Suggest and apply suitable test data

Algorithm Design and Problem‑Solving: Suggesting and Using Test Data

Why Test Data Is Essential 🎯

When you design an algorithm, you’re essentially writing a recipe. Just as a chef needs to try a dish with different ingredients to ensure it tastes good, you need to run your algorithm with a variety of input data to make sure it behaves correctly, efficiently, and robustly. Good test data helps you:

• Verify correctness (does it give the right answer?)
• Check performance (does it run fast enough?)
• Detect edge‑case bugs (does it handle the smallest or largest inputs?)
• Ensure reliability (does it handle unexpected or invalid data?)

Types of Test Data 📊

1. Typical (average) data – represents what users normally provide.
2. Boundary data – tests the limits of input ranges (e.g., minimum, maximum, just inside/outside limits).
3. Extreme data – very large or very small values to test scalability.
4. Random data – to catch hidden bugs that only appear with unpredictable patterns.
5. Error data – invalid or malformed inputs to test robustness.

How to Choose Test Data for an Algorithm

1. **Understand the problem specification** – note input size limits, data types, and required outputs.
2. **Identify critical values** – e.g., if the algorithm uses a loop from 1 to n, test with n = 0, 1, 2, 1000.
3. **Create a test data matrix** – list each test case with its purpose and expected outcome.
4. **Automate where possible** – use scripts to generate random or boundary data sets.
5. **Document each test case** – include the input, expected output, and reasoning.

Example: Sorting Algorithm Test Data

Suppose we design a quicksort algorithm that sorts an array of integers. Here’s a concise test data table:

Example: Binary Search Test Data

Binary search works on a sorted array. Test data should include cases where the target is present, absent, at the ends, and not in the array at all.

Testing a More Complex Problem: Maximum Subarray

The maximum subarray problem asks for the contiguous sub‑array with the greatest sum. Test data should cover positive numbers, negative numbers, and a mix of both.

1. All positives: e.g. [1, 2, 3, 4] → sum = 10.
2. All negatives: e.g. [-1, -2, -3] → best sum = -1 (single element).
3. Mixed: e.g. [-2, 1, -3, 4, -1, 2, 1, -5, 4] → sum = 6 (sub‑array [4, -1, 2, 1]).
4. Single element: [42] → sum = 42.
5. Large array: generate 10,000 random integers between -1000 and 1000 to test performance.

Practical Tips for Students 🧪

• Write a test harness that automatically runs your algorithm against all test cases and reports failures.
• Use assertions to check that the output matches the expected result.
• Keep a log of test case names, inputs, outputs, and whether they passed.
• When a test fails, debug incrementally – start with the simplest failing case.
• Remember that time complexity matters: for large n, test with n = 10^5 or more to see if your algorithm scales.

Summary of Key Points

1. Test data is like the ingredients for a recipe – you need variety to ensure a good result.
2. Cover typical, boundary, extreme, random, and error cases.
3. Document each test case: input, expected output, and purpose.
4. Automate testing where possible to save time and reduce human error.
5. Use test data to guide algorithm design: if you know the worst‑case input, you can optimise accordingly.