What is the time complexity of Process Tasks Using Servers?

The optimal solution has a time complexity of O(m log n).

What data structures are used to solve Process Tasks Using Servers?

This problem uses Array, Heap (Priority Queue). Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Process Tasks Using Servers?

Insight 1: Using priority queues (heaps) is crucial to efficiently find the available server with the smallest weight and to track when servers become free. Insight 2: Maintaining two priority queues - one for available servers and one for busy servers - allows for efficient management of server states.

Which companies ask LeetCode 1882. Process Tasks Using Servers in interviews?

This problem is frequently asked at Lyft, PayPal, X.

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Process Tasks Using Servers - LeetCode 1882 Solution

Process Tasks Using Servers - Complete Solution Guide

Process Tasks Using Servers is LeetCode problem 1882, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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 th server, and tasks[j] is the time needed to process the j th task in seconds . Tasks are assigned to the servers using a task queue . Initially, all servers are free, and the queue is empty . At second j , the j th task is inserted into the queue (starting with the 0 th task being inserted at second 0 ). As long as there are free se

Detailed Explanation

The problem requires simulating a task processing system using a set of servers with different weights. Tasks arrive at each second, and we need to assign each task to a server. The assignment criteria is to use a free server with the smallest weight (and smallest index in case of a tie). Servers become free after processing a task for a duration specified in the 'tasks' array. The output should be an array containing the indices of the servers assigned to each task.

Solution Approach

The provided solution utilizes two priority queues: `available_servers` and `busy_servers`. The `available_servers` queue stores available servers, prioritized by weight and then index. The `busy_servers` queue stores the finish time and index of servers currently processing tasks, prioritized by finish time. The algorithm simulates the task assignment process, iterating through the tasks and assigning each task to the appropriate server. The time variable keeps track of the current time.

Step-by-Step Algorithm

Step 1: Initialize `available_servers` with all servers, using a priority queue to maintain the server with the smallest weight at the top. Each server is represented as a tuple (weight, index).
Step 2: Initialize an empty `busy_servers` priority queue to track servers that are currently processing tasks. Each entry is a tuple (finish_time, server_index).
Step 3: Initialize an empty `ans` array to store the server index assigned to each task.
Step 4: Iterate through the `tasks` array. For each task, update the current time `time` to be the maximum of the current time and the task's index (representing its arrival time).
Step 5: Check `busy_servers` for servers that have finished processing. Move any servers whose finish time is less than or equal to the current time from `busy_servers` to `available_servers`. The server is identified by its index stored with the finish time.
Step 6: If `available_servers` is empty, it means all servers are busy. Advance the time to the finish time of the earliest finishing server, and free up any servers that finish at that time. This ensures that a server is available before assigning the next task.
Step 7: Assign the current task to the server at the top of the `available_servers` queue (server with the smallest weight and index). Record the server's index in the `ans` array.
Step 8: Calculate the finish time of the server after processing the current task and add the server (finish time, server index) to the `busy_servers` queue.
Step 9: After processing all tasks, return the `ans` array.

Key Insights

Insight 1: Using priority queues (heaps) is crucial to efficiently find the available server with the smallest weight and to track when servers become free.
Insight 2: Maintaining two priority queues - one for available servers and one for busy servers - allows for efficient management of server states.
Insight 3: The simulation needs to advance in time, and the current time is determined by either the arrival of a new task or the completion of a task by a busy server.

Complexity Analysis

Time Complexity: O(m log n)

Space Complexity: O(n)

Topics

This problem involves: Array, Heap (Priority Queue).

Companies

Asked at: Lyft, PayPal, X.

Process Tasks Using Servers | LeetCode 1882

Medium

Array Heap (Priority Queue)

Time: O(m log n)Space: O(n)

Solution Code

Available in:

import java.util.Arrays;
import java.util.PriorityQueue;

class Solution {
    public int[] assignTasks(int[] servers, int[] tasks) {
        int n = servers.length;
        int m = tasks.length;

        PriorityQueue<int[]> available_servers = new PriorityQueue<>((a, b) -> {
            if (a[0] != b[0]) {
                return a[0] - b[0];
            } else {
                return a[1] - b[1];
            }
        });
        for (int i = 0; i < n; i++) {
            available_servers.offer(new int[]{servers[i], i});
        }

