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112 lines
2.5 KiB
Java
112 lines
2.5 KiB
Java
import java.util.*;
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public class PrimesAndDivisors {
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public static int[] generatePrimes(int n) {
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boolean[] sieve = new boolean[n + 1];
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Arrays.fill(sieve, 2, n + 1, true);
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for (int i = 2; i * i <= n; i++)
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if (sieve[i])
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for (int j = i * i; j <= n; j += i)
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sieve[j] = false;
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int[] primes = new int[n + 1];
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int cnt = 0;
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for (int i = 0; i < sieve.length; i++)
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if (sieve[i])
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primes[cnt++] = i;
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return Arrays.copyOf(primes, cnt);
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}
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public static int[] generatePrimesLinear(int n) {
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int[] lp = new int[n + 1];
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int[] primes = new int[n + 1];
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int cnt = 0;
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for (int i = 2; i <= n; ++i) {
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if (lp[i] == 0) {
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lp[i] = i;
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primes[cnt++] = i;
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}
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for (int j = 0; j < cnt && primes[j] <= lp[i] && i * primes[j] <= n; ++j)
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lp[i * primes[j]] = primes[j];
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}
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return Arrays.copyOf(primes, cnt);
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}
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public static boolean isPrime(long n) {
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if (n <= 1)
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return false;
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for (long i = 2; i * i <= n; i++)
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if (n % i == 0)
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return false;
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return true;
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}
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public static int[] numberOfPrimeDivisors(int n) {
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int[] divisors = new int[n + 1];
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Arrays.fill(divisors, 2, n + 1, 1);
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for (int i = 2; i * i <= n; ++i)
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if (divisors[i] == 1)
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for (int j = i; j * i <= n; j++)
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divisors[j * i] = divisors[j] + 1;
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return divisors;
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}
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public static int[] generateDivisorTable(int n) {
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int[] divisor = new int[n + 1];
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for (int i = 1; i <= n; i++)
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divisor[i] = i;
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for (int i = 2; i * i <= n; i++)
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if (divisor[i] == i)
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for (int j = i * i; j <= n; j += i)
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divisor[j] = i;
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return divisor;
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}
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public static int phi(int n) {
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int res = n;
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for (int i = 2; i * i <= n; i++)
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if (n % i == 0) {
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while (n % i == 0)
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n /= i;
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res -= res / i;
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}
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if (n > 1)
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res -= res / n;
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return res;
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}
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public static int[] generatePhi(int n) {
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int[] res = new int[n + 1];
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for (int i = 1; i <= n; i++)
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res[i] = i;
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for (int i = 1; i <= n; i++)
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for (int j = i + i; j <= n; j += i)
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res[j] -= res[i];
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return res;
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}
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// Usage example
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public static void main(String[] args) {
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int n = 31;
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int[] primes1 = generatePrimes(n);
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int[] primes2 = generatePrimesLinear(n);
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System.out.println(Arrays.toString(primes1));
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System.out.println(Arrays.toString(primes2));
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System.out.println(Arrays.equals(primes1, primes2));
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System.out.println(Arrays.toString(numberOfPrimeDivisors(n)));
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System.out.println(Arrays.toString(generateDivisorTable(n)));
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n = 1000;
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int[] phi = generatePhi(n);
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for (int i = 0; i <= n; i++) {
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if (phi[i] != phi(i)) {
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System.err.println(i);
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}
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}
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}
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}
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