Add Max Fenwick Tree

data_structures/binary_tree/maximum_fenwick_tree.py

@@ -0,0 +1,50 @@
+class MaxFenwickTree:
+    """
+    Maximum Fenwick Tree
+    ---------
+    >>> ft = MaxFenwickTree(5)
+    >>> ft.query(0, 5)
+    0
+    >>> ft.update(2, 20)
+    >>> ft.query(0, 5)
+    20
+    >>> ft.update(5, 10)
+    >>> ft.query(2, 5)
+    10
+    >>> ft.update(2, 0)
+    >>> ft.query(0, 5)
+    10
+    """
+
+    def __init__(self, n: int):  # Create Fenwick tree with size n
+        self.n = n
+        self.arr = [0] * (n + 1)
+        self.tree = [0] * (n + 1)
+
+    def update(
+        self, i, val
+    ) -> None:  # Set value of index i (1-Based) to val in O(lg^2 N)
+        self.arr[i] = val
+        while i < self.n:
+            self.tree[i] = max(val, self.query(i, i - i & -i))
+            i += i & (-i)
+
+    def query(
+        self, l, r
+    ) -> int:  # Query maximum value from range (l, r] (1-Based) in O(lg N)
+        res = 0
+        while l < r:
+            ll = r - r & -r
+            if l < ll:
+                res = max(res, self.tree[r])
+                r = ll
+            else:
+                res = max(res, self.arr[r])
+                r -= 1
+        return res
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()