Create rotated_binary_search.py

searches/rotated_binary_search.py

@@ -0,0 +1,34 @@
+def rotated_binary_search(arr: list[int], key: int) -> int:
+    """
+    Performs binary search on a rotated sorted list.
+
+    Parameters:
+    arr (list[int]): A rotated sorted list of integers.
+    key (int): The element to search for.
+
+    Returns:
+    int: The index of the key in the list, or -1 if the key is not found.
+    """
+    low = 0
+    high = len(arr) - 1
+
+    while low <= high:
+        mid = (low + high) // 2
+
+        # Check if the mid element is the key
+        if arr[mid] == key:
+            return mid
+
+        # Check which side is sorted
+        if arr[low] <= arr[mid]:  # Left side is sorted
+            if arr[low] <= key < arr[mid]:  # Key is in the sorted left side
+                high = mid - 1
+            else:  # Key is in the right side
+                low = mid + 1
+        else:  # Right side is sorted
+            if arr[mid] < key <= arr[high]:  # Key is in the sorted right side
+                low = mid + 1
+            else:  # Key is in the left side
+                high = mid - 1
+
+    return -1  # Key not found