86 lines
3.0 KiB
Java
86 lines
3.0 KiB
Java
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/*
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This is a Java Program to Implement Sieve Of Atkin Algorithm. This is a program to find all primes less than a number.
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*/
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/**
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** Java Program to implement Sieve Of Atkin Prime generation
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**/
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import java.util.Scanner;
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/** Class SieveOfAtkin **/
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public class SieveOfAtkin
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{
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/** Function to calculate all primes less than n **/
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private boolean[] calcPrimes(int limit)
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{
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/** initialize the sieve **/
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boolean[] prime = new boolean[limit + 1];
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prime[2] = true;
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prime[3] = true;
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int root = (int) Math.ceil(Math.sqrt(limit));
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/** put in candidate primes:
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integers which have an odd number of
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representations by certain quadratic forms **/
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for (int x = 1; x < root; x++)
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{
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for (int y = 1; y < root; y++)
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{
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int n = 4 * x * x + y * y;
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if (n <= limit && (n % 12 == 1 || n % 12 == 5))
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prime[n] = !prime[n];
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n = 3 * x * x + y * y;
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if (n <= limit && n % 12 == 7)
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prime[n] = !prime[n];
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n = 3 * x * x - y * y;
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if ((x > y) && (n <= limit) && (n % 12 == 11))
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prime[n] = !prime[n];
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}
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}
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/** eliminate composites by sieving, omit multiples of its square **/
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for (int i = 5; i <= root; i++)
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if (prime[i])
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for (int j = i * i; j < limit; j += i * i)
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prime[j] = false;
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return prime;
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}
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/** Function to get all primes **/
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public void getPrimes(int N)
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{
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boolean[] primes = calcPrimes(N);
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display(primes);
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}
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/** Function to display all primes **/
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public void display(boolean[] primes)
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{
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System.out.print("\nPrimes = ");
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for (int i = 2; i < primes.length; i++)
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if (primes[i])
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System.out.print(i +" ");
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System.out.println();
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}
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/** Main function **/
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public static void main (String[] args)
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{
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Scanner scan = new Scanner(System.in);
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System.out.println("Sieve Of Atkin Prime Algorithm Test\n");
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/** Make an object of SieveOfAtkin class **/
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SieveOfAtkin soa = new SieveOfAtkin();
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/** Accept n **/
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System.out.println("Enter number to find all primes less than the number\n");
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int n = scan.nextInt();
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soa.getPrimes(n);
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}
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}
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/*
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Enter number to find all primes less than the number
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500
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Primes = 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
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101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197
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199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313
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317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439
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443 449 457 461 463 467 479 487 491 499
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