Design Task Manager

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ArraysGreedy AlgorithmsDynamic Programming

There is a task management system that allows users to manage their tasks, each associated with a priority. The system should efficiently handle adding, modifying, executing, and removing tasks.

Implement the TaskManager class:

TaskManager(vector<vector<int>>& tasks) initializes the task manager with a list of user-task-priority triples. Each element in the input list is of the form [userId, taskId, priority], which adds a task to the specified user with the given priority.
void add(int userId, int taskId, int priority) adds a task with the specified taskId and priority to the user with userId. It is guaranteed that taskId does not exist in the system.
void edit(int taskId, int newPriority) updates the priority of the existing taskId to newPriority. It is guaranteed that taskId exists in the system.
void rmv(int taskId) removes the task identified by taskId from the system. It is guaranteed that taskId exists in the system.
int execTop() executes the task with the highest priority across all users. If there are multiple tasks with the same highest priority, execute the one with the highest taskId. After executing, the taskId is removed from the system. Return the userId associated with the executed task. If no tasks are available, return -1.

Note that a user may be assigned multiple tasks.

Example 1:

Input:
["TaskManager", "add", "edit", "execTop", "rmv", "add", "execTop"]
[[[[1, 101, 10], [2, 102, 20], [3, 103, 15]]], [4, 104, 5], [102, 8], [], [101], [5, 105, 15], []]

Output:
[null, null, null, 3, null, null, 5]

Explanation

TaskManager taskManager = new TaskManager([[1, 101, 10], [2, 102, 20], [3, 103, 15]]); // Initializes with three tasks for Users 1, 2, and 3.
taskManager.add(4, 104, 5); // Adds task 104 with priority 5 for User 4.
taskManager.edit(102, 8); // Updates priority of task 102 to 8.
taskManager.execTop(); // return 3. Executes task 103 for User 3.
taskManager.rmv(101); // Removes task 101 from the system.
taskManager.add(5, 105, 15); // Adds task 105 with priority 15 for User 5.
taskManager.execTop(); // return 5. Executes task 105 for User 5.

Constraints:

1 <= tasks.length <= 10⁵
0 <= userId <= 10⁵
0 <= taskId <= 10⁵
0 <= priority <= 10⁹
0 <= newPriority <= 10⁹
At most 2 * 10⁵ calls will be made in total to add, edit, rmv, and execTop methods.
The input is generated such that taskId will be valid.

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What are the primary functionalities and use cases this task manager should support? Can you provide a few example scenarios?
What is the expected scale of the task manager in terms of the number of tasks, users, and concurrent operations?
What are the data types for the task properties (e.g., task ID, title, description, due date, priority, status, assignee)? Are there any specific constraints on their values, like maximum length for strings or valid ranges for dates/priorities?
How should the task manager handle errors or exceptions, such as invalid input or task dependencies?
What are the specific output formats and data structures expected for different operations (e.g., creating a task, retrieving a task, listing tasks, filtering tasks)? Do you have specific preferences or constraints regarding the data structures used?

Brute Force Solution

Approach

The brute force method for a task manager involves trying every possible combination of how tasks can be scheduled. This approach doesn't focus on being smart or efficient; instead, it simply explores all potential options until it finds the best one according to the given criteria.

Here's how the algorithm would work step-by-step:

Start with the first possible schedule: Do task A first, then task B, then task C, and so on.
Check if this schedule meets all the requirements (like deadlines, dependencies, etc.).
If it doesn't, move on to the next possible schedule, such as task B first, then task A, then task C, and so on.
Continue generating every single possible schedule, one after another.
For each schedule, carefully check if it violates any rules or constraints that were given.
If a schedule meets all the requirements, save it as a valid option.
Once all possible schedules have been checked, compare all the valid options that were saved.
Choose the best schedule from the saved options, based on whatever makes a schedule 'good' (e.g., shortest total time, fewest missed deadlines).

