Add RotatedBinarySearch (search in rotated sorted array) (#7202)

* feat: implement Smooth Sort algorithm with detailed JavaDoc and test class

* style: format LEONARDO array for improved readability with clang-format

* feat(sorts): add TournamentSort (winner-tree)

* test: add unit test for null array handling in TournamentSort

* feat(search): add rotated binary search

* test: add unit test for handling middle element in right sorted half of rotated array

---------

Co-authored-by: Ahmed Allam <60698204+AllamF5J@users.noreply.github.com>

src/main/java/com/thealgorithms/searches/RotatedBinarySearch.java

@@ -0,0 +1,60 @@
+package com.thealgorithms.searches;
+
+import com.thealgorithms.devutils.searches.SearchAlgorithm;
+
+/**
+ * Searches for a key in a sorted array that has been rotated at an unknown pivot.
+ *
+ * <p>
+ * Example:
+ * {@code [8, 9, 10, 1, 2, 3, 4, 5, 6, 7]}
+ *
+ * <p>
+ * This is a modified binary search. When the array contains no duplicates, the
+ * time complexity is {@code O(log n)}. With duplicates, the algorithm still
+ * works but may degrade to {@code O(n)} in the worst case.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Search_in_rotated_sorted_array">Search in rotated sorted array</a>
+ * @see SearchAlgorithm
+ */
+public final class RotatedBinarySearch implements SearchAlgorithm {
+
+    @Override
+    public <T extends Comparable<T>> int find(T[] array, T key) {
+        int left = 0;
+        int right = array.length - 1;
+
+        while (left <= right) {
+            int middle = (left + right) >>> 1;
+            int cmp = key.compareTo(array[middle]);
+            if (cmp == 0) {
+                return middle;
+            }
+
+            // Handle duplicates: if we cannot determine which side is sorted.
+            if (array[left].compareTo(array[middle]) == 0 && array[middle].compareTo(array[right]) == 0) {
+                left++;
+                right--;
+                continue;
+            }
+
+            // Left half is sorted.
+            if (array[left].compareTo(array[middle]) <= 0) {
+                if (array[left].compareTo(key) <= 0 && key.compareTo(array[middle]) < 0) {
+                    right = middle - 1;
+                } else {
+                    left = middle + 1;
+                }
+            } else {
+                // Right half is sorted.
+                if (array[middle].compareTo(key) < 0 && key.compareTo(array[right]) <= 0) {
+                    left = middle + 1;
+                } else {
+                    right = middle - 1;
+                }
+            }
+        }
+
+        return -1;
+    }
+}

src/test/java/com/thealgorithms/searches/RotatedBinarySearchTest.java

@@ -0,0 +1,53 @@
+package com.thealgorithms.searches;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+class RotatedBinarySearchTest {
+
+    @Test
+    void shouldFindElementInRotatedArrayLeftSide() {
+        RotatedBinarySearch search = new RotatedBinarySearch();
+        Integer[] array = {8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7};
+        assertEquals(2, search.find(array, 10));
+    }
+
+    @Test
+    void shouldFindElementInRotatedArrayRightSide() {
+        RotatedBinarySearch search = new RotatedBinarySearch();
+        Integer[] array = {8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7};
+        assertEquals(6, search.find(array, 2));
+    }
+
+    @Test
+    void shouldFindElementInNotRotatedArray() {
+        RotatedBinarySearch search = new RotatedBinarySearch();
+        Integer[] array = {1, 2, 3, 4, 5, 6, 7};
+        assertEquals(4, search.find(array, 5));
+    }
+
+    @Test
+    void shouldReturnMinusOneWhenNotFound() {
+        RotatedBinarySearch search = new RotatedBinarySearch();
+        Integer[] array = {4, 5, 6, 7, 0, 1, 2};
+        assertEquals(-1, search.find(array, 3));
+    }
+
+    @Test
+    void shouldHandleWhenMiddleIsGreaterThanKeyInRightSortedHalf() {
+        RotatedBinarySearch search = new RotatedBinarySearch();
+        Integer[] array = {6, 7, 0, 1, 2, 3, 4, 5};
+        assertEquals(2, search.find(array, 0));
+    }
+
+    @Test
+    void shouldHandleDuplicates() {
+        RotatedBinarySearch search = new RotatedBinarySearch();
+        Integer[] array = {2, 2, 2, 3, 4, 2};
+        int index = search.find(array, 3);
+        assertTrue(index >= 0 && index < array.length);
+        assertEquals(3, array[index]);
+    }
+}