Question

A friend of yours has written a function called common_name that takes two strings as input. The first is the one- or two-letter symbol for a chemical element, such as "He" or "Fe". The second is the two-letter international code for a language, such as "EN" (English) or "DE" (Deutsch, that is, German). You have been told that the function handles 106 elements and 26 languages. If you don't want to test every element with every language, then how many different inputs do you have to give it to feel confident that it works correctly? What assumptions are you making about those inputs in doing your calculation?

Short answer

You need to test 132 different inputs to ensure coverage of all elements and languages.

Step-by-step solution

Understand the Problem

We are asked to determine how many different input combinations we need to test for the `common_name` function, which takes two arguments: a chemical element symbol and a language code. The goal is to ensure the function is tested properly without having to try every possible combination.

Determine Total Combinations

The elements have a total of 106 different possible symbols, and the languages have 26 different possible codes. To find the total number of possible combinations, multiply the number of element symbols by the number of language codes: \(106 \times 26 = 2756\) combinations.

Consider Testing Strategy

Testing every single combination is not practical due to the large number involved. Instead, we can assume that a satisfactory test would involve ensuring every input type (element and language) is covered at least once. This assumption will sharply reduce the number of necessary tests.

Calculate Minimum Input Coverage

To ensure that every element and language code is tested, we should test 106 different element symbols and 26 different language codes. This means we would need at least \(106 + 26 = 132\) unique test inputs if each element and language are paired with at least one instance of the other.

Conclusion

Testing 132 different inputs should provide confidence that the function works correctly. We are making an assumption that each individual element symbol and language code functions properly when tested with at least one counterpart from the other category.

Key concepts

Function Testing

Function testing involves verifying that a function behaves as expected across a range of inputs. For functions like `common_name`, it is crucial to ensure that it can handle combinations of input elements effectively.

Function testing typically involves the following steps:

• Identify the range of valid inputs that the function can accept.
• Design test cases that cover normal use, edge cases, and erroneous inputs.
• Run these test cases and verify that the function produces the correct outputs.

By systematically testing each possible input or by using a subset that effectively covers all cases, you can gain confidence in the function's reliability and accuracy.

Input Combinations

When testing a function like `common_name`, it's important to think about input combinations. The more combinations there are, the more potential there is for bugs.

The `common_name` function has a vast array of possible inputs, with 106 chemical element symbols and 26 language codes. This results in a total of \[ 106 \times 26 = 2756 \] possible input combinations.

Testing every possible combination would be exhaustive and time-consuming. Instead, a strategic approach should be adopted. Evaluate whether testing a subset of these combinations will effectively reveal any errors or bugs. The goal is to ensure comprehensive testing without testing every single possibility.

Test Strategy

A solid test strategy is key when dealing with functions that require many combinations of inputs. Instead of testing all 2756 input combinations for `common_name`, a more strategic approach is recommended.

Here are a few strategies to consider:

• Boundary Testing: Identify and test the edge cases of input values.
• Equivalence Partitioning: Group inputs that should be processed in the same way and test a representative from each group.
• Pairwise Testing: Reduce the number of combinations by ensuring that each pair of input parameters is tested at least once.

These strategies help in reducing the overall number of tests, while still providing a good coverage and understanding of how the function performs in different scenarios.

Programming

Programming functions like `common_name` require careful consideration of their design and expected input combinations. Each function needs to be robust and handle a variety of inputs smoothly.

When programming such a function:

• Consider the possible range of inputs and validate them appropriately. This avoids errors and ensures the function remains robust.
• Think about edge cases and how the function should handle unexpected inputs.
• Implement error handling to provide meaningful responses rather than having the function 'break'.

By integrating thorough testing into the development process, a programmer can ensure that each function works as intended, providing reliability and resilience in real-world applications.