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, size: int) -> None:  # Create Fenwick tree with specified size
+        self.size = size
+        self.arr = [0] * (size + 1)
+        self.tree = [0] * (size + 1)
+
+    def update(
+        self, index: int, value: int
+    ) -> None:  # Set index (1-Based) to value in O(lg^2 N)
+        self.arr[index] = value
+        while index < self.size:
+            self.tree[index] = max(value, self.query(index, index - index & -index))
+            index += index & (-index)
+
+    def query(
+        self, left: int, right: int
+    ) -> int:  # Query maximum value from range (left, right] (1-Based) in O(lg N)
+        res = 0
+        while left < right:
+            x = right - right & -right
+            if left < x:
+                res = max(res, self.tree[right])
+                right = x
+            else:
+                res = max(res, self.arr[right])
+                right -= 1
+        return res
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()