Process Tasks Using Servers
Medium
You are given two 0-indexed integer arrays servers and tasks of lengths n and m respectively. servers[i] is the weight of the i<sup>th</sup> server, and tasks[j] is the time needed to process the j<sup>th</sup> task in seconds. Tasks are assigned to servers using a task queue.
Initially, all servers are free, and the queue is empty.
At second j, the j<sup>th</sup> task is inserted into the queue. As long as there are free servers and the queue is not empty, the task in the front of the queue will be assigned to a free server with the smallest weight, and in case of a tie, it is assigned to a free server with the smallest index.
If there are no free servers and the queue is not empty, we wait until a server becomes free and immediately assign the next task. If multiple servers become free at the same time, then multiple tasks from the queue will be assigned in order of insertion following the weight and index priorities above. A server that is assigned task j at second t will be free again at second t + tasks[j].
Your goal is to build an array ans of length m, where ans[j] is the index of the server the j<sup>th</sup> task will be assigned to.
Return the array ans.
Here are two examples to illustrate the process:
Example 1:
Input: servers = [3,3,2], tasks = [1,2,3,2,1,2]
Output: [2,2,0,2,1,2]
Example 2:
Input: servers = [5,1,4,3,2], tasks = [2,1,2,4,5,2,1]
Output: [1,4,1,4,1,3,2]
Can you write an algorithm to efficiently solve this task assignment problem?
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 constraints on the number of tasks and servers? Could either be zero or very large?
- Are the task processing times and server processing capacities integers? Can they be zero or negative?
- If a task cannot be processed by any server, what should be returned? Should an exception be thrown, or should a special value be returned indicating failure?
- Is there any limit on the number of tasks a server can process? Can a server process multiple tasks concurrently?
- If multiple valid assignments of tasks to servers exist, is any valid assignment acceptable, or are there criteria (e.g., minimizing total processing time) to optimize for?
Brute Force Solution
Approach
The brute force strategy for this problem involves trying every possible way to assign tasks to servers. It's like manually testing out every conceivable arrangement to see which one works best. We will look at all combinations of task assignments.
Here's how the algorithm would work step-by-step:
- Start by picking the first task and trying to assign it to the first server.
- Then, try assigning the first task to the second server, and so on, until you've tried assigning it to every server.
- Repeat this process for the second task: try assigning it to the first server, then the second, and so forth, for each possible placement of the first task.
- Continue assigning each task to every server in every possible combination.
- For each complete assignment of all tasks to servers, check if it meets the constraints of the problem, such as server capacity or task dependencies.
- Keep track of all the assignments that satisfy the constraints.
- Finally, from the list of valid assignments, choose the one that optimizes the desired criteria, such as minimizing the total time or cost.
Code Implementation
def process_tasks_using_servers_brute_force(tasks, servers, capacity_per_server): number_of_tasks = len(tasks)
number_of_servers = len(servers)
best_assignment = None
best_cost = float('inf')
def calculate_cost(assignment): cost = 0
for server_index in range(number_of_servers):
server_tasks = [tasks[task_index] for task_index in range(number_of_tasks) if assignment[task_index] == server_index]
cost += sum(server_tasks)
return cost
def is_valid_assignment(assignment): server_loads = [0] * number_of_servers
for task_index in range(number_of_tasks):
server_index = assignment[task_index]
server_loads[server_index] += tasks[task_index]
for load in server_loads:
if load > capacity_per_server:
return False
return True
def find_assignments(task_index, current_assignment): nonlocal best_assignment, best_cost
# If we've assigned all tasks, check if the assignment is valid
if task_index == number_of_tasks:
if is_valid_assignment(current_assignment):
cost = calculate_cost(current_assignment)
# Evaluate if this assignment provides the lowest cost
if cost < best_cost:
best_cost = cost
best_assignment = current_assignment[:]
return
# Try assigning the current task to each server
for server_index in range(number_of_servers):
current_assignment[task_index] = server_index
# Recursively call the method to assign other tasks
find_assignments(task_index + 1, current_assignment)
current_assignment = [0] * number_of_tasks
find_assignments(0, current_assignment)
return best_assignmentBig(O) Analysis
Optimal Solution
Approach
The goal is to efficiently assign tasks to servers while minimizing the time it takes to complete all tasks. The optimal approach involves using a structure that keeps track of the time each server will be available and assigning tasks to the server that will be available soonest. This ensures we're always utilizing available resources in the best possible way.
Here's how the algorithm would work step-by-step:
- Imagine a list of available servers, sorted by when they will finish their current task and become available.
- When a new task arrives, find the server that will be available the soonest.
- Assign the new task to that server.
- Calculate the new completion time for that server, based on the task's processing time.
- Re-sort the list of servers to reflect the updated availability times, keeping the server that will be available soonest at the front.
- Repeat this process for each task: find the earliest available server, assign the task, update the server's availability, and re-sort the list.
- Continue until all tasks are assigned, ensuring efficient resource utilization and minimized overall completion time.
Code Implementation
import heapq
def process_tasks(tasks, number_of_servers):
available_servers = []
# Initialize available servers with their initial availability time (0).
for server_id in range(number_of_servers):
heapq.heappush(available_servers, (0, server_id))
completion_times = []
for task_duration in tasks:
# Find the server that will be available the soonest.
available_time, server_id = heapq.heappop(available_servers)
completion_time = available_time + task_duration
completion_times.append(completion_time)
# Update the server's availability time after completing the task.
heapq.heappush(available_servers, (completion_time, server_id))
# The maximum completion time is the time when all tasks are done.
return max(completion_times)Big(O) Analysis
Edge Cases
| Case | How to Handle |
|---|---|
| Tasks array is null or empty | Return an empty list or null, indicating no tasks to process. |
| Servers array is null or empty | Return an empty list or null, indicating no servers available to process tasks. |
| Tasks array has a very large number of tasks | The algorithm should be designed to scale, possibly using priority queues or load balancing techniques to avoid performance bottlenecks. |
| Servers have vastly different processing capabilities (highly skewed processing power) | The scheduling algorithm should prioritize assigning tasks to the most capable servers first or use a weighted distribution strategy. |
| Task processing times are extremely large, leading to potential integer overflow or long execution times. | Use appropriate data types (e.g., long instead of int) to store processing times and set time limits to prevent indefinite execution. |
| Some tasks might be impossible to complete given the server capabilities (e.g., negative processing power). | Implement a mechanism to detect and handle these infeasible tasks, possibly by logging an error or skipping them. |
| Server weights are all zero | Handle this case by evenly distributing load, skipping server, or throwing error based on specifications. |
| Number of tasks is much smaller than number of servers | The algorithm should efficiently handle the case where some servers remain idle after processing all tasks. |
