#### Diameter of Binary Tree

p
```"""
The diameter/width of a tree is defined as the number of nodes on the longest path
between two end nodes.
"""

from __future__ import annotations

from dataclasses import dataclass

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

def depth(self) -> int:
"""
>>> root = Node(1)
>>> root.depth()
1
>>> root.left = Node(2)
>>> root.depth()
2
>>> root.left.depth()
1
>>> root.right = Node(3)
>>> root.depth()
2
"""
left_depth = self.left.depth() if self.left else 0
right_depth = self.right.depth() if self.right else 0
return max(left_depth, right_depth) + 1

def diameter(self) -> int:
"""
>>> root = Node(1)
>>> root.diameter()
1
>>> root.left = Node(2)
>>> root.diameter()
2
>>> root.left.diameter()
1
>>> root.right = Node(3)
>>> root.diameter()
3
"""
left_depth = self.left.depth() if self.left else 0
right_depth = self.right.depth() if self.right else 0
return left_depth + right_depth + 1

if __name__ == "__main__":
from doctest import testmod

testmod()
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
r"""
Constructed binary tree is
1
/ \
2	  3
/ \
4	 5
"""
print(f"{root.diameter() = }")  # 4
print(f"{root.left.diameter() = }")  # 3
print(f"{root.right.diameter() = }")  # 1
```