prime numbers

#include <bits/stdc++.h>

using namespace std;

vector<int> leastPrimceFactor;
vector<int> primes;

void sieve(int n) { // O(N)
    leastPrimceFactor.resize(n + 1, 0);
    for(int i = 2; i <= n; ++i) {
        if (leastPrimceFactor[i] == 0) {
            leastPrimceFactor[i] = i;
            primes.push_back(i);
        }
        for (int j = 0; i * primes[j] <= n; ++j) {
            leastPrimceFactor[i * primes[j]] = primes[j];
            if (primes[j] == leastPrimceFactor[i]) {
                break;
            }
        }
    }
}

bool isPrime(int n) { // O( sqrt(N) / ln(sqrt(N))) -> tests only primes smaller than sqrt(N)
    if(n == 2) return true;
    if(n < 2 || (n % 2 == 0)) return false;
    if(n < leastPrimceFactor.size()) return leastPrimceFactor[n] == n;

    int index = 0;

    while(primes[index] * primes[index] <= n) {
        if((n % primes[index]) == 0)
            return false;
        index++;
    }

    return true;
}

int main() {
    int L = 5;
    int R = 12;

    sieve(sqrt(R) + 1);

    while(L <= R) {
        if(isPrime(L))
            cout << L << ' ';
        ++L;
    }
    cout << endl;

    return 0;
}