#!/usr/bin/env python3

from typing import Any, List, Optional


class Node(object):
    def __init__(self, value: Any) -> None:
        self.left = None
        self.right = None
        self.value = value


class BinaryTree(object):
    def __init__(self):
        self.root = None
        self.count = 0
        self.traverse = None

    def get_root(self) -> Optional[Node]:
        return self.root

    def insert(self, value: Any):
        """
        Insert something into the tree.

        >>> t = BinaryTree()
        >>> t.insert(10)
        >>> t.insert(20)
        >>> t.insert(5)
        >>> len(t)
        3

        >>> t.get_root().value
        10

        """
        if self.root is None:
            self.root = Node(value)
            self.count = 1
        else:
            self._insert(value, self.root)

    def _insert(self, value: Any, node: Node):
        """Insertion helper"""
        if value < node.value:
            if node.left is not None:
                self._insert(value, node.left)
            else:
                node.left = Node(value)
                self.count += 1
        else:
            if node.right is not None:
                self._insert(value, node.right)
            else:
                node.right = Node(value)
                self.count += 1

    def __getitem__(self, value: Any) -> Optional[Node]:
        """
        Find an item in the tree and return its Node.  Returns
        None if the item is not in the tree.

        >>> t = BinaryTree()
        >>> t[99]

        >>> t.insert(10)
        >>> t.insert(20)
        >>> t.insert(5)
        >>> t[10].value
        10

        >>> t[99]

        """
        if self.root is not None:
            return self._find(value, self.root)
        return None

    def _find(self, value: Any, node: Node) -> Optional[Node]:
        """Find helper"""
        if value == node.value:
            return node
        elif (value < node.value and node.left is not None):
            return self._find(value, node.left)
        else:
            assert value > node.value
            if node.right is not None:
                return self._find(value, node.right)
        return None

    def __delitem__(self, value: Any) -> bool:
        """
        Delete an item from the tree and preserve the BST property.

                            50
                           /  \
                         25    75
                        /     /  \
                      22    66    85
                     /
                   13


        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)
        >>> t.insert(85)

        >>> for value in t.iterate_inorder():
        ...     print(value)
        13
        22
        25
        50
        66
        75
        85

        >>> del t[22]  # Note: bool result is discarded

        >>> for value in t.iterate_inorder():
        ...     print(value)
        13
        25
        50
        66
        75
        85

        >>> t.__delitem__(13)
        True
        >>> for value in t.iterate_inorder():
        ...     print(value)
        25
        50
        66
        75
        85

        >>> t.__delitem__(75)
        True
        >>> for value in t.iterate_inorder():
        ...     print(value)
        25
        50
        66
        85

        >>> t.__delitem__(99)
        False

        """
        if self.root is not None:
            ret = self._delete(value, None, self.root)
            if ret:
                self.count -= 1
                if self.count == 0:
                    self.root = None
            return ret
        return False

    def _delete(self, value: Any, parent: Optional[Node], node: Node) -> bool:
        """Delete helper"""
        if node.value == value:
            # Deleting a leaf node
            if node.left is None and node.right is None:
                if parent is not None:
                    if parent.left == node:
                        parent.left = None
                    else:
                        assert parent.right == node
                        parent.right = None
                return True

            # Node only has a right.
            elif node.left is None:
                assert node.right is not None
                if parent is not None:
                    if parent.left == node:
                        parent.left = node.right
                    else:
                        assert parent.right == node
                        parent.right = node.right
                return True

            # Node only has a left.
            elif node.right is None:
                assert node.left is not None
                if parent is not None:
                    if parent.left == node:
                        parent.left = node.left
                    else:
                        assert parent.right == node
                        parent.right = node.left
                return True

            # Node has both a left and right.
            else:
                assert node.left is not None and node.right is not None
                descendent = node.right
                while descendent.left is not None:
                    descendent = descendent.left
                node.value = descendent.value
                return self._delete(node.value, node, node.right)
        elif value < node.value and node.left is not None:
            return self._delete(value, node, node.left)
        elif value > node.value and node.right is not None:
            return self._delete(value, node, node.right)
        return False

    def __len__(self):
        """
        Returns the count of items in the tree.

        >>> t = BinaryTree()
        >>> len(t)
        0
        >>> t.insert(50)
        >>> len(t)
        1
        >>> t.__delitem__(50)
        True
        >>> len(t)
        0
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)
        >>> t.insert(85)
        >>> len(t)
        6

        """
        return self.count

    def __contains__(self, value: Any) -> bool:
        """
        Returns True if the item is in the tree; False otherwise.

