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Schedule Tasks on Minimum Machines

Explore how to schedule tasks efficiently on a limited number of machines by using heap data structures. Understand the core approach to assign tasks with overlapping times dynamically, ensuring minimal machine usage while respecting scheduling constraints.

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Statement

We are given an input array, tasks, where tasks[i] =[starti,endi]= [start_i, end_i] represents the start and end times of nn tasks. Our goal is to schedule these tasks on machines given the following criteria:

  1. A machine can execute only one task at a time.

  2. A machine can begin executing a new task immediately after completing the previous one.

  3. An unlimited number of machines are available.

Find the minimum number of machines required to complete these nn tasks.

Constraints:

  • n==n == tasks.length

  • 1≤1 \leq tasks.length ≤103\leq 10^3

  • 0≤0 \leq tasksi.start << tasksi.end ≤104\leq 10^4

Examples

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Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Schedule Tasks on Minimum Machines

1.

What is the minimum number of machines required to schedule the following tasks?

[[1,7],[8,9],[3,6],[9,14],[6,7]][[1, 7], [8, 9], [3, 6], [9, 14], [6, 7]]

A.

3

B.

2

C.

5

D.

1

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Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
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Try it yourself

Implement your solution in the following coding playground.

Python
usercode > main.py
def minimum_machines(tasks):



    # Replace this placeholder return statement with your code

    return -1
Schedule Tasks on Minimum Machines