Triangle Shape Classification by Side Lengths

A geometry validation service stores side-length triplets in a table and needs a per-row triangle category.

Table: Triangles

• A: length of side 1
• B: length of side 2
• C: length of side 3

(A, B, C) is unique per row.

For every row, assign exactly one label:

• Equilateral: all three sides are equal and the triplet forms a valid triangle.
• Isosceles: exactly two sides are equal and the triplet forms a valid triangle.
• Scalene: all three sides are different and the triplet forms a valid triangle.
• Not A Triangle: the three lengths fail triangle inequality.

Triangle validity rule (all must hold):

• A + B > C
• A + C > B
• B + C > A

Return one column:

• triangle_type

Return rows in any order.

Supported submission environments:

• SQL (SQLite 3.27.2)
• Pandas (Python)

Triangles:
| A  | B  | C  |
|----|----|----|
| 20 | 20 | 23 |
| 20 | 20 | 20 |
| 20 | 21 | 22 |
| 13 | 14 | 30 |

[
  {"triangle_type":"Equilateral"},
  {"triangle_type":"Isosceles"},
  {"triangle_type":"Not A Triangle"},
  {"triangle_type":"Scalene"}
]

Triangles:
| A | B | C |
|---|---|---|
| 5 | 5 | 9 |
| 5 | 5 | 10|
| 7 | 9 | 12|

[
  {"triangle_type":"Isosceles"},
  {"triangle_type":"Not A Triangle"},
  {"triangle_type":"Scalene"}
]

Triangles:
| A          | B          | C          |
|------------|------------|------------|
| 1000000000 | 1000000000 | 1000000000 |
| 1          | 1          | 2          |

[
  {"triangle_type":"Equilateral"},
  {"triangle_type":"Not A Triangle"}
]