Binary tree nodes

# Table: Tree
# 
# +-------------+------+
# | Column Name | Type |
# +-------------+------+
# | N           | int  |
# | P           | int  |
# +-------------+------+
# N is the column of unique values for this table.
# Each row includes N and P, where N represents the value of a node in Binary Tree, and P is the parent of N.
# 
# Write a solution to find the node type of the Binary Tree. Output one of the following for each node:
# 
# Root: if the node is the root node.
# 
# Leaf: if the node is the leaf node.
# 
# Inner: if the node is neither root nor leaf node.
# 
# Return the result table ordered by node value in ascending order.
# 
# The result format is in the following example.
#
# Example 1:
# Input:
# Tree table:
# +---+------+
# | N | P    |
# +---+------+
# | 1 | 2    |
# | 3 | 2    |
# | 6 | 8    |
# | 9 | 8    |
# | 2 | 5    |
# | 8 | 5    |
# | 5 | null |
# +---+------+
# Output:
# +---+-------+
# | N | Type  |
# +---+-------+
# | 1 | Leaf  |
# | 2 | Inner |
# | 3 | Leaf  |
# | 5 | Root  |
# | 6 | Leaf  |
# | 8 | Inner |
# | 9 | Leaf  |
# +---+-------+
# Explanation:
# - Node 5 is the root node since it has no parent node.
# - Nodes 1, 3, 6, and 9 are leaf nodes because they don't have any child nodes.
# - Nodes 2, and 8 are inner nodes as they serve as parents to some of the nodes in the structure.

import pandas as pd

def binary_tree_nodes(tree: pd.DataFrame) -> pd.DataFrame:
  parents = set(tree['P'].dropna())
  def get_type(row):
    if pd.isna(row['P']):
      return 'Root'
    if row['N'] in parents:
      return 'Inner'
    return 'Leaf'
  tree['Type'] = tree.apply(get_type, axis=1)
  return tree[['N', 'Type']].sort_values('N').reset_index(drop=True)