Update persistent_segment_tree.py

data_structures/persistent_segment_tree.py

@@ -7,19 +7,18 @@ class Node:
 
 class PersistentSegmentTree:
     def __init__(self, arr: list[int]) -> None:
+        """
+        Initialize the Persistent Segment Tree with the given array.
+
+        >>> pst = PersistentSegmentTree([1, 2, 3])
+        >>> pst.query(0, 0, 2)
+        6
+        """
         self.n = 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:
-        """
-        Builds a segment tree from the provided array.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3])
-        >>> root = pst._build([1, 2, 3], 0, 2)
-        >>> root.value  # Sum of the whole array
-        6
-        """
         if start == end:
             return Node(arr[start])
         mid = (start + end) // 2
@@ -31,41 +30,46 @@ class PersistentSegmentTree:
 
     def update(self, version: int, index: int, value: int) -> int:
         """
-        Updates the segment tree with a new value at the specified index.
+        Update the value at the given index and return the new version.
 
         >>> pst = PersistentSegmentTree([1, 2, 3])
         >>> version_1 = pst.update(0, 1, 5)
-        >>> pst.query(version_1, 0, 2)  # Query sum from index 0 to 2
+        >>> pst.query(version_1, 0, 2)
         9
         """
         new_root = self._update(self.roots[version], 0, self.n - 1, index, value)
         self.roots.append(new_root)
-        return len(self.roots) - 1  # return the index of the new version
+        return len(self.roots) - 1
 
     def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node:
         if start == end:
-            new_node = Node(value)
-            return new_node
+            return Node(value)
+
         mid = (start + end) // 2
         new_node = Node()
+
         if index <= mid:
             new_node.left = self._update(node.left, start, mid, index, value)
             new_node.right = node.right
         else:
             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
+
         return new_node
 
     def query(self, version: int, left: int, right: int) -> int:
         """
-        Queries the sum in the given range for the specified version.
+        Query the sum in the given range for the specified version.
 
         >>> pst = PersistentSegmentTree([1, 2, 3])
-        >>> version_1 = pst.update(0, 1, 5)
-        >>> pst.query(version_1, 0, 1)  # Query sum from index 0 to 1
+        >>> pst.query(0, 0, 2)
         6
-        >>> pst.query(version_1, 0, 2)  # Query sum from index 0 to 2
+        >>> version_1 = pst.update(0, 1, 5)
+        >>> pst.query(version_1, 0, 1)
+        6
+        >>> pst.query(version_1, 0, 2)
         9
         """
         return self._query(self.roots[version], 0, self.n - 1, left, right)
@@ -76,6 +80,12 @@ 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))
+
+
+if __name__ == "__main__":
+    import doctest
+    print("Running doctests...")
+    result = doctest.testmod()
+    print(f"Ran {result.attempted} tests, {result.failed} failed.")