Triangle condition

The triangle is one of the basic geometric figures. However, how to build it? First of all: we need three segments. However, they can not be any segments! They must meet the so-called triangle condition. The triangle condition.

Specification

Input

• \(a, b, c\) - natural numbers, segment lengths, \(a>0\), \(b>0\), \(c>0\).

Output

• TRUE if a triangle can be constructed from the given segments,
• FALSE otherwise.

Solution

In order to build a triangle from three segments, the following condition must be met: the length of each segment is less than the sum of the other two. From this it follows that we have three inequalities to check.

Alternatively, you can also check that the sum of the two smaller segments is greater than the length of the third, longest segment.

Pseudocode

function TriangleCondition(a, b, c):
    1. If a < b + c and b < a + c and c < a + b, then:
        2. Return TRUE
    3. otherwise:
        4. Return FALSE

Block diagram

%%{init: {"flowchart": {"curve": "linear"}, "theme": "neutral"} }%%
flowchart TD
    START(["TriangleCondition(a, b, c)"]) --> K1{"a < b + c
    and
    b < a + c
    and
    c < a + b"}
    K1 -- TRUE --> K2[/Return TRUE/]
    K2 --> STOP([STOP])
    K1 -- FALSE --> K4[/Return FALSE/]
    K4 --> STOP

Implementation

C++

Python