Add fast exponentiation algorithm (#5715)

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

@@ -0,0 +1,67 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the {@link FastExponentiation} class.
+ *
+ * <p>This class contains various test cases to verify the correctness of the fastExponentiation method.
+ * It covers basic functionality, edge cases, and exceptional cases.
+ */
+class FastExponentiationTest {
+
+    /**
+     * Tests fast exponentiation with small numbers.
+     */
+    @Test
+    void testSmallNumbers() {
+        assertEquals(1024, FastExponentiation.fastExponentiation(2, 10, 10000), "2^10 mod 10000 should be 1024");
+        assertEquals(81, FastExponentiation.fastExponentiation(3, 4, 1000), "3^4 mod 1000 should be 81");
+    }
+
+    /**
+     * Tests the behavior of the fast exponentiation method when using a modulus.
+     */
+    @Test
+    void testWithModulo() {
+        assertEquals(24, FastExponentiation.fastExponentiation(2, 10, 1000), "2^10 mod 1000 should be 24");
+        assertEquals(0, FastExponentiation.fastExponentiation(10, 5, 10), "10^5 mod 10 should be 0");
+    }
+
+    /**
+     * Tests the edge cases where base or exponent is 0.
+     */
+    @Test
+    void testBaseCases() {
+        assertEquals(1, FastExponentiation.fastExponentiation(2, 0, 1000), "Any number raised to the power 0 mod anything should be 1");
+        assertEquals(0, FastExponentiation.fastExponentiation(0, 10, 1000), "0 raised to any power should be 0");
+        assertEquals(1, FastExponentiation.fastExponentiation(0, 0, 1000), "0^0 is considered 0 in modular arithmetic.");
+    }
+
+    /**
+     * Tests fast exponentiation with a negative base to ensure correctness under modular arithmetic.
+     */
+    @Test
+    void testNegativeBase() {
+        assertEquals(9765625, FastExponentiation.fastExponentiation(-5, 10, 1000000007), "-5^10 mod 1000000007 should be 9765625");
+    }
+
+    /**
+     * Tests that a negative exponent throws an ArithmeticException.
+     */
+    @Test
+    void testNegativeExponent() {
+        assertThrows(ArithmeticException.class, () -> { FastExponentiation.fastExponentiation(2, -5, 1000); });
+    }
+
+    /**
+     * Tests that the method throws an IllegalArgumentException for invalid modulus values.
+     */
+    @Test
+    void testInvalidModulus() {
+        assertThrows(IllegalArgumentException.class, () -> { FastExponentiation.fastExponentiation(2, 5, 0); });
+    }
+}