        """
        return self.__getitem__(value) is not None

    def _iterate_preorder(self, node: Node):
        yield node.value
        if node.left is not None:
            yield from self._iterate_preorder(node.left)
        if node.right is not None:
            yield from self._iterate_preorder(node.right)

    def _iterate_inorder(self, node: Node):
        if node.left is not None:
            yield from self._iterate_inorder(node.left)
        yield node.value
        if node.right is not None:
            yield from self._iterate_inorder(node.right)

    def _iterate_postorder(self, node: Node):
        if node.left is not None:
            yield from self._iterate_postorder(node.left)
        if node.right is not None:
            yield from self._iterate_postorder(node.right)
        yield node.value

    def iterate_preorder(self):
        """
        Yield the tree's items in a preorder traversal sequence.

        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)

        >>> for value in t.iterate_preorder():
        ...     print(value)
        50
        25
        22
        13
        75
        66

        """
        if self.root is not None:
            yield from self._iterate_preorder(self.root)

    def iterate_inorder(self):
        """
        Yield the tree's items in a preorder traversal sequence.

        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)

        >>> for value in t.iterate_inorder():
        ...     print(value)
        13
        22
        25
        50
        66
        75

        """
        if self.root is not None:
            yield from self._iterate_inorder(self.root)

    def iterate_postorder(self):
        """
        Yield the tree's items in a preorder traversal sequence.

        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)

        >>> for value in t.iterate_postorder():
        ...     print(value)
        13
        22
        25
        66
        75
        50

        """
        if self.root is not None:
            yield from self._iterate_postorder(self.root)

    def _iterate_leaves(self, node: Node):
        if node.left is not None:
            yield from self._iterate_leaves(node.left)
        if node.right is not None:
            yield from self._iterate_leaves(node.right)
        if node.left is None and node.right is None:
            yield node.value

    def iterate_leaves(self):
        """
        Iterate only the leaf nodes in the tree.

        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)

        >>> for value in t.iterate_leaves():
        ...     print(value)
        13
        66

        """
        if self.root is not None:
            yield from self._iterate_leaves(self.root)

    def _iterate_by_depth(self, node: Node, depth: int):
        if depth == 0:
            yield node.value
        else:
            assert depth > 0
            if node.left is not None:
                yield from self._iterate_by_depth(node.left, depth - 1)
            if node.right is not None:
                yield from self._iterate_by_depth(node.right, depth - 1)

    def iterate_nodes_by_depth(self, depth: int):
        """
        Iterate only the leaf nodes in the tree.

        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(75)
        >>> t.insert(25)
        >>> t.insert(66)
        >>> t.insert(22)
        >>> t.insert(13)

        >>> for value in t.iterate_nodes_by_depth(2):
        ...     print(value)
        22
        66

        >>> for value in t.iterate_nodes_by_depth(3):
        ...     print(value)
        13

        """
        if self.root is not None:
            yield from self._iterate_by_depth(self.root, depth)

    def _depth(self, node: Node, sofar: int) -> int:
        depth_left = sofar + 1
        depth_right = sofar + 1
        if node.left is not None:
            depth_left = self._depth(node.left, sofar + 1)
        if node.right is not None:
            depth_right = self._depth(node.right, sofar + 1)
        return max(depth_left, depth_right)

    def depth(self):
        """
        Returns the max height (depth) of the tree in plies (edge distance
        from root).

        >>> t = BinaryTree()
        >>> t.depth()
        0

        >>> t.insert(50)
        >>> t.depth()
        1

        >>> t.insert(65)
        >>> t.depth()
        2

        >>> t.insert(33)
        >>> t.depth()
        2

        >>> t.insert(2)
        >>> t.insert(1)
        >>> t.depth()
        4

        """
        if self.root is None:
            return 0
        return self._depth(self.root, 0)

    def height(self):
        return self.depth()

    def repr_traverse(self, padding: str, pointer: str, node: Node, has_right_sibling: bool) -> str:
        if node is not None:
            self.viz += f'\n{padding}{pointer}{node.value}'
            if has_right_sibling:
                padding += "│  "
            else:
                padding += '   '

            pointer_right = "└──"
            if node.right is not None:
                pointer_left = "├──"
            else:
                pointer_left = "└──"

            self.repr_traverse(padding, pointer_left, node.left, node.right is not None)
            self.repr_traverse(padding, pointer_right, node.right, False)

    def __repr__(self):
        """
        Draw the tree in ASCII.

        >>> t = BinaryTree()
        >>> t.insert(50)
        >>> t.insert(25)
        >>> t.insert(75)
        >>> t.insert(12)
        >>> t.insert(33)
        >>> t.insert(88)
        >>> t.insert(55)
        >>> t
        50
        ├──25
        │  ├──12
        │  └──33
        └──75
           ├──55
           └──88
        """
        if self.root is None:
            return ""

        self.viz = f'{self.root.value}'
        pointer_right = "└──"
        if self.root.right is None:
            pointer_left = "└──"
        else:
            pointer_left = "├──"

        self.repr_traverse('', pointer_left, self.root.left, self.root.left is not None)
        self.repr_traverse('', pointer_right, self.root.right, False)
        return self.viz


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