Maximize optional tasks under daily limit

You are given an integer limit and two integer arrays required and optional of length n. For each day i, you must schedule required[i]. If time remains on that day (not exceeding limit), you may schedule at most one optional task; each optional task can be used at most once and can be assigned to any day. Goal: maximize the number of optional tasks scheduled across n days without exceeding the daily limit. Return: ( 1) the maximum count of scheduled optional tasks, and ( 2) one valid assignment of optional tasks to days (or indicate none for a day). Example: limit = 7 required = [4, 5, 2, 4] optional = [5, 6, 3, 4] One optimal plan schedules 2 optional tasks. Answer the following: - Describe an efficient algorithm, prove why it is correct, and analyze time and space complexity. - Implement the algorithm in the language of your choice. - How would your approach change if each optional task were tied to a specific day (i.e., optional[i] can only be used on day i)? - How would you handle cases where some required[i] > limit? - How would you generalize if up to k optional tasks could be scheduled per day?