Example of function to create some classes of methods to operate on trees. Doctests are annoying, but for now they suffice. Besides, this is not as tested as it should.

tree_make_mr.py

def make_mr(reduce_, f, base):
    def mr(self):
        if not self.children:
            return base(self)
        else:
            mapped = map(f, self.children)
            red = reduce_(mapped)
            return red
            # return reduce_(f(child) for child in self.children)
    return mr

class Node(object):
    """
    >>> Node(1).height()
    0
    >>> Node(1).count()
    1
    >>> Node.from_array([0, 0, 0, 1, 1, 1, 2, 2, 7]).height()
    3
    >>> Node.from_array([0, 0, 0, 1, 1, 1, 2, 2, 7]).count()
    9
    """
    def __init__(self, value, *children):
        """
        >>> Node(1)
        N(1)
        >>> Node(0, Node(1), Node(2))
        N(0, N(1), N(2))
        """
        self.value = value
        self.children = list(children)

    height = make_mr(lambda mapped_children: max(mapped_children) + 1,
                     lambda node: node.height(),
                     lambda node: 0)
    count =  make_mr(lambda mapped_children: sum(mapped_children) + 1,
                     lambda node: node.count(),
                     lambda node: 1)

    @classmethod
    def from_array(cls, arr):
        """
        >>> Node.from_array([0])
        N(0)
        >>> Node.from_array([0, 0, 0])
        N(0, N(1), N(2))
        >>> Node.from_array([0, 0, 0, 1, 1, 1, 2, 2, 7])
        N(0, N(1, N(3), N(4), N(5)), N(2, N(6), N(7, N(8))))
        >>> Node.from_array([1])
        Traceback (most recent call last):
            ...
        ValueError: Invalid array spec: missing root.
        >>> Node.from_array([0, 1])
        Traceback (most recent call last):
            ...
        ValueError: Invalid array spec: multiple roots.
        """
        if not arr:
            raise ValueError("Empty container")
        nodes = {}
        def add(node, child):
            new_node = cls(child)
            nodes[child] = new_node
            node.children.append(new_node)
        root_index = None
        for index, el in enumerate(arr):
            if index == el and root_index is None:
                root_index = index
                nodes.setdefault(index, cls(index))
            elif index == el:
                raise ValueError(
                        "Invalid array spec: multiple roots.")
            else:
                add(nodes.setdefault(el, cls(el)), index)
        if root_index is not None:
            return nodes[root_index]
        else:
            raise ValueError(
                "Invalid array spec: missing root.")

    def __str__(self):
        if self.children:
            return 'N(%s, %s)' % (
                    self.value, ', '.join(str(child) for child in
                        self.children))
        else:
            return 'N(%s)' % self.value

    __repr__ = __str__

if __name__ == "__main__":
    import doctest
    doctest.testmod()