fix: avoid out-of-bounds access in HowManyTimesRotated on small/unrotated arrays (#7626)

The old mid-1/mid+1 comparison indexed out of bounds for a 1-2 element
array and never terminated correctly for an unrotated array. Replaced
with a standard binary search for the rotation pivot.

Author: Saadanjum0

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

@@ -16,14 +16,15 @@
     The position of the minimum element will give the number of times the array has been rotated
     from its initial sorted position.
     Eg. For [2,5,6,8,11,12,15,18], 1 rotation gives [5,6,8,11,12,15,18,2], 2 rotations
-   [6,8,11,12,15,18,2,5] and so on. Finding the minimum element will take O(N) time but, we can  use
-   Binary Search to find the minimum element, we can reduce the complexity to O(log N). If we look
-   at the rotated array, to identify the minimum element (say a[i]), we observe that
-   a[i-1]>a[i]<a[i+1].
+   [6,8,11,12,15,18,2,5] and so on. Finding the minimum element will take O(N) time but, we can use
+   Binary Search to reduce the complexity to O(log N): at each step compare a[mid] with a[high].
+   If a[mid] > a[high], the minimum lies to the right, so low = mid + 1; otherwise it lies at mid
+   or to the left, so high = mid. This converges to the minimum's index without ever reading
+   a[mid-1] or a[mid+1], so it also works on arrays of size 0-2 and unrotated arrays.
 
     Some other test cases:
     1. [1,2,3,4] Number of rotations: 0 or 4(Both valid)
-    2. [15,17,2,3,5] Number of rotations: 3
+    2. [15,17,2,3,5] Number of rotations: 2
  */
 final class HowManyTimesRotated {
     private HowManyTimesRotated() {
@@ -44,20 +45,16 @@ public static void main(String[] args) {
     public static int rotated(int[] a) {
         int low = 0;
         int high = a.length - 1;
-        int mid = 0; // low + (high-low)/2 = (low + high)/2
 
-        while (low <= high) {
-            mid = low + (high - low) / 2;
-
-            if (a[mid] < a[mid - 1] && a[mid] < a[mid + 1]) {
-                break;
-            } else if (a[mid] > a[mid - 1] && a[mid] < a[mid + 1]) {
-                high = mid + 1;
-            } else if (a[mid] > a[mid - 1] && a[mid] > a[mid + 1]) {
-                low = mid - 1;
+        while (low < high) {
+            int mid = low + (high - low) / 2;
+            if (a[mid] > a[high]) {
+                low = mid + 1;
+            } else {
+                high = mid;
             }
         }
 
-        return mid;
+        return low;
     }
 }

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

@@ -2,7 +2,9 @@
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
 
+import java.util.concurrent.TimeUnit;
 import org.junit.jupiter.api.Test;
+import org.junit.jupiter.api.Timeout;
 
 public class HowManyTimesRotatedTest {
 
@@ -13,4 +15,20 @@ public void testHowManyTimesRotated() {
         int[] arr2 = {15, 17, 2, 3, 5};
         assertEquals(2, HowManyTimesRotated.rotated(arr2));
     }
+
+    /** An unrotated (already sorted) array should resolve to 0 rotations without hanging. */
+    @Test
+    @Timeout(value = 5, unit = TimeUnit.SECONDS, threadMode = Timeout.ThreadMode.SEPARATE_THREAD)
+    public void testHowManyTimesRotatedOnUnrotatedArray() {
+        int[] arr = {2, 5, 6, 8, 11, 12, 15, 18};
+        assertEquals(0, HowManyTimesRotated.rotated(arr));
+    }
+
+    /** Arrays of size 1 and 2 should not throw ArrayIndexOutOfBoundsException. */
+    @Test
+    public void testHowManyTimesRotatedOnSmallArrays() {
+        assertEquals(0, HowManyTimesRotated.rotated(new int[] {5}));
+        assertEquals(0, HowManyTimesRotated.rotated(new int[] {1, 2}));
+        assertEquals(1, HowManyTimesRotated.rotated(new int[] {2, 1}));
+    }
 }