forked from rchen8/algorithms
/
NumberTheory.java
80 lines (65 loc) · 1.55 KB
/
NumberTheory.java
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import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
public class NumberTheory {
private static ArrayList<Integer> prime;
private static void sieve(int n) {
boolean[] sieve = new boolean[n + 1];
Arrays.fill(sieve, true);
sieve[0] = false;
sieve[1] = false;
prime = new ArrayList<>();
for (int i = 2; i * i <= n; i++) {
if (sieve[i]) {
prime.add(i);
for (int j = i * 2; j <= n; j += i)
sieve[j] = false;
}
}
}
private static boolean isPrime(int n) {
if (n < 2)
return false;
if (n == 2 || n == 3)
return true;
if ((n & 1) == 0 || n % 3 == 0)
return false;
for (int i = 6; i * i <= n; i += 6)
if (n % (i - 1) == 0 || n % (i + 1) == 0)
return false;
return true;
}
private static HashMap<Integer, Integer> primeFactors(int n) {
HashMap<Integer, Integer> factors = new HashMap<>();
int index = 0, pf = prime.get(index);
while (n != 1 && pf * pf <= n) {
int count = 0;
while (n % pf == 0) {
n /= pf;
count++;
}
if (count != 0)
factors.put(pf, count);
pf = prime.get(++index);
}
if (n != 1)
factors.put(n, 1);
return factors;
}
private static int gcd(int a, int b) {
return b == 0 ? a : gcd(b, a % b);
}
private static int lcm(int a, int b) {
return a * (b / gcd(a, b));
}
private static int totient(int n) {
HashMap<Integer, Integer> factors = primeFactors(n);
for (int i : factors.keySet())
n -= n / i;
return n;
}
public static void main(String[] args) {
sieve(1_000_000);
System.out.println(totient(7654321));
}
}