## Problem Tasks must execute in the given order. Each task has a string ID, and at most one task can execute per day. Between two executions of the same ID, at least `cooldown` complete days must pass. Idle days may be inserted. Return the minimum number of calendar days needed to execute every task without reordering them. For example, with cooldown `2`, executions of the same ID on days `1` and `4` are valid because days `2` and `3` lie between them. ### Function Contract Implement `minimumFixedOrderScheduleDays(tasks, cooldown)`. ### Constraints & Assumptions - `0 <= len(tasks) <= 200,000`. - Task IDs are nonempty ASCII strings. - `0 <= cooldown <= 10^9`. - Day numbering starts at `1`; an empty task list takes `0` days. - The answer may exceed signed 32-bit range. ### Clarifying Questions to Ask - May tasks be reordered? No. - Does cooldown zero allow identical tasks on consecutive days? Yes. - Are idle days counted in the answer? Yes. ```hint Track the last scheduled day For the next task, its day is the larger of the next free day and `lastDay[task] + cooldown + 1`. ``` ### Examples ```text tasks = ["A","A"], cooldown = 2 -> 4 tasks = ["A","B","A"], cooldown = 2 -> 4 tasks = ["A","A","A"], cooldown = 0 -> 3 tasks = [], cooldown = 5 -> 0 ``` ### Evaluation Focus - Preserves fixed task order. - Interprets the number of complete intervening days correctly through `cooldown + 1`. - Handles zero cooldown, empty input, arbitrary string IDs, and large answers. - Runs in `O(n)` expected time with a hash map. ### Extensions to Discuss 1. How does the problem change if tasks may be reordered? 2. How would per-task cooldown values alter the state? 3. How could actual timestamps replace integer days?