You are given a time-ordered array `samples`, where `samples[i]` is the function name observed at integer timestamp `i`. Convert this trace into a list of events in the form `(function_name, start_time, end_time)`, where each event represents one maximal contiguous run of the same function. Use half-open intervals `[start_time, end_time)`. For example, if `samples = ["A", "A", "B", "B", "B", "A"]`, the output should be `[("A", 0, 2), ("B", 2, 5), ("A", 5, 6)]`. Follow-up: given an integer `k`, only treat a run as a valid event if the same function appears for at least `k` consecutive timestamps. Runs shorter than `k` should be discarded. Do not merge runs that were separated in the original trace, even if they have the same function name. Implement the transformation and discuss the time and space complexity.