实现轮筛以在给定范围之间生成素数的Java程序

质数是大于1的整数，它只能被1和它本身整除。前几个素数是 2 3 5 7 11 13 17 19 23。给定一个范围， L到R，任务是生成该范围中存在的所有素数。

例子

Input: 1 10
Output 2 3 5 7

Input: 20 30 
Output: 23 29

方法一：检查每个元素是否为素数。

• 在范围 L 到 R 中迭代
• 检查每个元素是否为素数
• 打印范围内的素数

例子

Java

// Java Program to Implement wheel Sieve to Generate Prime
// Numbers Between Given Range
 
import java.io.*;
 
class GFG {
    static boolean checkPrime(int n)
    {
        // Handling the edge case
        if (n == 1) {
            return false;
        }
        for (int i = 2; i <= Math.sqrt(n); ++i) {
 
            // checking the prime number
            if (n % i == 0) {
                return false;
            }
        }
 
        return true;
    }
    public static void main(String[] args)
    {
        // starting in a range
        int L = 1;
 
        // ending in a range
        int R = 20;
 
        for (int i = L; i <= R; ++i) {
 
            // printing the prime number
            if (checkPrime(i) == true) {
                System.out.print(i + " ");
            }
        }
    }
}

输出

2 3 5 7 11 13 17 19

• 时间复杂度：O(n * sqrt(n))
• 空间复杂度：O(1)

方法 2：使用 Eratosthenes 筛法生成所有素数

• 使用埃拉托色尼筛法生成所有素数（参考这篇文章）
• 标记所有素数的所有倍数 剩余数为左素数
• 直到值的最大范围
• 打印给定范围内的所有质数

例子

Java

// Java Program to Implement wheel Sieve to Generate Prime
// Numbers Between Given Range
 
import java.io.*;
 
class GFG {
 
    // Maximum range
    static boolean max[] = new boolean[1000001];
    static void fill()
    {
        // Maximum Range
        int n = 1000000;
 
        // Mark all numbers as a prime
        for (int i = 2; i <= n; ++i) {
            max[i] = true;
        }
        for (int i = 2; i <= Math.sqrt(n); ++i) {
 
            // if number is prime
            if (max[i] == true) {
 
                // mark all the factors
                // of i non prime
                for (int j = i * i; j <= n; j += i) {
                    max[j] = false;
                }
            }
        }
    }
 
    static void range(int L, int R)
    {
        for (int i = L; i <= R; ++i) {
 
            // checking the prime number
            if (max[i] == true) {
                // print the prime number
                System.out.print(i + " ");
            }
        }
    }
    public static void main(String[] args)
    {
        // starting in a range
        int L = 20;
 
        // ending in a range
        int R = 40;
 
        // mark all the numbers
        fill();
 
        // printing the prime numbers in range
        range(L, R);
    }
}

输出

23 29 31 37

• 时间复杂度： O(nlog(logn)
• 空间复杂度： O(1)

方法 3：使用轮筛生成所有质数。与上述方法相比，这种方法是一种非常优化的方法。在这种方法中，我们使用轮因式分解方法来查找给定范围内的素数。

例子

Java

// Java program to check if the
// given number is prime using
// Wheel Factorization Method
 
import java.util.*;
 
class GFG {
 
    // Function to check if a given
    // number x is prime or not
    static boolean isPrime(int N)
    {
        boolean isPrime = true;
 
        // The Wheel for checking
        // prime number
        int[] arr = { 7, 11, 13, 17, 19, 23, 29, 31 };
 
        // Base Case
        if (N < 2) {
            isPrime = false;
        }
 
        // Check for the number taken
        // as basis
        if (N % 2 == 0 || N % 3 == 0 || N % 5 == 0) {
            isPrime = false;
        }
 
        // Check for Wheel
        // Here i, acts as the layer
        // of the wheel
        for (int i = 0; i < Math.sqrt(N); i += 30) {
 
            // Check for the list of
            // Sieve in arr[]
            for (int c : arr) {
 
                // If number is greater
                // than sqrt(N) break
                if (c > Math.sqrt(N)) {
                    break;
                }
 
                // Check if N is a multiple
                // of prime number in the
                // wheel
                else {
                    if (N % (c + i) == 0) {
                        isPrime = false;
                        break;
                    }
                }
 
                // If at any iteration
                // isPrime is false,
                // break from the loop
                if (!isPrime)
                    break;
            }
        }
 
        if (isPrime)
            return true;
        else
            return false;
    }
 
    // Driver's Code
    public static void main(String args[])
    {
 
        // Range
        int L = 10;
        int R = 20;
        for (int i = L; i <= R; ++i) {
 
            // Function call for primality
            // check
 
            // if true
            if (isPrime(i) == true) {
 
                // print the prime number
                System.out.print(i + " ");
            }
        }
    }
}

输出

11 13 17 19