Add Fenwick regression doctests and 2000-item benchmark

Preserve all existing doctests while covering lost range maxima and decreases. Add an optional timeit benchmark for update and query workloads, as requested in #15485.

Author: dhairyajangir

data_structures/binary_tree/maximum_fenwick_tree.py

@@ -34,6 +34,26 @@ class MaxFenwickTree:
     >>> ft.update(0, 1000)
     >>> ft.query(0, 1)
     1000
+
+    Updating a smaller sibling preserves the maximum, including after decreases.
+    >>> ft = MaxFenwickTree(8)
+    >>> ft.update(4, 20)
+    >>> ft.update(5, 1)
+    >>> ft.query(0, 6)
+    20
+    >>> ft.update(4, 0)
+    >>> ft.query(0, 6)
+    1
+    >>> ft.update(5, 0)
+    >>> ft.query(0, 6)
+    0
+
+    Updating a child must also preserve the ancestor's own array value.
+    >>> ft = MaxFenwickTree(8)
+    >>> ft.update(5, 100)
+    >>> ft.update(4, 0)
+    >>> ft.query(0, 6)
+    100
     """
 
     def __init__(self, size: int) -> None:
@@ -112,5 +132,41 @@ def query(self, left: int, right: int) -> int:
 
 if __name__ == "__main__":
     import doctest
+    import sys
+    from timeit import repeat
 
     doctest.testmod()
+
+    # Run with --benchmark on each revision to compare the same 2,000-item workload.
+    if "--benchmark" in sys.argv:
+        size = 2000
+        values = [(index * 97) % size for index in range(size)]
+        updates = [(index, (index * 37) % size) for index in range(size)]
+        updates += [(index, values[index]) for index in reversed(range(size))]
+        queries = [(left, size) for left in range(size)]
+
+        # Build correct query buckets outside the timer, even on the buggy revision.
+        query_setup = """
+tree = MaxFenwickTree(size)
+tree.arr = values[:]
+tree.tree = [
+    max(values[tree.get_prev(index) + 1 : index + 1])
+    for index in range(size)
+]
+"""
+        for operation, statement, setup in (
+            (
+                "4000 updates",
+                "for index, value in updates: tree.update(index, value)",
+                "tree = MaxFenwickTree(size)",
+            ),
+            (
+                "2000 queries",
+                "for left, right in queries: tree.query(left, right)",
+                query_setup,
+            ),
+        ):
+            timings = repeat(
+                statement, setup=setup, repeat=5, number=1, globals=globals()
+            )
+            print(f"{size} items, {operation}: {min(timings):.6f} seconds (best of 5)")