Equivalence partitioning and boundary value analysis in Software Engineering - Time & Space Complexity

Time Complexity: Equivalence partitioning and boundary value analysis

O(n) exhaustive, O(p + b) EP+BVA

Understanding Time Complexity

When studying equivalence partitioning and boundary value analysis, it is important to understand how these techniques reduce the number of test cases compared to exhaustive testing.

We want to know how test case count grows relative to the input domain size.

Scenario Under Consideration

Compare exhaustive testing versus partition-based testing for a function with a defined input range.

Exhaustive testing:
    for each value in input_domain:          -- O(n)
        run test(value)

Partition + Boundary testing:
    partitions = split_into_classes(input_domain)  -- O(1)
    for each partition in partitions:               -- O(p)
        test one representative value
    for each boundary in boundaries:               -- O(b)
        test boundary value

Exhaustive testing checks every possible value. Partition and boundary testing checks a fixed number of carefully selected values.

Identify Repeating Operations

Look at what scales in each approach.

• Exhaustive: The test loop runs once per possible input value. For age 1-120, that is 120 tests for valid inputs alone.
• Partition + Boundary: The number of partitions (p) and boundaries (b) is determined by the specification, not the range size. Doubling the range does not double the tests.

How Execution Grows With Input

As the valid range grows, exhaustive testing grows linearly but partition testing stays constant.

Valid Range Size (n)	Exhaustive Tests	EP + BVA Tests
10 (age 1-10)	10+	9 (3 partition + 6 boundary)
120 (age 1-120)	120+	9
10,000 (ID 1-10000)	10,000+	9

Pattern observation: EP + BVA test count depends on the number of partitions and boundaries, not the range size. It is essentially O(1) relative to domain size.

Final Time Complexity

Exhaustive Testing: O(n) where n is the domain size

EP + BVA: O(p + b) where p is partitions and b is boundary values — typically constant for a given specification

This is why EP and BVA are standard techniques: they provide strong defect detection with a fixed, small number of tests regardless of input range size.

Common Mistake

[X] Wrong: "More test cases always means better testing."

[OK] Correct: Testing age=25 and age=50 both exercise the same valid partition. The second test adds time but no additional defect detection. EP and BVA maximize coverage per test case by selecting values that represent distinct behaviors.

Interview Connect

EP and BVA are among the most commonly asked testing techniques in QA and SDET interviews. Being able to derive a test set from a specification and explain why each value was chosen demonstrates strong testing fundamentals.

Self-Check

A function accepts a discount percentage from 0 to 100. How many equivalence partitions exist? What are the boundary values you would test?

Practice

1. Which of the following best describes equivalence partitioning in software testing?

easy

A. Running all possible input combinations exhaustively

B. Testing only the maximum input value of a range

C. Checking the software's response to invalid inputs only

D. Dividing input data into groups where test cases represent each group

Solution

1. Step 1: Understand equivalence partitioning concept

   Equivalence partitioning divides inputs into groups where all inputs in a group are expected to behave similarly.

2. Step 2: Match description to options

   Dividing input data into groups where test cases represent each group correctly states this grouping approach. Other options describe different testing ideas.

3. Final Answer:

   Dividing input data into groups where test cases represent each group -> Option D

4. Quick Check:

   Equivalence partitioning = Group inputs [OK]

Hint: Group inputs by behavior to reduce tests [OK]

Common Mistakes:

• Confusing equivalence partitioning with boundary value analysis
• Thinking it tests only invalid inputs
• Assuming it requires exhaustive testing

2. Which of the following is the correct boundary value test inputs for a field accepting integers from 1 to 10 inclusive?

easy

A. 1, 2, 9, 10

B. 1, 5, 10

C. 0, 1, 10, 11

D. 0, 5, 10

Solution

1. Step 1: Identify boundary values for range 1 to 10

   Boundaries are the edges: minimum (1), maximum (10), and just outside edges (0 and 11).

