#### Binary Tree Traversals

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# https://en.wikipedia.org/wiki/Tree_traversal
from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any

@dataclass
class Node:
data: int
left: Node | None = None
right: Node | None = None

def make_tree() -> Node | None:
r"""
The below tree
1
/ \
2   3
/ \
4   5
"""
tree = Node(1)
tree.left = Node(2)
tree.right = Node(3)
tree.left.left = Node(4)
tree.left.right = Node(5)
return tree

def preorder(root: Node | None) -> list[int]:
"""
Pre-order traversal visits root node, left subtree, right subtree.
>>> preorder(make_tree())
[1, 2, 4, 5, 3]
"""
return [root.data] + preorder(root.left) + preorder(root.right) if root else []

def postorder(root: Node | None) -> list[int]:
"""
Post-order traversal visits left subtree, right subtree, root node.
>>> postorder(make_tree())
[4, 5, 2, 3, 1]
"""
return postorder(root.left) + postorder(root.right) + [root.data] if root else []

def inorder(root: Node | None) -> list[int]:
"""
In-order traversal visits left subtree, root node, right subtree.
>>> inorder(make_tree())
[4, 2, 5, 1, 3]
"""
return inorder(root.left) + [root.data] + inorder(root.right) if root else []

def height(root: Node | None) -> int:
"""
Recursive function for calculating the height of the binary tree.
>>> height(None)
0
>>> height(make_tree())
3
"""
return (max(height(root.left), height(root.right)) + 1) if root else 0

def level_order(root: Node | None) -> Sequence[Node | None]:
"""
Returns a list of nodes value from a whole binary tree in Level Order Traverse.
Level Order traverse: Visit nodes of the tree level-by-level.
"""
output: list[Any] = []

if root is None:
return output

process_queue = deque([root])

while process_queue:
node = process_queue.popleft()
output.append(node.data)

if node.left:
process_queue.append(node.left)
if node.right:
process_queue.append(node.right)
return output

def get_nodes_from_left_to_right(
root: Node | None, level: int
) -> Sequence[Node | None]:
"""
Returns a list of nodes value from a particular level:
Left to right direction of the binary tree.
"""
output: list[Any] = []

def populate_output(root: Node | None, level: int) -> None:
if not root:
return
if level == 1:

output.append(root.data)
elif level > 1:
populate_output(root.left, level - 1)
populate_output(root.right, level - 1)

populate_output(root, level)
return output

def get_nodes_from_right_to_left(
root: Node | None, level: int
) -> Sequence[Node | None]:
"""
Returns a list of nodes value from a particular level:
Right to left direction of the binary tree.
"""
output: list[Any] = []

def populate_output(root: Node | None, level: int) -> None:
if root is None:
return
if level == 1:
output.append(root.data)
elif level > 1:
populate_output(root.right, level - 1)
populate_output(root.left, level - 1)

populate_output(root, level)
return output

def zigzag(root: Node | None) -> Sequence[Node | None] | list[Any]:
"""
ZigZag traverse:
Returns a list of nodes value from left to right and right to left, alternatively.
"""
if root is None:
return []

output: list[Sequence[Node | None]] = []

flag = 0
height_tree = height(root)

for h in range(1, height_tree + 1):
if not flag:
output.append(get_nodes_from_left_to_right(root, h))
flag = 1
else:
output.append(get_nodes_from_right_to_left(root, h))
flag = 0

return output

def main() -> None:  # Main function for testing.
"""
Create binary tree.
"""
root = make_tree()
"""
All Traversals of the binary are as follows:
"""

print(f"In-order Traversal: {inorder(root)}")
print(f"Pre-order Traversal: {preorder(root)}")
print(f"Post-order Traversal: {postorder(root)}", "\n")

print(f"Height of Tree: {height(root)}", "\n")

print("Complete Level Order Traversal: ")
print(level_order(root), "\n")

print("Level-wise order Traversal: ")

for level in range(1, height(root) + 1):
print(f"Level {level}:", get_nodes_from_left_to_right(root, level=level))

print("\nZigZag order Traversal: ")
print(zigzag(root))

if __name__ == "__main__":
import doctest

doctest.testmod()
main()