Sieve of Eratosthenes: What is it? And how to implement sieve in C++

What is Sieve of Eratosthenes

Sive of Eratosthenes is one an ancient algorithm that finds all prime numbers in a given range. It is also used for finding all divisors of a number with a faster time complexity.

Sieve Algorithm

The algorithm starts by generating a boolean array Boolarray to store whether i is a prime number or not. 2. Every number in the array is set to be TRUE by default. 3. The outer loop of the algorithm iterates Boolarray from 2 to sqrt(n) . - Inner loop iterates through j and accumulate by i(for all multiples of i), all multiples are marked FALSE(since these are not prime numbers). - Inner loop works by marking FALSE on all multiples of i

We are left with b with all prime numbers being TRUE in the range of 1 to n.

Time Complexity

The time complexity of the above logic is O(n log log n). The outer loop runs for sqrt(n), while the inner loop runs roughly n / i times.

Example in C++

#include<iostream>
using namespace std;

int main(){
    int n;
    cin>>n;
    bool Boolarray[n+1];
    for(int i = 2; i <= n; i++) {
    Boolarray[i]=true;
    }
    for (int i = 2; i * i <= n; i++) {
    if (Boolarray[j] == true) {
        for (int j = 2 * i; j <= n; j += i) {
        Boolarray[k] = false;
        }
    }
    }
    for(int i = 2; i <= n; i++) {
        if(Boolarray[i]==true)
            cout<<i<<" ";
    }
    return 0;
}