Mastering Black‑Box Tests for Polynomial Add‑Multiply Programs

Black‑box testing concentrates on a program's inputs and outputs, treating the code as an opaque box; by also examining the implementation, testers can design more comprehensive test cases and improve test effectiveness.

Program Overview

The target program computes the sum and product of two univariate polynomials. The input consists of two lines; each line begins with the count of non‑zero terms followed by pairs of coefficient and exponent in descending order. The output also has two lines: the product polynomial first, then the sum polynomial, both listed by descending exponent. A zero polynomial is represented as 0,0.

Example input and expected output are illustrated in the following images:

Implementation Framework

The program uses a linked list to store polynomial terms, which offers flexibility compared with arrays. The main functions are: Creat() – builds the linked list from input data. multiple() – performs polynomial multiplication and returns the result list. add() – performs polynomial addition and returns the result list. PrintLink() – prints the resulting polynomial in the required format.

Function flow diagrams are shown below:

Test Design and Verification

1. Critical Test – Empty Polynomial

Running the program with an empty polynomial causes pointer dereferencing of a NULL head node, leading to corrupted output and a segmentation fault. The fix is to add a check for head->next == NULL before accessing the list.

2. Equivalence‑Class Testing

Addition Function ( add() )

The function must handle three coefficient comparison cases: greater, equal, or smaller. The equal‑coefficient case is tricky because the sum may become zero, requiring the node to be removed and its memory freed.

Multiplication Function ( multiple() )

Multiplication uses two nested while loops to simulate term‑by‑term multiplication, delegating insertion of intermediate results to insert(). The three exponent comparison cases (greater, smaller, equal) mirror those in addition, and when the resulting coefficient is zero, the node must be freed.

3. Loop and Branch Considerations

Branches correspond to equivalence‑class partitions, while loops map to boundary‑value tests. Faults such as non‑terminating loops can cause crashes or infinite execution. An example scenario shows a receiver repeatedly attempting reconnection after a user cancels the operation, because the cancel logic is missing.

Practical Advice for Test Engineers

Continuously question the “why” behind each test case to uncover hidden defects.

Recognize that the absence of failures in a test suite does not guarantee the product is bug‑free; strive for thorough exposure.

Automate repetitive tasks using scripts (batch, shell) when the long‑term cost benefit is positive.

Strengthen coding fundamentals—master at least one language (e.g., C++) and deepen data‑structure knowledge.

Practice problem‑solving on platforms like 牛客网, PTA, OpenJudge, and analyze why submissions are rejected to improve logical thinking and test‑case design.

By following these guidelines, testers can enhance their skill set, design more robust test cases, and contribute effectively to software quality.