python coding test course, assigning meeting rooms

Problem Description

The problem of assigning meeting rooms involves optimally assigning meeting rooms based on the start and end times of multiple meetings. If the given meetings overlap, additional meeting rooms need to be assigned, so the goal is to maximize the number of meetings that can be held without overlaps.

Problem Definition

Given the start and end times of meetings in list format, calculate how many meetings can be conducted simultaneously through room assignment.

Input Format

[[start_time1, end_time1], [start_time2, end_time2], ...]

Output Format

Maximum number of possible meetings

Example

Input: [[1, 3], [2, 4], [3, 5], [6, 8]]
Output: 3

Solution Process

This problem can be solved using a greedy algorithm. First, sort the meetings based on their end times, then select the meeting that ends first, and continue to select subsequent meetings that do not overlap with the last selected meeting.

Step 1: Data Organization

First, sort the given list of meetings based on their end times. This allows for conducting meetings while using the least amount of resources.

Step 2: Determine Meeting Attendance

Select the first meeting from the sorted list, and if the next meeting starts at or after the end time of this meeting, select that meeting. Repeat this process to select as many meetings as possible.

Step 3: Implementation

Now, let’s implement the above process in Python code.

python
def max_conferences(conferences):
    # Sort the conference list based on end times
    conferences.sort(key=lambda x: x[1])
    
    # Select the first conference
    count = 1
    last_end_time = conferences[0][1]
    
    # Iterate over the remaining conferences
    for i in range(1, len(conferences)):
        if conferences[i][0] >= last_end_time:  # If start time is greater than or equal to the last end time
            count += 1
            last_end_time = conferences[i][1]  # Update the last end time
    
    return count

# Example input
meetings = [[1, 3], [2, 4], [3, 5], [6, 8]]
result = max_conferences(meetings)
print("Maximum number of meetings:", result)

Step 4: Code Explanation

Code Explanation

  • Sorting: The first line where `conferences.sort(key=lambda x: x[1])` sorts the list based on the end times of each meeting.
  • Meeting Selection: The following loop checks if each meeting starts after the last selected meeting has ended, and selects it accordingly.
  • Returning Result: Finally, it returns the number of selected meetings.

Step 5: Complexity Analysis

The time complexity of this algorithm is O(n log n) for sorting, and O(n) for selecting meetings, resulting in a total complexity of O(n log n). The space complexity is O(1).

Step 6: Additional Practice Problems

After understanding the basic concepts of greedy algorithms through this problem, it is beneficial to tackle various additional practice problems. For example:

  • When the start and end times of meetings are given in arbitrary ranges, can all meetings be held with the least number of rooms?
  • Implement a system for reserving meeting rooms that allows users to add and check meetings themselves.

Conclusion

In this lecture, we explored how to solve problems using greedy algorithms through the “Assigning Meeting Rooms” problem. I hope this will help you improve your algorithm problem-solving skills. In the next lecture, we will cover an even wider range of algorithm problems.

References