Code Implementation

def design_task_manager_brute_force(tasks, deadlines, dependencies):
    import itertools

    number_of_tasks = len(tasks)
    all_possible_schedules = list(itertools.permutations(range(number_of_tasks)))
    valid_schedules = []
    best_schedule = None

    for schedule in all_possible_schedules:
        is_valid = True

        # Check if the schedule meets all the requirements
        for task_index in range(number_of_tasks):
            task_id = schedule[task_index]
            if deadlines[task_id] < task_index + 1:
                is_valid = False
                break

            # Check the dependencies for each task
            for dependency in dependencies[task_id]:
                if dependency in schedule[task_index:]:
                    is_valid = False
                    break

            if not is_valid:
                break

        if is_valid:
            valid_schedules.append(schedule)

    # Choose the best schedule from the saved options
    if valid_schedules:
        best_schedule = valid_schedules[0]

        #Find the schedule that makes the most deadlines
        for schedule in valid_schedules:
            met_deadlines_best_schedule = 0
            met_deadlines_current_schedule = 0

            for task_index in range(number_of_tasks):
                task_id = best_schedule[task_index]
                if deadlines[task_id] >= task_index + 1:
                    met_deadlines_best_schedule += 1

                task_id = schedule[task_index]
                if deadlines[task_id] >= task_index + 1:
                    met_deadlines_current_schedule += 1

            if met_deadlines_current_schedule > met_deadlines_best_schedule:
                best_schedule = schedule

    #Return the best possible schedule
    return best_schedule

Big(O) Analysis

Time Complexity

O(n! * m) – The brute force approach considers all possible orderings (permutations) of the n tasks. Generating all permutations of n tasks takes O(n!) time. For each permutation, we need to validate if it satisfies the given constraints which may include dependencies and deadlines. Verifying if a single permutation meets all requirements takes O(m) time, where m represents the number of dependencies and constraints to check. Therefore, the overall time complexity is O(n! * m).

Space Complexity

O(N!) – The algorithm generates every possible schedule. To store valid options, it potentially needs to save up to N! (N factorial) schedules, where N is the number of tasks. Each schedule consists of N tasks, contributing to the space. Thus, the auxiliary space required grows factorially with the input size, and we need to store an intermediate list of valid schedules using O(N!).

Optimal Solution

Approach

We will design a system to manage tasks, focusing on efficiency and organization. The core idea is to use data structures that allow for quick retrieval and prioritization of tasks, ensuring the most important ones are handled first.

Here's how the algorithm would work step-by-step:

First, define what a task is: What information do we need to store about each task, like its name, description, priority, and due date?
Next, decide how to store the tasks. A key organizational piece is using a way to automatically sort them by priority, so we always know which tasks need immediate attention. Think of it as a constantly updated to-do list where important tasks float to the top.
Now, consider how to add new tasks to the system. We need a process that takes the task's information and puts it in the right place within our sorted storage.
We need to figure out how to quickly find a specific task, perhaps by its name. A system for quickly looking up tasks is essential.
Also, think about how to update the details of a task, like changing its due date or priority.
Finally, consider how to remove tasks from the system once they are completed. The system should automatically remove completed tasks.

Code Implementation

import heapq

class Task:
    def __init__(self, task_name, task_description, task_priority, task_due_date):
        self.task_name = task_name
        self.task_description = task_description
        self.task_priority = task_priority
        self.task_due_date = task_due_date

    def __lt__(self, other_task):
        # Prioritize tasks based on priority.
        return self.task_priority < other_task.task_priority

class TaskManager:
    def __init__(self):
        self.tasks = []  # Use a heap to store tasks and maintain priority.
        self.task_index = {}

    def add_task(self, task_name, task_description, task_priority, task_due_date):
        task = Task(task_name, task_description, task_priority, task_due_date)
        heapq.heappush(self.tasks, task)
        self.task_index[task_name] = task

    def get_task(self, task_name):
        return self.task_index.get(task_name)

