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package numbertheory;
import static java.util.stream.Collectors.summingInt;
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
public class Factorization {
// returns prime_divisor -> power
// O(sqrt(n)) complexity
public static Map<Long, Integer> factorize(long n) {
List<Long> factors = new ArrayList<>();
for (long d = 2; d * d <= n; d++) {
while (n % d == 0) {
factors.add(d);
n /= d;
}
}
if (n > 1) {
factors.add(n);
}
return factors.stream().collect(Collectors.groupingBy(Function.identity(), summingInt(v -> 1)));
}
public static int[] getAllDivisors(int n) {
List<Integer> divisors = new ArrayList<>();
for (int d = 1; d * d <= n; d++)
if (n % d == 0) {
divisors.add(d);
if (d * d != n)
divisors.add(n / d);
}
return divisors.stream().sorted().mapToInt(Integer::valueOf).toArray();
}
// returns divisor of n or -1 if failed: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm#Algorithm
// O(n^(1/4)) complexity
public static long pollard(long n) {
Random rnd = new Random(1);
long x = Math.abs(rnd.nextLong()) % n;
long y = x;
while (true) {
x = g(x, n);
y = g(g(y, n), n);
if (x == y)
return -1;
long d = gcd(Math.abs(x - y), n);
if (d != 1)
return d;
}
}
static long gcd(long a, long b) {
return a == 0 ? b : gcd(b % a, a);
}
static long g(long x, long n) {
return (41 * x + 1) % n;
}
// returns divisor of n: https://en.wikipedia.org/wiki/Fermat%27s_factorization_method
public static long ferma(long n) {
long x = (long) Math.sqrt(n);
long y = 0;
long r = x * x - y * y - n;
while (true) {
if (r == 0)
return x != y ? x - y : x + y;
else if (r > 0) {
r -= y + y + 1;
++y;
} else {
r += x + x + 1;
++x;
}
}
}
// Usage example
public static void main(String[] args) {
System.out.println(factorize(24));
System.out.println(Arrays.toString(getAllDivisors(16)));
long n = 1000_003L * 100_000_037;
System.out.println(pollard(n));
System.out.println(ferma(n));
}
}