segmented sieve

import java.util.Arrays;
import java.util.Scanner;

public class SegmentedSieve {

    // Function to implement basic Sieve of Eratosthenes for primes up to √R
    public static void simpleSieve(int limit, boolean[] primes) {
        Arrays.fill(primes, true);
        primes[0] = primes[1] = false;
        for (int p = 2; p * p <= limit; p++) {
            if (primes[p]) {
                for (int i = p * p; i <= limit; i += p) {
                    primes[i] = false;
                }
            }
        }
    }

    // Function to print all prime numbers in the range [L, R] using the segmented sieve approach
    public static void segmentedSieve(int L, int R) {
        // Find all primes up to √R using simple sieve
        int limit = (int) Math.sqrt(R) + 1;
        boolean[] primes = new boolean[limit + 1];
        simpleSieve(limit, primes);

        // Create a boolean array for the range [L, R]
        boolean[] isPrime = new boolean[R - L + 1];
        Arrays.fill(isPrime, true);

        // Use the primes found to mark non-primes in the range [L, R]
        for (int p = 2; p <= limit; p++) {
            if (primes[p]) {
                // Find the first multiple of p in the range [L, R]
                int start = Math.max(p * p, (L + p - 1) / p * p);

                // Mark multiples of p as non-prime in the range [L, R]
                for (int j = start; j <= R; j += p) {
                    isPrime[j - L] = false;
                }
            }
        }

        // Print all primes in the range [L, R]
        System.out.println("Primes in the range [" + L + ", " + R + "] are:");
        for (int i = 0; i <= R - L; i++) {
            if (isPrime[i]) {
                System.out.print((i + L) + " ");
            }
        }
        System.out.println();
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter the range (L R): ");
        int L = scanner.nextInt();
        int R = scanner.nextInt();
        scanner.close();

        // Call the segmented sieve function to find primes in the range [L, R]
        segmentedSieve(L, R);
    }
}