diff --git a/data_structures/persistent_segment_tree.py b/data_structures/persistent_segment_tree.py
index f7d0bdbbc..4b1670819 100644
--- a/data_structures/persistent_segment_tree.py
+++ b/data_structures/persistent_segment_tree.py
@@ -1,20 +1,18 @@
-from typing import List, Optional
-
+from __future__ import annotations
 
 class Node:
     def __init__(self, value: int = 0) -> None:
         self.value: int = value
-        self.left: Optional[Node] = None
-        self.right: Optional[Node] = None
-
+        self.left: Node | None = None
+        self.right: Node | None = None
 
 class PersistentSegmentTree:
-    def __init__(self, arr: List[int]) -> None:
+    def __init__(self, arr: list[int]) -> None:
         self.n: int = len(arr)
-        self.roots: List[Node] = []
+        self.roots: list[Node] = []
         self.roots.append(self._build(arr, 0, self.n - 1))
 
-    def _build(self, arr: List[int], start: int, end: int) -> Node:
+    def _build(self, arr: list[int], start: int, end: int) -> Node:
         """
         Builds a segment tree from the provided array.
 
@@ -83,7 +81,8 @@ class PersistentSegmentTree:
             new_node.left = node.left
             new_node.right = self._update(node.right, mid + 1, end, index, value)
 
-        new_node.value = new_node.left.value + new_node.right.value
+        new_node.value = (new_node.left.value if new_node.left else 0) + \
+                         (new_node.right.value if new_node.right else 0)
 
         return new_node
 
@@ -122,15 +121,12 @@ class PersistentSegmentTree:
         if left <= start and right >= end:
             return node.value
         mid = (start + end) // 2
-        return self._query(node.left, start, mid, left, right) + self._query(
-            node.right, mid + 1, end, left, right
-        )
-
+        return (self._query(node.left, start, mid, left, right) +
+                self._query(node.right, mid + 1, end, left, right))
 
 # Running the doctests
 if __name__ == "__main__":
     import doctest
-
     print("Running doctests...")
     result = doctest.testmod()
     print(f"Ran {result.attempted} tests, {result.failed} failed.")