**Approach (brief)** I would create a small, focused unit-test suite that covers boundaries, pathological inputs, algorithmic and numeric stability. Each test includes rationale and an automated assertion (examples in Python/pytest style).**Test cases, why they matter, and assertions**- **Empty list** — function should raise a predictable error (ValueError) or return None.python
with pytest.raises(ValueError):
findMedian([])
- **Single element** — median equals that element.python
assert findMedian([42]) == 42
- **Odd count** — median is middle element after sorting.python
assert findMedian([3,1,2]) == 2
- **Even count** — define behavior: average of two middle values or lower/higher; assert accordingly.python
assert findMedian([1,4,2,3]) == 2.5
- **Already sorted / reverse sorted** — ensures no dependency on input order.python
assert findMedian([1,2,3,4,5]) == 3
assert findMedian([5,4,3,2,1]) == 3
- **Duplicates** — median should handle repeats.python
assert findMedian([2,2,2,2]) == 2
assert findMedian([1,2,2,3]) == 2
- **Negative numbers & mixed signs** — numeric correctness across sign.python
assert findMedian([-5,-1,0,1,3]) == 0
- **Large integers (overflow risk)** — use extremes to reveal sum/average overflow if implemented naïvely.python
big = [2**63-1, 2**63-2] # platform-dependent; use language max ints
assert findMedian(big) == ( (2**63-1 + 2**63-2) / 2 )
- **Floating-point result precision** — assert with tolerance for halves/averages.python
assert math.isclose(findMedian([1,2]), 1.5, rel_tol=1e-9)
- **Very large lists / performance** — assert execution time or non-exhaustive memory usage; use property or timebox.python
with time_limit(0.5):
findMedian(large_random_list_of_1e6)
**Notes on algorithmic/numeric issues** - Tests with extreme ints detect overflow if implementation sums then divides; prefer median by selection or use safe averaging (a + (b - a)/2). - Duplicates and sorted/reversed inputs detect order assumptions. - Timeboxed large-input tests detect O(n log n) vs required O(n) preferences. These automated assertions fit into CI and provide fast, focused regression signals for correctness and stability.