data_structures.binary_tree.persistent_segment_tree
===================================================

.. py:module:: data_structures.binary_tree.persistent_segment_tree


Attributes
----------

.. autoapisummary::

   data_structures.binary_tree.persistent_segment_tree.result


Classes
-------

.. autoapisummary::

   data_structures.binary_tree.persistent_segment_tree.Node
   data_structures.binary_tree.persistent_segment_tree.PersistentSegmentTree


Module Contents
---------------

.. py:class:: Node

   .. py:attribute:: left
      :type:  Node | None
      :value: None



   .. py:attribute:: right
      :type:  Node | None
      :value: None



   .. py:attribute:: value
      :type:  int


.. py:class:: PersistentSegmentTree(arr: list[int])

   .. py:method:: _build(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



   .. py:method:: _query(node: Node, 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



   .. py:method:: _update(node: Node, start: int, end: int, index: int, value: int) -> Node

      Update the node for the specified index and value and return 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



   .. py:method:: query(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



   .. py:method:: update(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



   .. py:attribute:: n
      :type:  int


   .. py:attribute:: roots
      :type:  list[Node]
      :value: []



.. py:data:: result