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 <[email protected]>

Author: sozelfist

DIRECTORY.md

@@ -15,6 +15,7 @@
             * [MazeRecursion](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/MazeRecursion.java)
             * [MColoring](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/MColoring.java)
             * [NQueens](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/NQueens.java)
+            * [ParenthesesGenerator](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/ParenthesesGenerator.java)
             * [Permutation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/Permutation.java)
             * [PowerSum](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/PowerSum.java)
             * [WordSearch](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/backtracking/WordSearch.java)

src/main/java/com/thealgorithms/backtracking/ParenthesesGenerator.java

@@ -0,0 +1,50 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * This class generates all valid combinations of parentheses for a given number of pairs using backtracking.
+ */
+public final class ParenthesesGenerator {
+    private ParenthesesGenerator() {
+    }
+
+    /**
+     * Generates all valid combinations of parentheses for a given number of pairs.
+     *
+     * @param n The number of pairs of parentheses.
+     * @return A list of strings representing valid combinations of parentheses.
+     * @throws IllegalArgumentException if n is less than 0.
+     */
+    public static List<String> generateParentheses(final int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("The number of pairs of parentheses cannot be nagative");
+        }
+        List<String> result = new ArrayList<>();
+        generateParenthesesHelper(result, "", 0, 0, n);
+        return result;
+    }
+
+    /**
+     * Helper function for generating all valid combinations of parentheses recursively.
+     *
+     * @param result  The list to store valid combinations.
+     * @param current The current combination being formed.
+     * @param open    The number of open parentheses.
+     * @param close   The number of closed parentheses.
+     * @param n       The total number of pairs of parentheses.
+     */
+    private static void generateParenthesesHelper(List<String> result, final String current, final int open, final int close, final int n) {
+        if (current.length() == n * 2) {
+            result.add(current);
+            return;
+        }
+        if (open < n) {
+            generateParenthesesHelper(result, current + "(", open + 1, close, n);
+        }
+        if (close < open) {
+            generateParenthesesHelper(result, current + ")", open, close + 1, n);
+        }
+    }
+}

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));
+    }
+}