From eb9e2b73c6bd31ce4cc9f6233b23c3cddd16bf18 Mon Sep 17 00:00:00 2001
From: Putul Singh <127419636+putul03@users.noreply.github.com>
Date: Sat, 19 Oct 2024 16:27:52 +0530
Subject: [PATCH] Update persistent_segment_tree.py

---
 data_structures/persistent_segment_tree.py | 24 ++++++++++------------
 1 file changed, 11 insertions(+), 13 deletions(-)

diff --git a/data_structures/persistent_segment_tree.py b/data_structures/persistent_segment_tree.py
index 884075437..e3a842791 100644
--- a/data_structures/persistent_segment_tree.py
+++ b/data_structures/persistent_segment_tree.py
@@ -1,17 +1,18 @@
+from typing import List, Optional
+
 class Node:
     def __init__(self, value: int = 0) -> None:
-        self.value = value
-        self.left = None
-        self.right = None
-
+        self.value: int = value
+        self.left: Optional[Node] = None
+        self.right: Optional[Node] = None
 
 class PersistentSegmentTree:
-    def __init__(self, arr: list[int]) -> None:
-        self.n = len(arr)
-        self.roots: list[Node] = []
+    def __init__(self, arr: List[int]) -> None:
+        self.n: int = len(arr)
+        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.
 
@@ -119,15 +120,12 @@ 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.")