Triangle Judgement - Practice Coding Problems

Triangle Judgement - Problem

Database Easy

You have a table Triangle containing the lengths of three line segments.

Write an SQL query to report for every three line segments whether they can form a triangle.

A triangle can be formed if the sum of any two sides is greater than the third side. This must be true for all three combinations:

x + y > z
x + z > y
y + z > x

Return the result table in any order.

Table Schema

Triangle

Column Name	Type	Description
`x` PK	int	Length of first line segment
`y` PK	int	Length of second line segment
`z` PK	int	Length of third line segment

Primary Key: (x, y, z)

Note: Each row contains the lengths of three line segments that need to be tested for triangle formation

Input & Output

Example 1 — Basic Triangle Test

Input Table:

x	y	z
13	15	30
10	20	15

Output:

x	y	z	triangle
13	15	30	No
10	20	15	Yes

💡 Note:

For the first row: 13 + 15 = 28, which is not greater than 30, so it cannot form a triangle.

For the second row: 10 + 20 = 30 > 15, 10 + 15 = 25 > 20, and 20 + 15 = 35 > 10. All conditions are satisfied, so it can form a triangle.

Example 2 — Edge Cases

Input Table:

x	y	z
1	1	1
1	2	3

Output:

x	y	z	triangle
1	1	1	Yes
1	2	3	No

💡 Note:

For equilateral triangle (1,1,1): All sides equal, so 1+1=2 > 1 for all combinations - forms a triangle.

For degenerate case (1,2,3): 1+2=3 which equals the third side, not greater than it - cannot form a triangle.

Constraints

1 ≤ x, y, z ≤ 100
All side lengths are positive integers

Visualization

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Understanding the Visualization

Input

Three line segment lengths

Check

Apply triangle inequality theorem

Result

Yes if triangle, No otherwise

Key Takeaway

🎯 Key Insight: Use CASE WHEN with triangle inequality conditions to validate geometric constraints in SQL

Asked in

A Amazon 15 M Microsoft 12

Use CASE WHEN with triangle inequality conditions: x+y>z AND x+z>y AND y+z>x to determine if three segments can form a triangle.

Table Schema

Triangle

Column Name	Type	Description
`x` PK	int	Length of first line segment
`y` PK	int	Length of second line segment
`z` PK	int	Length of third line segment

Primary Key: (x, y, z)

Note: Each row contains the lengths of three line segments that need to be tested for triangle formation

Common Approaches

Approach	Time	Space	Notes
✓ Conditional Logic with CASE	O(n)	O(1)	Use CASE WHEN to check triangle inequality conditions

Conditional Logic with CASE — Algorithm Steps

Step 1: Select all columns from Triangle table
Step 2: Use CASE WHEN to check all three triangle inequality conditions
Step 3: Return 'Yes' if triangle can be formed, 'No' otherwise

Visualization

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Step-by-Step Walkthrough

Input

Three side lengths x, y, z

Check

Apply triangle inequality

Result

Yes or No for triangle

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through all rows

✓ Linear Growth

Space Complexity

O(1)

Constant extra space for calculations

✓ Linear Space

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Medium Frequency

~8 min Avg. Time

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Ln 1, Col 1

Smart Actions

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Table Schema

Input & Output

Constraints

Visualization

Related Problems

Table Schema

Common Approaches

Conditional Logic with CASE — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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