        PriorityQueue<long[]> busy_servers = new PriorityQueue<>((a, b) -> {
            if (a[0] != b[0]) {
                return Long.compare(a[0], b[0]);
            } else {
                return Long.compare(a[1], b[1]);
            }
        });

        int[] ans = new int[m];
        long time = 0;

        for (int task_idx = 0; task_idx < m; task_idx++) {
            time = Math.max(time, task_idx);

            while (!busy_servers.isEmpty() && busy_servers.peek()[0] <= time) {
                long[] finished_server = busy_servers.poll();
                int server_idx = (int) finished_server[1];
                available_servers.offer(new int[]{servers[server_idx], server_idx});
            }

            if (available_servers.isEmpty()) {
                time = busy_servers.peek()[0];
                while (!busy_servers.isEmpty() && busy_servers.peek()[0] <= time) {
                    long[] finished_server = busy_servers.poll();
                    int server_idx = (int) finished_server[1];
                    available_servers.offer(new int[]{servers[server_idx], server_idx});
                }
            }

            int[] server = available_servers.poll();
            int server_idx = server[1];
            ans[task_idx] = server_idx;

            int task_duration = tasks[task_idx];
            long finish_time = time + task_duration;
            busy_servers.offer(new long[]{finish_time, server_idx});
        }

        return ans;
    }
}

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Problem Info

Description

Problem 1882: Process Tasks Using Servers - Detailed explanation and solution approaches.

Topics

Array Heap (Priority Queue)

Companies

LyftPayPalX

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:1882

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

9 steps

1
Step 1: Initialize `available_servers` with all servers, using a priority queue to maintain the server with the smallest weight at the top. Each server is represented as a tuple (weight, index).
2
Step 2: Initialize an empty `busy_servers` priority queue to track servers that are currently processing tasks. Each entry is a tuple (finish_time, server_index).
3
Step 3: Initialize an empty `ans` array to store the server index assigned to each task.
4
Step 4: Iterate through the `tasks` array. For each task, update the current time `time` to be the maximum of the current time and the task's index (representing its arrival time).
5
Step 5: Check `busy_servers` for servers that have finished processing. Move any servers whose finish time is less than or equal to the current time from `busy_servers` to `available_servers`. The server is identified by its index stored with the finish time.
6
Step 6: If `available_servers` is empty, it means all servers are busy. Advance the time to the finish time of the earliest finishing server, and free up any servers that finish at that time. This ensures that a server is available before assigning the next task.
7
Step 7: Assign the current task to the server at the top of the `available_servers` queue (server with the smallest weight and index). Record the server's index in the `ans` array.
8
Step 8: Calculate the finish time of the server after processing the current task and add the server (finish time, server index) to the `busy_servers` queue.
9
Step 9: After processing all tasks, return the `ans` array.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(m log n)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by the heap operations within the loop processing the tasks. The space complexity is determined by the maximum size of the priority queues, which depends on the number of servers.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Using a Sorted List

Instead of priority queues, a sorted list could be used to keep track of available servers. Inserting and deleting from a sorted list would require maintaining its sorted order.

Time: O(m * n), in worst case. Finding smallest weight and index server in available servers will take O(n) timeSpace: O(n)

Trade-offs: This approach could be simpler to implement initially, but it has a higher time complexity, making it less efficient for larger inputs.

✨

Key Insights

1Insight 1: Using priority queues (heaps) is crucial to efficiently find the available server with the smallest weight and to track when servers become free.
2Insight 2: Maintaining two priority queues - one for available servers and one for busy servers - allows for efficient management of server states.
3Insight 3: The simulation needs to advance in time, and the current time is determined by either the arrival of a new task or the completion of a task by a busy server.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: All servers are busy. The solution handles this by advancing the time to the next available server's finish time and making it available before assigning the new task.
Edge case 2: Multiple servers become free at the same time. The solution ensures the tasks are assigned based on the weight and index priority of the servers being freed.
Edge case 3: Tasks arrive faster than they can be processed. The solution correctly simulates the queuing effect by waiting for servers to become available.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to update the current time `time` to the task arrival time can lead to incorrect server assignments.

✗Common mistake 2: Not handling the case where all servers are busy, causing the algorithm to potentially assign tasks to servers that are still processing other tasks.

✗Common mistake 3: Incorrectly prioritizing servers when multiple servers are available or multiple tasks arrive at the same time can lead to incorrect results. Make sure you apply the weight-then-index rule correctly.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Task scheduling in a cloud computing environment, where servers have different processing capabilities and tasks need to be assigned efficiently to minimize processing time.

🏦Real-world scenario 2: Resource allocation in a data center, where different resources (e.g., CPU, memory) need to be assigned to different jobs based on their requirements and the availability of resources.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 22, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Process Tasks Using Servers"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether heap (priority queue) techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?