# Also do the 2026.05.06 homework
#
# Implement insertion, removal and search in a binary search tree.
# Properties of binary search trees:
# - Each node has at most two children
# - The left subtree of a node contains only nodes with values less than the node's value
# - The right subtree of a node contains only nodes with values greater than the node's value
#
# Example of what such a tree would look like:
#       10
#      /  \
#     5   15
#    / \    \
#   3   7   20
#
# Example of an *invalid* tree:
#       10
#      /  \
#     5   15
#    / \    \
#   3   7   20
#    \
#     12
#
# Don't worry about balancing the tree for now, we will cover that later


class Node:
    def __init__(self, value, left=None, right=None):
        self.value = value
        self.left: Node | None = left
        self.right: Node | None = right


class BinarySearchTree:
    def __init__(self, root=None):
        self.root: Node | None = root

    def find_prev_node(self, value):
        prev_node: Node | None = None
        node = self.root
        while node is not None:
            prev_node = node
            if node.value >= value:
                node = node.left
            else:
                node = node.right

        return prev_node

    def find_existing_node_and_parent(self, value):
        prev_node: Node | None = None
        node = self.root

        while node is not None:
            if value == node.value:
                return node, prev_node

            prev_node = node
            if value < node.value:
                node = node.left
            else:
                node = node.right

        return None, None

    def insert(self, value):
        prev_node = self.find_prev_node(value)
        if prev_node is None:
            self.root = Node(value)
            return

        if prev_node.value >= value:
            prev_node.left = Node(value)
        else:
            prev_node.right = Node(value)

    def remove(self, value):
        node, prev_node = self.find_existing_node_and_parent(value)
        if prev_node is None and node is not None:
            self.root = None
            return
        elif node is not None:
            if prev_node.value >= value:
                prev_node.left = None
            else:
                prev_node.right = None

    def search(self, value):
        node = self.root

        while node is not None:
            if value == node.value:
                return node
            elif value < node.value:
                node = node.left
            else:
                node = node.right
        return None


print("================ Inserts ================")

test_tree = BinarySearchTree()
test_tree.insert(5)
test_tree.insert(3)
print(test_tree.root.left.value)

test_tree.insert(4)
test_tree.insert(6)
print(test_tree.root.left.right.value)
print(test_tree.root.right.value)

print("================ Searches ================")

# is the search result giving us the expected node?
print(test_tree.search(4) == test_tree.root.left.right)
print(test_tree.search(6) == test_tree.root.right)
print(test_tree.search(20) is None)

print("================ Removals ================")

test_tree.remove(4)
print(test_tree.root.left.right)
test_tree.remove(6)
print(test_tree.root.right)
test_tree.remove(3)
print(test_tree.root.left)
test_tree.remove(5)
print(test_tree.root)