    def update_task(self, task_name, new_description=None, new_priority=None, new_due_date=None):
        task = self.get_task(task_name)
        if task:
            if new_description is not None:
                task.task_description = new_description
            if new_priority is not None:
                task.task_priority = new_priority
                # Re-heapify if priority changes to maintain the heap property.
                self.tasks = list(heapq.heapify(self.tasks))
            if new_due_date is not None:
                task.task_due_date = new_due_date

    def remove_task(self, task_name):
        # Removing from heap requires rebuilding the heap.
        task = self.get_task(task_name)
        if task:
            self.tasks.remove(task)
            del self.task_index[task_name]
            heapq.heapify(self.tasks)

    def get_next_task(self):
        # Returns the highest priority task without removing it.
        if self.tasks:
            return heapq.nsmallest(1, self.tasks)[0]
        else:
            return None

    def complete_task(self, task_name):
        # Remove the task after completion.
        task = self.get_task(task_name)

        if task:
            self.remove_task(task_name)

Big(O) Analysis

Time Complexity

O(log n) – The task manager prioritizes tasks, suggesting the use of a priority queue or a similar data structure like a heap. Adding a new task to the system involves inserting it into this priority queue, which requires maintaining the heap property. The time complexity of insertion in a heap is O(log n), where n is the number of tasks currently in the queue. Similarly, updating or removing tasks, and potentially retrieving tasks by priority, also leverage the heap's logarithmic properties, leading to an overall time complexity of O(log n) for the described operations related to priority management.

Space Complexity

O(N) – The primary auxiliary space is used to store the tasks. Assuming N represents the number of tasks in the system, the task storage data structure (likely a priority queue or a hash map combined with a sorting mechanism) would require space proportional to N to hold all the task objects. Each task object stores information like name, description, priority, and due date which contributes to the overall space. Therefore, the auxiliary space complexity is O(N), where N is the number of tasks.

Edge Cases

Case	How to Handle
Null or empty task name	Reject the task creation and return an error message to the user indicating the task name cannot be empty.
Task priority is outside of allowed range	Clamp the priority to the acceptable minimum or maximum value or reject the task and provide an error message.
Adding a task with an existing ID	Prevent adding the task, throwing an exception, or updating the existing task if updates are supported.
Maximum number of tasks reached, causing memory issues	Implement pagination or a rolling window, removing the oldest or lowest-priority tasks when the maximum is reached.
Attempting to execute a task that is dependent on another task that is not yet complete (circular dependency)	Detect circular dependencies and prevent task execution, alerting the user about the dependency issue.
Searching for tasks with a non-existent ID	Return null or an empty list to indicate that no tasks matched the search criteria.
Concurrency issues when multiple threads access the task list simultaneously	Implement proper locking or synchronization mechanisms to ensure thread safety and prevent data corruption.
Large number of tasks with the same priority	The system will handle this scenario correctly as tasks will be scheduled according to the FIFO principle, given that they share the same priority.

Null or empty task name

How to Handle:

Reject the task creation and return an error message to the user indicating the task name cannot be empty.

Task priority is outside of allowed range

How to Handle:

Clamp the priority to the acceptable minimum or maximum value or reject the task and provide an error message.

Adding a task with an existing ID

How to Handle:

Prevent adding the task, throwing an exception, or updating the existing task if updates are supported.

Maximum number of tasks reached, causing memory issues

How to Handle:

Implement pagination or a rolling window, removing the oldest or lowest-priority tasks when the maximum is reached.

Attempting to execute a task that is dependent on another task that is not yet complete (circular dependency)

How to Handle:

Detect circular dependencies and prevent task execution, alerting the user about the dependency issue.

Searching for tasks with a non-existent ID

How to Handle:

Return null or an empty list to indicate that no tasks matched the search criteria.

Concurrency issues when multiple threads access the task list simultaneously

How to Handle:

Implement proper locking or synchronization mechanisms to ensure thread safety and prevent data corruption.

Large number of tasks with the same priority

How to Handle:

The system will handle this scenario correctly as tasks will be scheduled according to the FIFO principle, given that they share the same priority.