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Problem
Table: Triangle
+-------------+------+
| Column Name | Type |
+-------------+------+
| x | int |
| y | int |
| z | int |
+-------------+------+
In SQL, (x, y, z) is the primary key column for this table.
Each row of this table contains the lengths of three line segments.
Report for every three line segments whether they can form a triangle.
Return the result table in any order.
Example
Output
Try it YourSelf
Solution
To assess the validity of triangles defined by sets of three values (x, y, z), the approach involves employing a SQL query on the 'Triangle' table. The query utilizes a CASE statement to evaluate the conditions of the triangle inequality theorem, determining whether the sum of any two sides is greater than the length of the third side. The result will be a clear classification of each set as either forming a valid ('Yes') or invalid ('No') triangle, providing a straightforward analysis of the geometric properties within the 'Triangle' dataset."
SELECT x, y, z, CASE WHEN x + y > z AND y + z > x AND x + z > y THEN 'Yes' ELSE 'No' end triangle FROM Triangle
Let's break down the SQL query step by step.
Step 1: SELECT Statement
This query selects columns x
, y
, and z
from the triangle
table and adds a new column named triangle
. The CASE
statement checks whether the given set of values (x, y, z) satisfies the conditions for forming a triangle.
Step 2: Evaluate the CASE statement
The conditions within the WHEN
clause check whether the sum of any two sides is greater than the third side. The conditions are:
CASE WHEN x + y > z AND y + z > x AND x + z > y THEN 'Yes' ELSE 'No'
x + y > z
: The sum of sidex
and sidey
is greater than sidez
.y + z > x
: The sum of sidey
and sidez
is greater than sidex
.x + z > y
: The sum of sidex
and sidez
is greater than sidey
.
If all three conditions are true, then the CASE
statement evaluates to 'Yes,' indicating that the given values can form a valid triangle.
If any of the conditions is false, the ELSE
clause is triggered, and the CASE
statement evaluates to 'No,' indicating that the values cannot form a valid triangle.
Final Output:
+----+----+----+----------+ | x | y | z | triangle | +----+----+----+----------+ | 13 | 15 | 30 | No | | 10 | 20 | 15 | Yes | +----+----+----+----------+
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