primes are positive integers > 1
        int r = n-1; // Adjust range to exclude n
        vector<long long> primes = Sieve(sqrt(r));
        vector<bool> segsieve(r-l+1, true);

        for(auto p : primes){
            long long start = max(p*p, l + (p - l % p) % p);  // starting point to mark
            for(long long j = start; j <= r; j += p){
                segsieve[j - l] = false;
            }
        }

        primes.clear();
        for(int i = 0; i <= r-l; i++){
            if(segsieve[i])
                primes.push_back(i+l);
        }

        return primes.size();
    }
};

64140