Java的eratosthenes问题筛

Question

I am trying to make sieve of eratosthenes, i am currently having a problem. The probelm is that during the calculation method, the program won't continue to the next prime number. I think the problem is with the while loop but i don't know how to fix it. Can someone help me?

Thank you

import java.util.*;
import java.io.*;

public class Primes_below_N {

    static Vector<Integer> numbers = new Vector<Integer>();
    static BufferedReader br = new BufferedReader(new InputStreamReader(
            System.in));

    public static void main(String[] args) throws IOException {
        System.out.print("Please enter a number: ");
        int LIMIT = Integer.parseInt(br.readLine());
        populate(LIMIT);
        calculatePrimes(LIMIT);
        print(numbers);

    }

    // populate a 'numbers' with a numbers upto limit
    public static void populate(int limit) {
        for (int i = 1; i <= limit; i++) {
            numbers.add(i);
        }
    }

    // calculate prime numbers
    public static void calculatePrimes(int limit) {
        int p = 2;
        int nextPrime = 1;
        while (Math.pow(p, 2) < limit) {
            for (int i = 0; i < numbers.size(); ++i) {
                if (numbers.get(i) % 2 == 0 && numbers.get(i) != i) {
                    numbers.remove(i);
                }
            }
            p = numbers.get(nextPrime);
            nextPrime += 1;
        }
    }

    public static void print(Vector<Integer> list) {
        for (int i : list) {
            System.out.println(i);
        }
    }

}

Answer 1

The problem is with these two line:

• if (numbers.get(i) % 2 == 0 && numbers.get(i) != i)

It should be if (numbers.get(i) % p == 0 && numbers.get(i) != p)

• p = numbers.get(nextPrime); nextPrime += 1;

The order should be reverse ie nextPrime++; p = numbers.get(nextPrime); nextPrime++; p = numbers.get(nextPrime);

Also as a side note: the algorithm says to Create a list of consecutive integers from two to n: (2, 3, 4, ..., n) and not from (1, 2, .... , n)

---

I have taken an exact copy of your code and changed the lines which I have mentioned earlier (Marked as CHANGE 1 & CHANGE 2).

package test;

import java.util.*;
import java.io.*;

import java.util.*;
import java.io.*;

public class Primes_below_N {

    static Vector<Integer> numbers = new Vector<Integer>();
    static BufferedReader br = new BufferedReader(new InputStreamReader(
            System.in));

    public static void main(String[] args) throws IOException {
        System.out.print("Please enter a number: ");
        int LIMIT = Integer.parseInt(br.readLine());
        populate(LIMIT);
        calculatePrimes(LIMIT);
        print(numbers);

    }

    // populate a 'numbers' with a numbers upto limit
    public static void populate(int limit) {
        for (int i = 1; i <= limit; i++) {
            numbers.add(i);
        }
    }

    // calculate prime numbers
    public static void calculatePrimes(int limit) {
        int p = 2;
        int nextPrime = 1;
        while (Math.pow(p, 2) < limit) {
            for (int i = 0; i < numbers.size(); ++i) {

                // CHANGE 1 - IF block change
                if (numbers.get(i) % p == 0 && numbers.get(i) != p) {
                    numbers.remove(i);
                }
            }

            // CHANGE 2 - Reorder
            nextPrime += 1; 
            p = numbers.get(nextPrime);

        }
    }

    public static void print(Vector<Integer> list) {
        for (int i : list) {
            System.out.print(i + ", "); // Changed for single line printing
        }
    }

}

Test1

>>Input: Please enter a number: 50

>>Output: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,

One is coming because of your code.

Test2

>>Input: Please enter a number: 100

>>Output: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,

As you can see for 100 there are 25 prime numbers (excluding 1)

Answer 2

I looks like you missed a few points on the algorithm. At face value I'd guess that code is NEVER going to return. WHILE p squared is less than limit DO foreach entry in the list... Nope, never... well not in the lifetime of the universe anyway.

Have a good read through the wikipedia article on the Sieve of Erastothenes: http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes . It's even got a great visualisation which SHOWS you how the algorithm works.

Answer 3

One issue you will need to address is that as you are applying the sieve, you're removing elements from numbers , and so the indices i and nextPrime aren't pointing where you think they're pointing. It might help you to print console output to the effect

System.out.println("Loop index: " + i);

at the beginning of the for loop, and also

System.out.println("Got prime: " + p);

right after getting the prime.

It sounds like you're looking for just a hint, so I'll leave it at that.