Equivalence Class And Boundary Test Design

What's being tested

These questions test equivalence-class partitioning and boundary-value analysis for algorithm and data-structure problems. You must reduce a huge input space into representative valid, invalid, empty, minimal, maximal, duplicate, and adversarial cases, then state precise expected outputs. Strong answers connect each case to a likely implementation failure rather than listing random examples.

Patterns & templates

• Equivalence classes — partition inputs by behavior: empty, singleton, ordinary, duplicate-heavy, invalid, already processed, and impossible-result cases.

• Boundary testing — check values at, just below, and just above limits: 0, 1, n, n-1, maximum size, and overflow-prone magnitudes.

• Array templates — include empty arrays, one element, sorted and reverse-sorted inputs, all-equal values, negatives, repeated values, and answers at both endpoints.

• String templates — test empty strings, one character, whitespace, mixed case, punctuation, repeated characters, Unicode assumptions, and prefixes that almost match.

• Expected outputs — verify ordering, multiplicity, indices versus values, stable tie behavior, and whether the function mutates its input.

• Complexity-aware adversaries — use large monotonic, duplicate-heavy, or highly unbalanced inputs to expose accidental O(n²) behavior or recursion-depth failures.

• Oracle design — derive expected results independently, preferably with a simple brute-force implementation for small inputs; avoid duplicating the candidate algorithm.

Common pitfalls

Pitfall: Testing only ordinary examples misses empty inputs, singleton behavior, duplicate handling, and “no solution” semantics.

Pitfall: Saying “test large inputs” without specifying the exact constraint boundary fails to distinguish n = limit from n = limit + 1.

Pitfall: Confusing invalid-input behavior with a valid empty result; explicitly state whether the API returns an error, sentinel, exception, or empty collection.

Practice these

The practice cards below cover the canonical variants — solve all of them and time yourself.