Triangle Judgement - Practice Coding Problems

Triangle Judgement - Problem

Database Easy

🔺 Triangle Judgement

Given a table containing the lengths of three line segments for each row, your task is to determine whether these three segments can form a valid triangle.

The Challenge: In geometry, three line segments can form a triangle if and only if the sum of any two sides is greater than the third side. This is known as the Triangle Inequality Theorem.

Database Schema:

Table: Triangle
+-------------+------+
| Column Name | Type |
+-------------+------+
| x           | int  |
| y           | int  |
| z           | int  |
+-------------+------+
(x, y, z) is the primary key

Goal: Write a SQL query that returns each row with an additional column indicating whether the three segments can form a triangle. Return "Yes" if they can form a triangle, "No" otherwise.

Triangle Rule: For sides a, b, and c to form a triangle:
• a + b > c
• a + c > b
• b + c > a
All three conditions must be satisfied!

Input & Output

example_1.sql — Basic Triangle

$ Input: Triangle table: +---+---+---+ | x | y | z | +---+---+---+ | 3 | 4 | 5 | +---+---+---+

› Output: +---+---+---+----------+ | x | y | z | triangle | +---+---+---+----------+ | 3 | 4 | 5 | Yes | +---+---+---+----------+

💡 Note: This is a classic 3-4-5 right triangle. All conditions are satisfied: 3+4=7>5, 3+5=8>4, 4+5=9>3

example_2.sql — Invalid Triangle

$ Input: Triangle table: +---+---+---+ | x | y | z | +---+---+---+ | 1 | 1 | 3 | +---+---+---+

› Output: +---+---+---+----------+ | x | y | z | triangle | +---+---+---+----------+ | 1 | 1 | 3 | No | +---+---+---+----------+

💡 Note: The sum of the two smaller sides (1+1=2) is not greater than the largest side (3), violating the triangle inequality

example_3.sql — Multiple Rows

$ Input: Triangle table: +---+---+---+ | x | y | z | +---+---+---+ | 13| 15| 30| | 10| 20| 15| +---+---+---+

› Output: +---+---+---+----------+ | x | y | z | triangle | +---+---+---+----------+ | 13| 15| 30| No | | 10| 20| 15| Yes | +---+---+---+----------+

💡 Note: First row: 13+15=28 < 30, so No. Second row: all conditions satisfied (10+20>15, 10+15>20, 20+15>10), so Yes

Visualization

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Understanding the Visualization

Measure the Segments

We have three line segments with lengths x, y, and z

Test First Condition

Check if segments x and y together can span more than segment z

Test Remaining Conditions

Verify the other two inequality conditions

Form Triangle or Reject

If all conditions pass, segments can form a triangle

Key Takeaway

🎯 Key Insight: Three line segments can form a triangle if and only if the sum of any two sides is strictly greater than the third side. This fundamental geometric principle ensures the segments can actually connect to form a closed triangular shape.

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through all rows in the table

✓ Linear Growth

Space Complexity

O(1)

No additional space needed beyond the result set

✓ Linear Space

Constraints

All side lengths x, y, z are positive integers
1 ≤ x, y, z ≤ 100
The table contains at least 1 row
Key Rule: For a valid triangle, sum of any two sides must be strictly greater than the third side

Asked in

a Amazon 25 ⊞ Microsoft 18 ○ Oracle 15 IBM IBM 12

The optimal solution uses a single CASE statement with the triangle inequality theorem: check if (x + y > z) AND (x + z > y) AND (y + z > x). This one-pass approach efficiently determines triangle validity in O(1) time per row with clear, readable SQL logic.

Common Approaches

Approach	Time	Space	Notes
✓ Basic SQL with Explicit Conditions	O(n)	O(1)	Check each triangle inequality condition separately using multiple AND conditions

Basic SQL with Explicit Conditions — Algorithm Steps

Check if x + y > z
Check if x + z > y
Check if y + z > x
Return 'Yes' only if all three conditions are true
Return 'No' otherwise

Visualization

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Step-by-Step Walkthrough

Check First Condition

Verify if x + y > z

Check Second Condition

Verify if x + z > y

Check Third Condition

Verify if y + z > x

Final Decision

Return 'Yes' only if all conditions pass

Code -

solution.c — C

// SQL Solution (C string for demonstration)
char* sqlQuery = "\
SELECT x, y, z, \
       CASE \
           WHEN (x + y > z) AND (x + z > y) AND (y + z > x) \
           THEN 'Yes' \
           ELSE 'No' \
       END AS triangle \
FROM Triangle;";

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through all rows in the table

✓ Linear Growth

Space Complexity

O(1)

No additional space needed beyond the result set

✓ Linear Space

Constraints

All side lengths x, y, z are positive integers
1 ≤ x, y, z ≤ 100
The table contains at least 1 row
Key Rule: For a valid triangle, sum of any two sides must be strictly greater than the third side

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🔺 Triangle Judgement

Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

Basic SQL with Explicit Conditions — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

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