114 lines
3.7 KiB
Java
114 lines
3.7 KiB
Java
import java.util.Arrays;
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import java.util.ArrayList;
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import java.util.List;
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public class SphenicNumbers {
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public static void main(String[] args) {
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final int limit = 1000000;
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final int imax = limit / 6;
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boolean[] sieve = primeSieve(imax + 1);
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boolean[] sphenic = new boolean[limit + 1];
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for (int i = 0; i <= imax; ++i) {
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if (!sieve[i])
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continue;
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int jmax = Math.min(imax, limit / (i * i));
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if (jmax <= i)
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break;
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for (int j = i + 1; j <= jmax; ++j) {
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if (!sieve[j])
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continue;
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int p = i * j;
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int kmax = Math.min(imax, limit / p);
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if (kmax <= j)
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break;
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for (int k = j + 1; k <= kmax; ++k) {
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if (!sieve[k])
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continue;
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assert(p * k <= limit);
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sphenic[p * k] = true;
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}
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}
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}
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System.out.println("Sphenic numbers < 1000:");
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for (int i = 0, n = 0; i < 1000; ++i) {
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if (!sphenic[i])
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continue;
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++n;
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System.out.printf("%3d%c", i, n % 15 == 0 ? '\n' : ' ');
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}
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System.out.println("\nSphenic triplets < 10,000:");
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for (int i = 0, n = 0; i < 10000; ++i) {
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if (i > 1 && sphenic[i] && sphenic[i - 1] && sphenic[i - 2]) {
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++n;
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System.out.printf("(%d, %d, %d)%c",
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i - 2, i - 1, i, n % 3 == 0 ? '\n' : ' ');
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}
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}
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int count = 0, triplets = 0, s200000 = 0, t5000 = 0;
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for (int i = 0; i < limit; ++i) {
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if (!sphenic[i])
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continue;
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++count;
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if (count == 200000)
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s200000 = i;
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if (i > 1 && sphenic[i - 1] && sphenic[i - 2]) {
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++triplets;
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if (triplets == 5000)
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t5000 = i;
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}
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}
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System.out.printf("\nNumber of sphenic numbers < 1,000,000: %d\n", count);
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System.out.printf("Number of sphenic triplets < 1,000,000: %d\n", triplets);
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List<Integer> factors = primeFactors(s200000);
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assert(factors.size() == 3);
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System.out.printf("The 200,000th sphenic number: %d = %d * %d * %d\n",
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s200000, factors.get(0), factors.get(1),
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factors.get(2));
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System.out.printf("The 5,000th sphenic triplet: (%d, %d, %d)\n",
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t5000 - 2, t5000 - 1, t5000);
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}
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private static boolean[] primeSieve(int limit) {
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boolean[] sieve = new boolean[limit];
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Arrays.fill(sieve, true);
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if (limit > 0)
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sieve[0] = false;
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if (limit > 1)
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sieve[1] = false;
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for (int i = 4; i < limit; i += 2)
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sieve[i] = false;
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for (int p = 3, sq = 9; sq < limit; p += 2) {
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if (sieve[p]) {
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for (int q = sq; q < limit; q += p << 1)
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sieve[q] = false;
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}
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sq += (p + 1) << 2;
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}
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return sieve;
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}
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private static List<Integer> primeFactors(int n) {
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List<Integer> factors = new ArrayList<>();
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if (n > 1 && (n & 1) == 0) {
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factors.add(2);
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while ((n & 1) == 0)
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n >>= 1;
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}
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for (int p = 3; p * p <= n; p += 2) {
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if (n % p == 0) {
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factors.add(p);
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while (n % p == 0)
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n /= p;
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}
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}
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if (n > 1)
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factors.add(n);
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return factors;
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}
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}
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