Classifying triangles by lengths

# Table: Triangles
# 
# +-------------+------+
# | Column Name | Type |
# +-------------+------+
# | A           | int  |
# | B           | int  |
# | C           | int  |
# +-------------+------+
# (A, B, C) is the primary key for this table.
# Each row include the lengths of each of a triangle's three sides.
# 
# Write a query to find the type of triangle. Output one of the following for each row:
# 
# Equilateral: It's a triangle with 3 sides of equal length.
# 
# Isosceles: It's a triangle with 2 sides of equal length.
# 
# Scalene: It's a triangle with 3 sides of differing lengths.
# 
# Not A Triangle: The given values of A, B, and C don't form a triangle.
# 
# Return the result table in any order.
# 
# The result format is in the following example.
#
# Example 1:
# Input:
# Triangles table:
# +----+----+----+
# | A  | B  | C  |
# +----+----+----+
# | 20 | 20 | 23 |
# | 20 | 20 | 20 |
# | 20 | 21 | 22 |
# | 13 | 14 | 30 |
# +----+----+----+
# Output:
# +----------------+
# | triangle_type  |
# +----------------+
# | Isosceles      |
# | Equilateral    |
# | Scalene        |
# | Not A Triangle |
# +----------------+
# Explanation:
# - Values in the first row from an Isosceles triangle, because A = B.
# - Values in the second row from an Equilateral triangle, because A = B = C.
# - Values in the third row from an Scalene triangle, because A != B != C.
# - Values in the fourth row cannot form a triangle, because the combined value of sides A and B is not larger than that of side C.

import pandas as pd

def type_of_triangle(triangles: pd.DataFrame) -> pd.DataFrame:
  def classify(row):
    a, b, c = row['A'], row['B'], row['C']
    if a + b <= c or a + c <= b or b + c <= a:
      return 'Not A Triangle'
    if a == b == c:
      return 'Equilateral'
    if a == b or b == c or a == c:
      return 'Isosceles'
    return 'Scalene'
  triangles['triangle_type'] = triangles.apply(classify, axis=1)
  return triangles[['triangle_type']]