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In the world of programming, logic is the guiding principle that powers the flow of an application. When approaching a problem such as determining if three values can be the sides of a triangle, clear and systematic thinking becomes essential. The logic involves defining a sequence of operations, usually broken down into clear steps to achieve a result. For this problem, it starts with understanding the triangle inequality theorem, which serves as the foundation of the logic used here. This theorem provides explicit conditions that must be satisfied for any set of three numbers to actually form a triangle. By systematically checking these conditions one by one, starting with the smallest sum and moving to larger sums, you ensure that the logic flows in a correct and ordered manner.

Conditional statements are the building blocks of decision-making in programming. They enable a program to execute different codes based on the evaluation of a condition, thus allowing dynamic decision processes. Here, conditional statements are used to verify each condition outlined by the triangle inequality theorem.

• First, the program checks if the sum of the first two numbers is greater than the third.
• Next, it evaluates whether the sum of the first and third numbers surpasses the second.
• Lastly, it ensures the sum of the second and third numbers is greater than the first.

These if-else constructs are critical because they decide the pathway the program should take, either confirming the possibility of a triangle or denying it if any condition is unsatisfied.

Input validation is a crucial step to ensure that the application receives correct and usable data, safeguarding the logic and calculations that follow. When users provide input, it could easily be erroneous, like zeros in this scenario, which do not make sense as sides of a triangle.

• The program should prompt users until they provide valid non-zero input.
• Implement checks to reject zero or negative numbers and reprompt the user.
• Alert the user politely about invalid entries to guide correct input collection effectively.

This careful scrutiny at the input stage prevents logic errors later on and avoids unwarranted outcomes or crashes, ensuring smooth execution.

Algorithm design refers to constructing a clear plan that outlines how a problem will be solved in a structured series of actions. In this exercise, designing an algorithm involves laying out an explicit set of steps to determine triangle validity.

• Begin by prompting and retrieving the three non-zero input values from the user.
• Perform input validation to ensure data correctness.
• Utilize conditional statements to systematically evaluate the triangle inequality conditions.
• Output the result, stating clearly whether the inputs can form a triangle or not.

An effective algorithm efficiently navigates through each of these steps, minimizing unnecessary calculations and ensuring that it promptly informs the user of the result according to the defined logic.