python coding test course, dividing segments into groups

Hello! In this post, I will explain a coding test problem using Python, which is “Dividing Line Segments into Groups.” This problem involves designing and implementing an algorithm to appropriately group line segments. Through this problem, you can learn the basic way of thinking about handling line segments and enhance your algorithmic thinking.

Problem Description

Given a set of line segments on a straight line. Each line segment is represented by a start point and an end point. In this case, line segments that overlap or are adjacent to each other are grouped together. The problem is to calculate how many different groups can be divided when a list of line segments is given. For example, when there are the following line segments:

[(1, 5), (2, 3), (6, 8), (7, 10)]

The above line segments can be grouped as follows:

Group 1: [(1, 5), (2, 3)]

        Group 2: [(6, 8), (7, 10)]

Input/Output Format

Input

The first line contains the number of line segments n (1 ≤ n ≤ 100,000). In the following n lines, the start and end points of each line segment (start, end) are provided. It is assumed that the end point is always greater than the start point.

Output

Print the number of overlapping line segment groups.

Problem Solving Approach

To solve this problem, you can think of sorting the line segments and dividing them into groups. The typical approach is as follows:

Sort the line segments based on the start point. If the start points are the same, sort by the end point.
Iterate through the sorted line segments, and if the end point of the current segment is greater than or equal to the end point of the previous segment, group them together.
Count the number of groups and print the final result.

Implementation

Now, based on the above approach, let’s implement the code in Python. The code is as follows:



def count_groups(segments):

    # Sort the segments by start point and use end point for ties

    segments.sort(key=lambda x: (x[0], x[1]))

    groups = 0

    current_end = -1
    for start, end in segments:

        if start > current_end:

            # A new group starts.

            groups += 1

            current_end = end

        else:

            # It is included in the current group.

            current_end = max(current_end, end)
    return groups

# Get input n = int(input()) segments = [tuple(map(int, input().split())) for _ in range(n)] result = count_groups(segments) print(result)

Code Explanation

The code above operates in the following way:

segments.sort(): Sorts the list of segments. During this, a key is set to sort by the start point and, for ties, by the end point.
Variable groups: A variable to count the number of groups, initialized to 0.
Variable current_end: A variable to track the end point of the current group, initialized to -1.
While iterating through the segments, if the start point is greater than the end point of the current group, a new group starts, and the count of groups increases. Otherwise, the end point of the current group is updated.

Complexity Analysis

The time complexity of the above algorithm is as follows:

Sorting step: O(n log n)
Group calculation step: O(n)

Therefore, the overall time complexity is O(n log n).

Conclusion

Through this problem, we implemented an algorithm to divide line segments into groups. This algorithm easily handles cases where line segments overlap. While preparing for coding tests, encountering various problems and contemplating solutions greatly helps in building skills. I hope you continue to challenge yourselves with more algorithm problems and practice!