4 METHODS NEED TO BE IMPLEMENTED

#INTRUCTIONS ARE WITHIN THE CODE MAKE SURE IT WORKS     #USE PYTHON 3.9    """    === Module Description ===    Your task in this prep is to implement each of the unimplemented Tree methods    in this file.    The starter code has a recursive template that includes the "size-one" case;    you may or may not choose to use this in your final implementations.    """    from __future__ import annotations        from typing import Any, Optional            class Tree:        """A recursive tree data structure.            Note the relationship between this class and RecursiveList; the only major        difference is that _rest has been replaced by _subtrees to handle multiple        recursive sub-parts.        """        # === Private Attributes ===        # The item stored at this tree's root, or None if the tree is empty.        _root: Optional[Any]        # The list of all subtrees of this tree.        _subtrees: list[Tree]            # === Representation Invariants ===        # - If self._root is None then self._subtrees is an empty list.        #   This setting of attributes represents an empty Tree.        #        #   Note: self._subtrees may be empty when self._root is not None.        #   This setting of attributes represents a tree consisting of just one        #   node.            def __init__(self, root: Any, subtrees: list[Tree]) -> None:            """Initialize a new Tree with the given root value and subtrees.                If  is None, the tree is empty.            Precondition: if  is None, then  is empty.            """            self._root = root            self._subtrees = subtrees            def is_empty(self) -> bool:            """Return True if this tree is empty.                >>> t1 = Tree(None, [])            >>> t1.is_empty()            True            >>> t2 = Tree(3, [])            >>> t2.is_empty()            False            """            return self._root is None            def __len__(self) -> int:            """Return the number of items contained in this tree.                >>> t1 = Tree(None, [])            >>> len(t1)            0            >>> t2 = Tree(3, [Tree(4, []), Tree(1, [])])            >>> len(t2)            3            """            if self.is_empty():                return 0            else:                size = 1  # count the root                for subtree in self._subtrees:                    size += subtree.__len__()  # could also do len(subtree) here                return size            # TODO: implement this method!        def num_positives(self) -> int:            """Return the number of positive integers in this tree.                Precondition: all items in this tree are integers.                Remember, 0 is *not* positive.                >>> t1 = Tree(17, [])            >>> t1.num_positives()            1            >>> t2 = Tree(-10, [])            >>> t2.num_positives()            0            >>> t3 = Tree(1, [Tree(-2, []), Tree(10, []), Tree(-30, [])])            >>> t3.num_positives()            2            """            # if self.is_empty():            #     ...            # elif self._subtrees == []:            #     ...            # else:            #     ...            #     for subtree in self._subtrees:            #         ... subtree.num_positives() ...            #     ...            pass            # TODO: implement this method!        def maximum(self: Tree) -> int:            """Return the maximum item stored in this tree.                Return 0 if this tree is empty.                Precondition: all values in this tree are positive integers.                >>> t1 = Tree(17, [])            >>> t1.maximum()            17            >>> t3 = Tree(1, [Tree(12, []), Tree(10, []), Tree(30, [])])            >>> t3.maximum()            30            """            # if self.is_empty():            #     ...            # elif self._subtrees == []:            #     ...            # else:            #     ...            #     for subtree in self._subtrees:            #         ... subtree.maximum() ...            #     ...            pass            # TODO: implement this method!        def height(self: Tree) -> int:            """Return the height of this tree.                Please refer to the prep readings for the definition of tree height.                >>> t1 = Tree(17, [])            >>> t1.height()            1            >>> t2 = Tree(1, [Tree(-2, []), Tree(10, []), Tree(-30, [])])            >>> t2.height()            2            """            # if self.is_empty():            #     ...            # elif self._subtrees == []:            #     ...            # else:            #     ...            #     for subtree in self._subtrees:            #         ... subtree.height() ...            #     ...            pass            # TODO: implement this method!        def __contains__(self, item: Any) -> bool:            """Return whether this tree contains .                >>> t = Tree(1, [Tree(-2, []), Tree(10, []), Tree(-30, [])])            >>> t.__contains__(-30)  # Could also write -30 in t.            True            >>> t.__contains__(148)            False            """            # if self.is_empty():            #     ...            # elif self._subtrees == []:            #     ...            # else:            #     ...            #     for subtree in self._subtrees:            #         ... subtree.__contains__(...) ...            #     ...            pass            if __name__ == '__main__':        import doctest            doctest.testmod()            import python_ta            python_ta.check_all()