feat: add solovay strassen primality test (#5692)

* feat: add solovay strassen primality test

* chore: add wikipedia link

* fix: format and coverage

* fix: mvn stylecheck

* fix: PMD errors

* refactor: make random final

---------

Co-authored-by: Alex Klymenko <alexanderklmn@gmail.com>

src/test/java/com/thealgorithms/maths/SolovayStrassenPrimalityTestTest.java

@@ -0,0 +1,122 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.BeforeEach;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.MethodSource;
+
+/**
+ * Unit tests for the {@link SolovayStrassenPrimalityTest} class.
+ * This class tests the functionality of the Solovay-Strassen primality test implementation.
+ */
+class SolovayStrassenPrimalityTestTest {
+
+    private static final int RANDOM_SEED = 123; // Seed for reproducibility
+    private SolovayStrassenPrimalityTest testInstance;
+
+    /**
+     * Sets up a new instance of {@link SolovayStrassenPrimalityTest}
+     * before each test case, using a fixed random seed for consistency.
+     */
+    @BeforeEach
+    void setUp() {
+        testInstance = SolovayStrassenPrimalityTest.getSolovayStrassenPrimalityTest(RANDOM_SEED);
+    }
+
+    /**
+     * Provides test cases for prime numbers with various values of n and k (iterations).
+     *
+     * @return an array of objects containing pairs of n and k values
+     */
+    static Object[][] primeNumbers() {
+        return new Object[][] {{2, 1}, {3, 1}, {5, 5}, {7, 10}, {11, 20}, {13, 10}, {17, 5}, {19, 1}};
+    }
+
+    /**
+     * Tests known prime numbers with various values of n and k (iterations).
+     *
+     * @param n the number to be tested for primality
+     * @param k the number of iterations to use in the primality test
+     */
+    @ParameterizedTest
+    @MethodSource("primeNumbers")
+    void testPrimeNumbersWithDifferentNAndK(int n, int k) {
+        assertTrue(testInstance.solovayStrassen(n, k), n + " should be prime");
+    }
+
+    /**
+     * Provides test cases for composite numbers with various values of n and k (iterations).
+     *
+     * @return an array of objects containing pairs of n and k values
+     */
+    static Object[][] compositeNumbers() {
+        return new Object[][] {{4, 1}, {6, 5}, {8, 10}, {9, 20}, {10, 1}, {12, 5}, {15, 10}};
+    }
+
+    /**
+     * Tests known composite numbers with various values of n and k (iterations).
+     *
+     * @param n the number to be tested for primality
+     * @param k the number of iterations to use in the primality test
+     */
+    @ParameterizedTest
+    @MethodSource("compositeNumbers")
+    void testCompositeNumbersWithDifferentNAndK(int n, int k) {
+        assertFalse(testInstance.solovayStrassen(n, k), n + " should be composite");
+    }
+
+    /**
+     * Tests edge cases for the primality test.
+     * This includes negative numbers and small integers (0 and 1).
+     */
+    @Test
+    void testEdgeCases() {
+        assertFalse(testInstance.solovayStrassen(-1, 10), "-1 should not be prime");
+        assertFalse(testInstance.solovayStrassen(0, 10), "0 should not be prime");
+        assertFalse(testInstance.solovayStrassen(1, 10), "1 should not be prime");
+
+        // Test small primes and composites
+        assertTrue(testInstance.solovayStrassen(2, 1), "2 is a prime number (single iteration)");
+        assertFalse(testInstance.solovayStrassen(9, 1), "9 is a composite number (single iteration)");
+
+        // Test larger primes and composites
+        long largePrime = 104729; // Known large prime number
+        long largeComposite = 104730; // Composite number (even)
+
+        assertTrue(testInstance.solovayStrassen(largePrime, 20), "104729 is a prime number");
+        assertFalse(testInstance.solovayStrassen(largeComposite, 20), "104730 is a composite number");
+
+        // Test very large numbers (may take longer)
+        long veryLargePrime = 512927357; // Known very large prime number
+        long veryLargeComposite = 512927358; // Composite number (even)
+
+        assertTrue(testInstance.solovayStrassen(veryLargePrime, 20), Long.MAX_VALUE - 1 + " is likely a prime number.");
+
+        assertFalse(testInstance.solovayStrassen(veryLargeComposite, 20), Long.MAX_VALUE + " is a composite number.");
+    }
+
+    /**
+     * Tests the Jacobi symbol calculation directly for known values.
+     * This verifies that the Jacobi symbol method behaves as expected.
+     */
+    @Test
+    void testJacobiSymbolCalculation() {
+        // Jacobi symbol (a/n) where n is odd and positive
+        int jacobi1 = testInstance.calculateJacobi(6, 11); // Should return -1
+        int jacobi2 = testInstance.calculateJacobi(5, 11); // Should return +1
+
+        assertEquals(-1, jacobi1);
+        assertEquals(+1, jacobi2);
+
+        // Edge case: Jacobi symbol with even n or non-positive n
+        int jacobi4 = testInstance.calculateJacobi(5, -11); // Should return 0 (invalid)
+        int jacobi5 = testInstance.calculateJacobi(5, 0); // Should return 0 (invalid)
+
+        assertEquals(0, jacobi4);
+        assertEquals(0, jacobi5);
+    }
+}