Implement Parentheses Generator (#5096)

* chore: add `ParenthesesGenerator` to `DIRECTORY.md`

* feat: implement Parentheses Generator

* ref: change `ParenthesesGenerator`s method to `static`

* ref: use parametrized tests

* ref: handling exception when `n < 0`

* chore: update docstrings

* ref: make `ParenthesesGenerator` to be a proper utility

* chore(docs): add private constructor docstring

* ref(tests): move bad name suggestions

* style: remove reduntant comments

---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

src/test/java/com/thealgorithms/backtracking/ParenthesesGeneratorTest.java

@@ -0,0 +1,33 @@
+package com.thealgorithms.backtracking;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.List;
+import java.util.stream.Stream;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+public class ParenthesesGeneratorTest {
+    @ParameterizedTest
+    @MethodSource("regularInputStream")
+    void regularInputTests(int input, List<String> expected) {
+        assertEquals(expected, ParenthesesGenerator.generateParentheses(input));
+    }
+
+    @ParameterizedTest
+    @MethodSource("negativeInputStream")
+    void throwsForNegativeInputTests(int input) {
+        assertThrows(IllegalArgumentException.class, () -> ParenthesesGenerator.generateParentheses(input));
+    }
+
+    private static Stream<Arguments> regularInputStream() {
+        return Stream.of(Arguments.of(0, List.of("")), Arguments.of(1, List.of("()")), Arguments.of(2, List.of("(())", "()()")), Arguments.of(3, List.of("((()))", "(()())", "(())()", "()(())", "()()()")),
+            Arguments.of(4, List.of("(((())))", "((()()))", "((())())", "((()))()", "(()(()))", "(()()())", "(()())()", "(())(())", "(())()()", "()((()))", "()(()())", "()(())()", "()()(())", "()()()()")));
+    }
+
+    private static Stream<Arguments> negativeInputStream() {
+        return Stream.of(Arguments.of(-1), Arguments.of(-5), Arguments.of(-10));
+    }
+}