Part XII · Algorithm Engineering, Java Practice and Tutorial Publishing
69. Testing, Debugging and Proving DSA Solutions
7 lessons•37 topics•Beginner to Expert
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69.01Outline
Test case strategy
- Empty input
- Singleton
- Duplicate elements
- Already sorted
- Reverse sorted
- Extreme values
- Very large input
69.02Outline
Boundary and adversarial tests
- Off-by-one
- Null references
- Negative coordinates
- Overflow
- Cycles
- Disconnected graphs
69.03Outline
Brute-force oracle
- Generate small cases
- Compare optimized vs brute force
- Exhaustive enumeration
- Differential testing
69.04Outline
Randomized testing
- Property-based test generation
- Reproducible seed
- Shrinking failing inputs
- Invariant checking
69.05Outline
Algorithm-specific checks
- Binary search predicate monotonicity
- Heap invariant
- BST ordering
- DSU connectivity
- Segment tree lazy correctness
69.06Outline
Proof templates
- Loop invariant
- Induction
- Exchange argument
- Contradiction
- Cut property
- DP induction
69.07Outline
Complexity verification
- Count operations
- Detect quadratic behavior
- Recursion depth
- Peak space
- Amortized argument