2. Step 2: Check options for correct boundary inputs

   0, 1, 10, 11 includes 0 (just below min), 1 (min), 10 (max), and 11 (just above max), which is correct for boundary testing.

3. Final Answer:

   0, 1, 10, 11 -> Option C

4. Quick Check:

   Boundary values = edges and just outside [OK]

Hint: Test edges plus one inside and outside values [OK]

Common Mistakes:

• Testing only valid inputs ignoring just outside boundaries
• Choosing random middle values instead of edges
• Missing one side of the boundary

3. Consider a function that accepts an integer input from 1 to 5 inclusive. Which set of test inputs covers both equivalence partitioning and boundary value analysis?

medium

A. [0, 1, 3, 5, 6]

B. [1, 2, 3, 4, 5]

C. [1, 5]

D. [2, 3, 4]

Solution

1. Step 1: Identify equivalence partitions and boundaries

   Partitions: invalid below (<=0), valid (1-5), invalid above (>=6). Boundaries: 1 and 5 plus just outside 0 and 6.

2. Step 2: Check which option covers all partitions and boundaries

   [0, 1, 3, 5, 6] includes 0 (below), 1 (min boundary), 3 (valid middle), 5 (max boundary), and 6 (above), covering partitions and boundaries.

3. Final Answer:

   [0, 1, 3, 5, 6] -> Option A

4. Quick Check:

   Partitions + boundaries = test edges and groups [OK]

Hint: Include invalid, valid, and boundary values [OK]

Common Mistakes:

• Ignoring invalid partitions
• Testing only boundaries without middle values
• Choosing only valid inputs

4. A tester wrote these test inputs for a field accepting values 10 to 20 inclusive: [9, 10, 15, 20, 21]. The test failed to catch a bug at input 21. What is the likely mistake?

medium

A. They only tested valid inputs and ignored invalid ones

B. They did not include invalid inputs below 10

C. They missed testing the exact boundary values

D. They did not test the boundary just above the max value correctly

Solution

1. Step 1: Analyze test inputs and bug location

   Inputs include 9 (below min), 10 (min), 15 (middle), 20 (max), and 21 (just above max). Bug at 21 means boundary above max was tested.

2. Step 2: Identify mistake causing bug miss

   Since bug was missed at 21, likely the test did not properly check or handle the boundary just above max, possibly due to incorrect validation or test setup.

3. Final Answer:

   They only tested valid inputs and ignored invalid ones -> Option A

4. Quick Check:

   Boundary above max must be tested carefully [OK]

Hint: Check boundaries just outside valid range carefully [OK]

Common Mistakes:

• Assuming testing 21 is enough without checking handling
• Ignoring off-by-one errors at boundaries
• Not validating test setup correctness

5. You have a form field that accepts ages from 18 to 60 inclusive. Using equivalence partitioning and boundary value analysis, which of the following test sets is the most effective to detect input errors?

hard

A. [18, 19, 20, 59, 60]

B. [17, 18, 30, 60, 61]

C. [18, 30, 60]

D. [16, 18, 60, 62]

Solution

1. Step 1: Define equivalence partitions and boundaries for age 18-60

   Partitions: invalid below 18, valid 18-60, invalid above 60. Boundaries: 18 (min), 60 (max), and just outside 17 and 61.

2. Step 2: Evaluate options for coverage

   [17, 18, 30, 60, 61] includes 17 (below min), 18 (min), 30 (valid middle), 60 (max), and 61 (above max), covering all partitions and boundaries effectively.

3. Final Answer:

   [17, 18, 30, 60, 61] -> Option B

4. Quick Check:

   Test invalid, valid, and boundary values for best coverage [OK]

Hint: Test just below, at, inside, and just above boundaries [OK]

Common Mistakes:

• Ignoring invalid partitions
• Testing only valid inputs
• Missing boundary values just outside range