diff --git a/data_structures/persistent_segment_tree.py b/data_structures/persistent_segment_tree.py
index 05194fa20..1cd526a29 100644
--- a/data_structures/persistent_segment_tree.py
+++ b/data_structures/persistent_segment_tree.py
@@ -1,13 +1,11 @@
 from __future__ import annotations
 
-
 class Node:
     def __init__(self, value: int = 0) -> None:
         self.value: int = value
         self.left: Node | None = None
         self.right: Node | None = None
 
-
 class PersistentSegmentTree:
     def __init__(self, arr: list[int]) -> None:
         self.n: int = len(arr)
@@ -17,15 +15,6 @@ class PersistentSegmentTree:
     def _build(self, arr: list[int], start: int, end: int) -> Node:
         """
         Builds a segment tree from the provided array.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3, 4])
-        >>> root = pst._build([1, 2, 3, 4], 0, 3)
-        >>> root.value  # Sum of the whole array
-        10
-        >>> root.left.value  # Sum of the left half
-        3
-        >>> root.right.value  # Sum of the right half
-        7
         """
         if start == end:
             return Node(arr[start])
@@ -39,37 +28,18 @@ class PersistentSegmentTree:
     def update(self, version: int, index: int, value: int) -> int:
         """
         Updates the value at the given index and returns the new version.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3, 4])
-        >>> version_1 = pst.update(0, 1, 5)  # Update index 1 to 5
-        >>> pst.query(version_1, 0, 3)  # Query sum of all elements in new version
-        13
-        >>> pst.query(0, 0, 3)  # Original version remains unchanged
-        10
-        >>> version_2 = pst.update(version_1, 3, 6)  # Update index 3 to 6 in version_1
-        >>> pst.query(version_2, 0, 3)  # Query sum of all elements in newest version
-        15
         """
         new_root = self._update(self.roots[version], 0, self.n - 1, index, value)
         self.roots.append(new_root)
         return len(self.roots) - 1
 
-    def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node:
+    def _update(self, node: Node | None, start: int, end: int, index: int, value: int) -> Node:
         """
         Updates the node for the specified index and value and returns the new node.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3, 4])
-        >>> old_root = pst.roots[0]
-        >>> new_root = pst._update(old_root, 0, 3, 1, 5)  # Update index 1 to 5
-        >>> new_root.value  # New sum after update
-        13
-        >>> old_root.value  # Old root remains unchanged
-        10
-        >>> new_root.left.value  # Updated left child
-        6
-        >>> new_root.right.value  # Right child remains the same
-        7
         """
+        if node is None:  # Handle the None case
+            node = Node()  # Create a new node if None
+
         if start == end:
             return Node(value)
 
@@ -83,56 +53,31 @@ class PersistentSegmentTree:
             new_node.left = node.left  # Ensure left node is the same as the original
             new_node.right = self._update(node.right, mid + 1, end, index, value)
 
-        new_node.value = new_node.left.value + (
-            new_node.right.value if new_node.right else 0
-        )
+        new_node.value = new_node.left.value + (new_node.right.value if new_node.right else 0)
 
         return new_node
 
     def query(self, version: int, left: int, right: int) -> int:
         """
         Queries the sum in the given range for the specified version.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3, 4])
-        >>> pst.query(0, 0, 3)  # Sum of all elements in original version
-        10
-        >>> pst.query(0, 1, 2)  # Sum of elements at index 1 and 2 in original version
-        5
-        >>> version_1 = pst.update(0, 1, 5)  # Update index 1 to 5
-        >>> pst.query(version_1, 0, 3)  # Sum of all elements in new version
-        13
-        >>> pst.query(version_1, 1, 2)  # Sum of elements at index 1 and 2
-        8
         """
         return self._query(self.roots[version], 0, self.n - 1, left, right)
 
-    def _query(self, node: Node, start: int, end: int, left: int, right: int) -> int:
+    def _query(self, node: Node | None, start: int, end: int, left: int, right: int) -> int:
         """
         Queries the sum of values in the range [left, right] for the given node.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3, 4])
-        >>> root = pst.roots[0]
-        >>> pst._query(root, 0, 3, 1, 2)  # Sum of elements at index 1 and 2
-        5
-        >>> pst._query(root, 0, 3, 0, 3)  # Sum of all elements
-        10
-        >>> pst._query(root, 0, 3, 2, 3)  # Sum of elements at index 2 and 3
-        7
         """
         if node is None or left > end or right < start:
             return 0
         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.")