Application and Implementation of Greedy Algorithm in Interval Scheduling

Application and implementation of greedy algorithm in interval scheduling.

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Introduction.

In modern life, we often encounter the problem of time management.

For example, how to schedule multiple meetings, courses or events in one day so that they do not conflict with each other and maximize the use of time? This is the classic interval scheduling problem.

This article will show how to use the greedy algorithm to solve this problem and optimize the results by picking the activity that ends the earliest.

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What is an interval scheduling problem?.

The interval scheduling problem can be described as: Given a set of activities, each activity has a start time and an end time, we need to select some of these activities so that they do not overlap each other, and the number of activities selected is as large as possible.

A common application scenario for this problem is the arrangement of meeting rooms, ensuring that only one meeting is using the meeting room at the same time.

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Introduction to Greedy Algorithms.

The greedy algorithm is a step-by-step method of building a solution, selecting the current optimal option at each step, in order to finally get the global optimal solution.

In the interval scheduling problem, we can use the greedy algorithm to solve the problem by preferentially selecting the activity that ends the earliest.

This approach is called the "Earliest Deadline First" (EDF) strategy.

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The steps of the greedy algorithm to solve the interval scheduling problem.

1. # Sort #: First sort all activities in descending order of end time.

If the end time is the same, it is sorted by the start time.

2. # Select Activity #: Start with the first activity after sorting and add it to the result set.

The next activity is then checked in turn, and if it does not overlap with the selected activity, it is added to the result set.

3. # Repeat #: Repeat step 2 until all activities have been checked.

4. # Output result #: The final result set is the selected non-overlapping activity set.

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Code implementation.

The following is an example code for implementing the above greedy algorithm in Python:

lass Activity:
    def __init__(self, start, end):
        self.start = start
        self.end = end

    def __repr__(self):
        return f"Activity(start={self.start}, end={self.end})"

def select_activities(activities):
    # Step 1: Sort activities by their ending times
    sorted_activities = sorted(activities, key=lambda x: (x.end, x.start))
    
    # Step 2: Initialize the result set and the last selected activity's end time
    selected_activities = []
    last_end_time = 0
    
    # Step 3: Iterate through sorted activities and select non-overlapping ones
    for activity in sorted_activities:
        if activity.start >= last_end_time:
            selected_activities.append(activity)
            last_end_time = activity.end
    
    return selected_activities

# Example usage
activities = [Activity(1, 3), Activity(2, 5), Activity(4, 6), Activity(6, 7)]
selected = select_activities(activities)
print("Selected activities:", selected)

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Interpret the code.

1. # Define activity class #: ActivityClass is used to represent an activity, including start and end times.

2. # Sort Activity #: Use sortedFunctions are sorted by the end time of the activity, or by the start time if the end time is the same.

3. # Select Activity #: Initialize an empty result set and a variable to track the end time of the last selected activity.

Traverse the sorted activity list, and if the start time of the current activity is greater than or equal to the end time of the last selected activity, add it to the result set and update the end time of the last selected activity.

4. # output result #: returns the selected active set.

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Practical application cases.

Suppose you are a project manager and need to schedule project meetings within a week.

You have a schedule for the following meetings: - Meeting A: 9:00 - 10:30 - Meeting B: 9:15-11:00 - Meeting C: 10:00-11:30 - Meeting D: 11:00-12:30 - Conference E: 12:00-13:00 Using the above greedy algorithm, we can arrive at the following arrangement: - Select Session A (9:00 - 10:30) -Selected meeting C (10:00-11:30) -Selected meeting E (12:00-13:00) In this way, we chose three non-overlapping meetings, which maximized the utilization rate of the meeting room.

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Summarize.

The application of greedy algorithm in interval scheduling problem is very intuitive and efficient.

By prioritizing the activities that end the earliest, we can quickly find a set of non-overlapping activities to maximize resource utilization.

This method is not only suitable for meeting room arrangement, but also for other similar resource allocation problems, such as task scheduling, curriculum scheduling, etc.

I hope this article can help you better understand and apply greedy algorithms to solve practical problems.