Add Tower of Hanoi recursive algorithm (#7235)

* Add Tower of Hanoi recursive algorithm with tests

* Fix SpotBugs issues and format TowerOfHanoi tests

* Enhance existing TowerOfHanoi and remove duplicate recursion version

* Fix clang-format issue

---------

Co-authored-by: Deniz Altunkapan <deniz.altunkapan@outlook.com>

src/test/java/com/thealgorithms/puzzlesandgames/TowerOfHanoiTest.java

@@ -1,14 +1,31 @@
 package com.thealgorithms.puzzlesandgames;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
 import static org.junit.jupiter.api.Assertions.assertTrue;
 
 import java.util.ArrayList;
 import java.util.List;
+import java.util.stream.Stream;
 import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
 
 public class TowerOfHanoiTest {
 
+    @ParameterizedTest
+    @MethodSource("diskCountAndMoveCount")
+    void testMoveCountMatchesFormula(int disks, int expectedMoves) {
+        List<String> result = new ArrayList<>();
+        TowerOfHanoi.shift(disks, "A", "B", "C", result);
+        assertEquals(expectedMoves, result.size());
+    }
+
+    private static Stream<Arguments> diskCountAndMoveCount() {
+        return Stream.of(Arguments.of(1, 1), Arguments.of(2, 3), Arguments.of(3, 7), Arguments.of(4, 15), Arguments.of(5, 31), Arguments.of(10, 1023));
+    }
+
     @Test
     public void testHanoiWithOneDisc() {
         List<String> result = new ArrayList<>();
@@ -39,6 +56,15 @@ public class TowerOfHanoiTest {
         assertEquals(expected, result);
     }
 
+    @Test
+    public void testHanoiWithDifferentPoles() {
+        List<String> result = new ArrayList<>();
+        TowerOfHanoi.shift(2, "X", "Y", "Z", result);
+
+        List<String> expected = List.of("Move 1 from X to Y", "Move 2 from X to Z", "Move 1 from Y to Z");
+        assertEquals(expected, result);
+    }
+
     @Test
     public void testHanoiWithZeroDiscs() {
         List<String> result = new ArrayList<>();
@@ -47,4 +73,10 @@ public class TowerOfHanoiTest {
         // There should be no moves if there are 0 discs
         assertTrue(result.isEmpty());
     }
+
+    @Test
+    public void testHanoiWithNegativeDiscsThrows() {
+        List<String> result = new ArrayList<>();
+        assertThrows(IllegalArgumentException.class, () -> TowerOfHanoi.shift(-1, "Pole1", "Pole2", "Pole3", result));
+    }
 }