refactor: change packages (#5430)

* refactor: change package

* refactor: fix name

---------

Co-authored-by: alxkm <alx@alx.com>

src/main/java/com/thealgorithms/maths/EulersFunction.java

@@ -0,0 +1,47 @@
+package com.thealgorithms.maths;
+
+/**
+ * Utility class for computing
+ * <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>.
+ */
+public final class EulersFunction {
+    private EulersFunction() {
+    }
+
+    /**
+     * Validates that the input is a positive integer.
+     *
+     * @param n the input number to validate
+     * @throws IllegalArgumentException if {@code n} is non-positive
+     */
+    private static void checkInput(int n) {
+        if (n <= 0) {
+            throw new IllegalArgumentException("n must be positive.");
+        }
+    }
+
+    /**
+     * Computes the value of Euler's totient function for a given input.
+     * This function has a time complexity of O(sqrt(n)).
+     *
+     * @param n the input number
+     * @return the value of Euler's totient function for the given input
+     * @throws IllegalArgumentException if {@code n} is non-positive
+     */
+    public static int getEuler(int n) {
+        checkInput(n);
+        int result = n;
+        for (int i = 2; i * i <= n; i++) {
+            if (n % i == 0) {
+                while (n % i == 0) {
+                    n /= i;
+                }
+                result -= result / i;
+            }
+        }
+        if (n > 1) {
+            result -= result / n;
+        }
+        return result;
+    }
+}

src/main/java/com/thealgorithms/maths/SieveOfEratosthenes.java

@@ -0,0 +1,66 @@
+package com.thealgorithms.maths;
+
+import java.util.Arrays;
+
+/**
+ * @brief utility class implementing <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes">Sieve of Eratosthenes</a>
+ */
+public final class SieveOfEratosthenes {
+    private SieveOfEratosthenes() {
+    }
+
+    private static void checkInput(int n) {
+        if (n <= 0) {
+            throw new IllegalArgumentException("n must be positive.");
+        }
+    }
+
+    private static Type[] sievePrimesTill(int n) {
+        checkInput(n);
+        Type[] isPrimeArray = new Type[n + 1];
+        Arrays.fill(isPrimeArray, Type.PRIME);
+        isPrimeArray[0] = Type.NOT_PRIME;
+        isPrimeArray[1] = Type.NOT_PRIME;
+
+        double cap = Math.sqrt(n);
+        for (int i = 2; i <= cap; i++) {
+            if (isPrimeArray[i] == Type.PRIME) {
+                for (int j = 2; i * j <= n; j++) {
+                    isPrimeArray[i * j] = Type.NOT_PRIME;
+                }
+            }
+        }
+        return isPrimeArray;
+    }
+
+    private static int countPrimes(Type[] isPrimeArray) {
+        return (int) Arrays.stream(isPrimeArray).filter(element -> element == Type.PRIME).count();
+    }
+
+    private static int[] extractPrimes(Type[] isPrimeArray) {
+        int numberOfPrimes = countPrimes(isPrimeArray);
+        int[] primes = new int[numberOfPrimes];
+        int primeIndex = 0;
+        for (int curNumber = 0; curNumber < isPrimeArray.length; ++curNumber) {
+            if (isPrimeArray[curNumber] == Type.PRIME) {
+                primes[primeIndex++] = curNumber;
+            }
+        }
+        return primes;
+    }
+
+    /**
+     * @brief finds all of the prime numbers up to the given upper (inclusive) limit
+     * @param n upper (inclusive) limit
+     * @exception IllegalArgumentException n is non-positive
+     * @return the array of all primes up to the given number (inclusive)
+     */
+    public static int[] findPrimesTill(int n) {
+        return extractPrimes(sievePrimesTill(n));
+    }
+
+    private enum Type {
+        PRIME,
+        NOT_PRIME,
+    }
+}