Find mode or minimum with time-space tradeoffs

For an unsorted array of integers, implement two functions: (1) return the minimum value; (2) return the value that appears most frequently (the mode). For the mode, compare a sorting-based approach with a hash-map counting approach, and, if the value range is known and small, a counting-array approach. Discuss the time–space tradeoffs, how to reduce runtime by using more space, and how your choices change under streaming input or strict memory limits.