← Mastercard Interview Insights
My first instinct was two separate linear scans, which works but doubles the comparisons.
Start by clarifying the problem constraints (e.g., array size, whether it can be empty, data types) and then present the optimal pairwise comparison algorithm that finds both min and max in about 3n/2 comparisons. Explain the algorithm step-by-step, analyze its time complexity, and compare it to the naive approach to highlight the efficiency gain.
Pro tip: Mention that for small arrays (n <= 2), the naive approach is actually optimal, and for general n, the pairwise method reduces comparisons by ~25% compared to the naive 2n-2 approach. This shows you understand edge cases and practical trade-offs.
Ask about array size, whether it can be empty, if elements are distinct, and if there are any memory constraints. This ensures you understand the problem fully before diving into the solution.
Explain that initializing min and max to the first element and then comparing each subsequent element to both min and max takes 2(n-1) comparisons in the worst case. This sets a baseline for optimization.
Describe how to process elements in pairs: compare the two elements of each pair to each other (1 comparison), then compare the smaller to the current min and the larger to the current max (2 comparisons per pair). Handle the case of an odd number of elements by comparing the last element to both min and max (2 comparisons).
Show that for n even, total comparisons = 3n/2 - 2; for n odd, total comparisons = 3(n-1)/2 + 2 = (3n-1)/2. Emphasize that this is optimal and the time complexity remains O(n).
Mention handling of empty array (return null or throw exception), single element (min=max=element), and two elements (1 comparison). Also note that for small n, the naive approach may be simpler and equally efficient.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.