Triangle Judgement

Given three line segments, determine if they can form a valid triangle. This is a fundamental problem in geometry and computer graphics, with applications in collision detection, rendering, and geometric algorithms.

Problem Description

You are given three non-negative integers, representing the lengths of three line segments. Your task is to write a function or program that determines whether these three lengths can form a valid triangle.

A triangle can be formed by three line segments if and only if the sum of the lengths of any two sides is strictly greater than the length of the third side.

Key Requirements:

• The function should accept three numerical inputs representing the lengths of the sides.
• The function should return a boolean value: true if a triangle can be formed, and false otherwise.

Expected Behavior:

• If all three triangle inequality conditions are met, the result should be true.
• If any of the triangle inequality conditions are not met, the result should be false.

Edge Cases to Consider:

• What happens if one or more of the side lengths are zero?
• What happens if the sum of two sides is exactly equal to the third side? (This forms a degenerate triangle, which is typically not considered a "valid" triangle in most geometric contexts.)

Examples

Example 1:

Input: a = 3, b = 4, c = 5
Output: true
Explanation:
3 + 4 > 5 (7 > 5) - True
3 + 5 > 4 (8 > 4) - True
4 + 5 > 3 (9 > 3) - True
All conditions are met, so a triangle can be formed.

Example 2:

Input: a = 1, b = 2, c = 5
Output: false
Explanation:
1 + 2 > 5 (3 > 5) - False
Since one condition fails, a triangle cannot be formed. The other conditions are:
1 + 5 > 2 (6 > 2) - True
2 + 5 > 1 (7 > 1) - True

Example 3: (Degenerate Triangle)

Input: a = 2, b = 3, c = 5
Output: false
Explanation:
2 + 3 > 5 (5 > 5) - False
The sum of two sides is equal to the third side, forming a straight line, not a valid triangle.

Example 4: (Zero Length Side)

Input: a = 0, b = 4, c = 5
Output: false
Explanation:
0 + 4 > 5 (4 > 5) - False
A side with zero length cannot form a triangle.

Constraints

• The lengths of the sides will be non-negative integers.
• The maximum value for any side length will be 1000.
• The input will consist of exactly three numerical values.

Notes

• Remember the definition of a "valid" triangle: the sum of any two sides must be strictly greater than the third side.
• Consider the mathematical properties of triangle inequalities carefully.
• The order of the input lengths does not matter.