This question evaluates algorithmic problem-solving and data-structure knowledge, specifically competencies in array traversal, frequency counting, and analysis of time-space complexity and optimization trade-offs.

Given an unsorted integer array, write functions to: (a) find the minimum value; and (b) find any value that occurs most frequently (if multiple values tie for highest frequency, return any one). Provide a straightforward baseline, then analyze its time and space complexity. Follow-up: Reduce running time by trading additional memory (e.g., using auxiliary data structures); describe the trade-offs and implement the improved version.