Split exponential search recursion into a flat int-only core (#15389)

Follow-up to #15384. Replace the ``right: int | None`` sentinel on the
recursive path with a thin wrapper that defaults ``right`` once, then
delegates to a nested ``_search(left, right)`` core whose indices are
always concrete ints. This matches the wrapper/core shape already used by
``binary_search.py`` and keeps the recursion flat so the window can only
shrink.

Author: priya-sundaram-dev

searches/exponential_search.py

@@ -47,21 +47,29 @@ def binary_search_by_recursion(
     >>> binary_search_by_recursion([0, 5, 7, 10, 15], 16)
     -1
     """
-    if right is None:
-        right = len(sorted_collection) - 1
     if list(sorted_collection) != sorted(sorted_collection):
         raise ValueError("sorted_collection must be sorted in ascending order")
-    if right < left:
-        return -1
+    if right is None:
+        right = len(sorted_collection) - 1
 
-    midpoint = left + (right - left) // 2
+    # Recursive core: ``left`` and ``right`` are always concrete indices here, so the
+    # window can only shrink. Keeping the recursion flat (no ``None`` sentinel, no
+    # re-expansion) is what prevents the runaway recursion when the item sits below
+    # ``sorted_collection[0]`` and ``right`` legitimately drops below ``left``.
+    def _search(left: int, right: int) -> int:
+        if right < left:
+            return -1
 
-    if sorted_collection[midpoint] == item:
-        return midpoint
-    elif sorted_collection[midpoint] > item:
-        return binary_search_by_recursion(sorted_collection, item, left, midpoint - 1)
-    else:
-        return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
+        midpoint = left + (right - left) // 2
+
+        if sorted_collection[midpoint] == item:
+            return midpoint
+        elif sorted_collection[midpoint] > item:
+            return _search(left, midpoint - 1)
+        else:
+            return _search(midpoint + 1, right)
+
+    return _search(left, right)
 
 
 def exponential_search(sorted_collection: list[int], item: int) -> int: