Schedule Fixed-Order Tasks with a Cooldown

Problem Statement

You are given an array of integers tasks representing task IDs that must be processed strictly in the order they appear, and an integer cooldown.

Each task takes exactly one day to complete, and at most one task can be performed per day. Once a task with ID x is completed on day d, another task with the same ID x cannot be scheduled until at least cooldown calendar days have elapsed. That is, the earliest subsequent day that task x can be executed is d + cooldown + 1.

Days where no task can be performed are considered idle days. Return the total number of calendar days needed to execute all tasks in the given order.

Interface

def min_days_to_complete_tasks(tasks: list[int], cooldown: int) -> int:
    pass

Examples

Example 1

Input: tasks = [1, 2, 1, 3, 2, 1], cooldown = 2
Output: 7
Explanation:
- Day 1: Execute task 1 (last ran day 1)
- Day 2: Execute task 2 (last ran day 2)
- Day 3: Idle (task 1 cannot run until day 1 + 2 + 1 = 4)
- Day 4: Execute task 1 (last ran day 4)
- Day 5: Execute task 3 (last ran day 5)
- Day 6: Execute task 2 (earliest allowed was day 2 + 2 + 1 = 5 <= 6)
- Day 7: Execute task 1 (earliest allowed was day 4 + 2 + 1 = 7 <= 7)
Total days taken: 7.

Example 2

Input: tasks = [1, 1, 1], cooldown = 3
Output: 9
Explanation:
- Day 1: Execute task 1
- Days 2-4: Idle
- Day 5: Execute task 1
- Days 6-8: Idle
- Day 9: Execute task 1
Total days taken: 9.

Constraints

• 1 <= len(tasks) <= 2 * 10^5
• 0 <= tasks[i] <= 10^9
• 0 <= cooldown <= 10^5

Edge Cases

• cooldown = 0: Tasks execute back-to-back without any idle days, taking len(tasks) days.
• All tasks distinct: No idle days are ever needed regardless of cooldown value.