Classifying Triangles by Lengths - Practice Coding Problems

Classifying Triangles by Lengths - Problem

Database Easy

Given a table containing the three side lengths of various triangles, write a SQL query to classify each triangle based on its geometric properties.

Table: Triangles

Column Name	Type
A	int
B	int
C	int

Where (A, B, C) represents the primary key, and each row contains the lengths of a triangle's three sides.

Classification Rules:

Equilateral: All three sides are equal (A = B = C)
Isosceles: Exactly two sides are equal
Scalene: All three sides are different
Not A Triangle: The sides don't satisfy the triangle inequality theorem

Triangle Inequality: For three sides to form a valid triangle, the sum of any two sides must be greater than the third side: A + B > C, A + C > B, and B + C > A.

Return the result table with each triangle classified appropriately. The order doesn't matter.

Input & Output

example_1.sql — Basic Triangle Types

$ Input: Triangles table: +---+---+---+ | A | B | C | +---+---+---+ | 20| 20| 23| | 20| 20| 20| | 20| 21| 22| | 13| 14| 30| +---+---+---+

› Output: +---+---+---+---------------+ | A | B | C | triangle_type | +---+---+---+---------------+ | 20| 20| 23| Isosceles | | 20| 20| 20| Equilateral | | 20| 21| 22| Scalene | | 13| 14| 30| Not A Triangle| +---+---+---+---------------+

💡 Note: Row 1: Two sides equal (A=B=20), so Isosceles. Row 2: All sides equal (20,20,20), so Equilateral. Row 3: All sides different, so Scalene. Row 4: 13+14=27 < 30, violates triangle inequality.

example_2.sql — Edge Cases

$ Input: Triangles table: +---+---+---+ | A | B | C | +---+---+---+ | 10| 10| 20| | 15| 15| 15| | 7 | 8 | 9 | +---+---+---+

› Output: +---+---+---+---------------+ | A | B | C | triangle_type | +---+---+---+---------------+ | 10| 10| 20| Not A Triangle| | 15| 15| 15| Equilateral | | 7 | 8 | 9 | Scalene | +---+---+---+---------------+

💡 Note: Row 1: 10+10=20, which equals C, so not a valid triangle (needs to be greater than). Row 2: All sides equal. Row 3: All sides different and valid triangle.

example_3.sql — Isosceles Variations

$ Input: Triangles table: +---+---+---+ | A | B | C | +---+---+---+ | 5 | 12| 5 | | 8 | 6 | 6 | | 4 | 4 | 7 | +---+---+---+

› Output: +---+---+---+---------------+ | A | B | C | triangle_type | +---+---+---+---------------+ | 5 | 12| 5 | Isosceles | | 8 | 6 | 6 | Isosceles | | 4 | 4 | 7 | Isosceles | +---+---+---+---------------+

💡 Note: All three rows show different patterns of isosceles triangles: A=C, B=C, and A=B respectively. Each has exactly two equal sides.

Constraints

1 ≤ A, B, C ≤ 100
The table contains at least 1 row
All side lengths are positive integers
Triangle inequality: A + B > C, A + C > B, B + C > A must all be true for valid triangles

Visualization

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Understanding the Visualization

Validate Triangle

Check if three sides can form a valid triangle using triangle inequality

Count Equal Sides

Determine how many sides are equal to each other

Apply Classification

Use the equality pattern to classify the triangle type

Return Result

Output the appropriate triangle classification

Key Takeaway

🎯 Key Insight: Always validate the triangle inequality first, then use equality patterns to classify valid triangles efficiently using SQL CASE statements.

Asked in

a Amazon 25 ⊞ Microsoft 18 G Google 15 f Meta 12

The optimal solution uses a single CASE statement to first validate the triangle inequality theorem, then classify triangles based on equality patterns of their sides. The key insight is checking A + B > C AND A + C > B AND B + C > A first, then using nested conditions to distinguish between Equilateral (all equal), Isosceles (two equal), and Scalene (all different) triangles.

Common Approaches

Approach	Time	Space	Notes
✓ Basic Conditional Classification	O(1)	O(1)	Use nested CASE statements to check each condition sequentially

Basic Conditional Classification — Algorithm Steps

Check triangle inequality: A+B>C AND A+C>B AND B+C>A
If valid, check if all three sides are equal (Equilateral)
If not equilateral, check if any two sides are equal (Isosceles)
If no sides are equal, classify as Scalene
If triangle inequality fails, classify as 'Not A Triangle'

Visualization

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Step-by-Step Walkthrough

Check Triangle Inequality

Verify if A+B>C, A+C>B, and B+C>A

Check Equilateral

If valid triangle, check if A=B=C

Check Isosceles

If not equilateral, check if any two sides are equal

Classify as Scalene

If no sides are equal, it's scalene

Code -

solution.c — C

// SQL query as C string
#include <stdio.h>

const char* getTriangleQuery() {
    return "SELECT A, B, C, "
           "CASE "
           "    WHEN A + B <= C OR A + C <= B OR B + C <= A THEN 'Not A Triangle' "
           "    WHEN A = B AND B = C THEN 'Equilateral' "
           "    WHEN A = B OR B = C OR A = C THEN 'Isosceles' "
           "    ELSE 'Scalene' "
           "END AS triangle_type "
           "FROM Triangles;";
}

int main() {
    printf("%s\n", getTriangleQuery());
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Each row is processed with constant time operations

✓ Linear Growth

Space Complexity

O(1)

No additional space needed beyond the result set

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Basic Conditional Classification — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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