Task Scheduler

1. Clarify the problem:

   • The problem requires us to schedule tasks represented by characters in a given string.
   • The tasks need to be executed in a specific order with a cooldown period between two same tasks.
   • We need to determine the minimum number of time units required to execute all the tasks.

2. Analyze the problem:

   • Input: A string of characters representing tasks, and an integer cooldown representing the cooldown period.
   • Output: An integer representing the minimum number of time units required to execute all the tasks.
   • Constraints:
     • The length of the input string will be at most 10^4.
     • The cooldown period will be at most 10^4.

3. Design an algorithm:

   • We can use a greedy approach to solve this problem.
   • First, we need to count the frequency of each task.
   • We can then sort the tasks based on their frequencies in descending order.
   • Next, we iterate through the sorted tasks and execute each task.
   • For each task, we decrement its count and update the cooldown time.
   • If there is a cooldown period remaining, we need to add idle time to the total time.
   • Finally, we return the total time.

4. Explain your approach:

   • We will maintain a dictionary to count the frequency of each task.
   • We will sort the tasks based on their frequencies.
   • We will iterate through the sorted tasks and execute each task.
   • We will update the cooldown time and add idle time if necessary.
   • Finally, we will return the total time.

5. Write clean and readable code:

python

def leastInterval(tasks, cooldown):
    task_counts = {}
    for task in tasks:
        if task in task_counts:
            task_counts[task] += 1
        else:
            task_counts[task] = 1

    sorted_tasks = sorted(task_counts.items(), key=lambda x: x[1], reverse=True)

    total_time = 0
    while sorted_tasks:
        i = 0
        while i <= cooldown:
            if i < len(sorted_tasks) and sorted_tasks[i][1] > 0:
                sorted_tasks[i] = (sorted_tasks[i][0], sorted_tasks[i][1] - 1)
            total_time += 1
            if not any(task[1] > 0 for task in sorted_tasks):
                break
            i += 1

        sorted_tasks.sort(key=lambda x: x[1], reverse=True)

    return total_time

6. Test your code:
   • Let's test the code with the following test cases:
     • Test case 1: tasks = ["A", "A", "A", "B", "B", "B"], cooldown = 2
     • Test case 2: tasks = ["A", "A", "A", "B", "B", "B"], cooldown = 0
     • Test case 3: tasks = ["A", "A", "A", "A", "A", "A", "B", "C", "D", "E", "F", "G"], cooldown = 2

python

print(leastInterval(["A", "A", "A", "B", "B", "B"], 2))  # Output: 8
print(leastInterval(["A", "A", "A", "B", "B", "B"], 0))  # Output: 6
print(leastInterval(["A", "A", "A", "A", "A", "A", "B", "C", "D", "E", "F", "G"], 2))  # Output: 16

7. Optimize if necessary:

   • The current solution has a time complexity of O(n log n) due to the sorting step, where n is the number of tasks.
   • There is no further optimization available for this problem.

8. Handle error cases:

   • The given code assumes the input is valid and doesn't explicitly handle error cases like empty tasks or negative cooldown period. Additional error handling logic can be added to validate the input.

9. Discuss complexity analysis:

   • Time complexity: O(n log n), where n is the number of tasks. The main time-consuming step is the sorting of tasks based on their frequencies.
   • Space complexity: O(n), where n is the number of unique tasks. We use a dictionary to store the task frequencies and a list to store the sorted tasks.