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+"""CSC111 Winter 2022 Prep 4: Programming Exercises
+
+Instructions (READ THIS FIRST!)
+===============================
+
+Your task in this prep is to implement each of the unimplemented Tree methods in this file.
+Use the recursive Tree method code template---decide whether to include the "size-one" base case
+by determining whether it would be redundant.
+
+We have marked each place you need to write code with the word "TODO".
+As you complete your work in this file, delete each TODO comment.
+
+You may add additional doctests, but they will not be graded. You should test your work
+carefully before submitting it!
+
+Copyright and Usage Information
+===============================
+
+This file is provided solely for the personal and private use of students
+taking CSC111 at the University of Toronto St. George campus. All forms of
+distribution of this code, whether as given or with any changes, are
+expressly prohibited. For more information on copyright for CSC111 materials,
+please consult our Course Syllabus.
+
+This file is Copyright (c) 2022 Mario Badr, David Liu, and Diane Horton.
+"""
+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+    difference is that _rest has been replaced by _subtrees to handle multiple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.
+
+    Representation Invariants:
+        - self._root is not None or self._subtrees == []
+        - all(not subtree.is_empty() for subtree in self._subtrees)
+    """
+    # Private Instance Attributes:
+    #   - _root:
+    #       The item stored at this tree's root, or None if the tree is empty.
+    #   - _subtrees:
+    #       The list of subtrees of this tree. This attribute is empty when
+    #       self._root is None (representing an empty tree). However, this attribute
+    #       may be empty when self._root is not None, which represents a tree consisting
+    #       of just one item.
+    _root: Optional[Any]
+    _subtrees: list[Tree]
+
+    def __init__(self, root: Optional[Any], subtrees: list[Tree]) -> None:
+        """Initialize a new Tree with the given root value and subtrees.
+
+        If root is None, the tree is empty.
+
+        Preconditions:
+            - root is not none or subtrees == []
+        """
+        self._root = root
+        self._subtrees = subtrees
+
+    def is_empty(self) -> bool:
+        """Return whether 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 write len(subtree)
+            return size
+
+    ############################################################################
+    # Prep exercises start here
+    ############################################################################
+    def num_negatives(self) -> int:
+        """Return the number of negative integers in this tree.
+
+        Preconditions:
+            - all items in this tree are integers
+
+        Remember, 0 is *not* negative.
+
+        >>> t1 = Tree(17, [])
+        >>> t1.num_negatives()
+        0
+        >>> t1 = Tree(-17, [])
+        >>> t1.num_negatives()
+        1
+        >>> t1 = Tree(-17, [Tree(-1, [Tree(-20, [])]), Tree(-15, []), Tree(0, []), Tree(2, [Tree(-20, [])])])
+        >>> t1.num_negatives()
+        5
+        """
+        if self.is_empty():
+            return 0
+        elif not self._subtrees:
+            return int(self._root < 0)
+        else:
+            return int(self._root < 0) + sum(s.num_negatives() for s in self._subtrees)
+
+    def maximum(self: Tree) -> int:
+        """Return the maximum value stored in this tree.
+
+        Return 0 if this tree is empty.
+
+        Preconditions:
+            - all values in this tree are positive integers.
+
+        >>> t1 = Tree(17, [])
+        >>> t1.maximum()
+        17
+        >>> t1 = Tree(17, [Tree(18, []), Tree(2, [Tree(19, [])])])
+        >>> t1.maximum()
+        19
+        """
+        if self.is_empty():
+            return 0
+        elif not self._subtrees:
+            return int(self._root)
+        else:
+            return max(s.maximum() for s in self._subtrees)
+
+    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
+        >>> t1 = Tree(17, [Tree(18, []), Tree(2, [Tree(19, [])])])
+        >>> t1.height()
+        3
+        """
+        if self.is_empty():
+            return 1
+        elif not self._subtrees:
+            return 1
+        else:
+            return 1 + max(s.height() for s in self._subtrees)
+
+    def __contains__(self, item: Any) -> bool:
+        """Return whether this tree contains <item>.
+
+        >>> t = Tree(1, [])
+        >>> t.__contains__(-30)  # Could also write -30 in t
+        False
+        >>> t.__contains__(1)
+        True
+        >>> t = Tree(17, [Tree(18, []), Tree(2, [Tree(19, [Tree('A', [])])])])
+        >>> 19 in t
+        True
+        >>> 2 in t
+        True
+        >>> 3 in t
+        False
+        >>> 'A' in t
+        True
+        """
+        if self.is_empty():
+            return False
+        elif not self._subtrees:
+            return self._root == item
+        else:
+            return self._root == item or any(item in s for s in self._subtrees)
+
+
+if __name__ == '__main__':
+    import python_ta.contracts
+    python_ta.contracts.check_all_contracts()
+
+    import doctest
+    doctest.testmod()
+
+    import python_ta
+    python_ta.check_all(config={
+        'max-line-length': 100,
+        'disable': ['E1136']
+    })