C++ Coding Test Course, Dividing Line Segments into Groups

Among modern programming languages, C++ is a very popular language due to its speed and efficiency. It is widely used in various fields and becomes a powerful tool, especially in solving algorithmic problems. In this article, we will look at the process of solving an algorithmic problem titled “Dividing Line Segments into Groups” step by step.

Problem Description

The given problem is to divide multiple line segments into groups such that they do not overlap. Two line segments overlap if the endpoint of one segment is before the starting point of another segment while still being after the endpoint of the other segment. Let’s explore the necessary steps and methods to solve this problem.

Example Problem

Let’s assume the following line segments are given:

    Line Segment 1: (1, 3)
    Line Segment 2: (2, 5)
    Line Segment 3: (6, 8)
    Line Segment 4: (7, 9)
    Line Segment 5: (10, 12)
    

Dividing the above line segments into groups could result in the following groups:

• Group 1: {(1, 3), (2, 5)}
• Group 2: {(6, 8), (7, 9)}
• Group 3: {(10, 12)}

Problem Solving Process

Step 1: Problem Analysis

To solve the problem, we must first clarify the input and output formats. The line segments are represented by two integers (start point, endpoint), and overlapping segments must be grouped together. Later, we need to output the number of groups.

Step 2: Approach

To determine whether the line segments overlap, we need to sort the segments by their starting points and then check each line segment in turn to see whether they overlap. A new group can be formed only if they do not overlap.

Step 3: Algorithm Design

The algorithm we will use is as follows:

• Sort all line segments based on the starting point.
• Iterate through the sorted segments, comparing the current group’s endpoint with the starting point of the next segment.
• If they overlap, update the current group’s endpoint; if they do not overlap, start a new group.

Step 4: Implementation

Below is the code implemented in C++:

#include 
#include 
#include 

using namespace std;

struct LineSegment {
    int start;
    int end;
};

bool compare(LineSegment a, LineSegment b) {
    return a.start < b.start;
}

int groupLineSegments(vector& segments) {
    if (segments.empty()) return 0;

    // Sort segments based on the starting point
    sort(segments.begin(), segments.end(), compare);
    
    int groupCount = 1;
    int currentEnd = segments[0].end;

    for (int i = 1; i < segments.size(); i++) {
        if (segments[i].start <= currentEnd) {
            // If they overlap, update currentEnd
            currentEnd = max(currentEnd, segments[i].end);
        } else {
            // If they don't overlap, start a new group
            groupCount++;
            currentEnd = segments[i].end;
        }
    }

    return groupCount;
}

int main() {
    vector segments = {{1, 3}, {2, 5}, {6, 8}, {7, 9}, {10, 12}};
    int result = groupLineSegments(segments);
    
    cout << "Number of groups: " << result << endl;
    return 0;
}

Step 5: Code Execution Result

When executing the above code, you can get the following result:

Number of groups: 3

Conclusion

In this tutorial, we solved the problem of 'Dividing Line Segments into Groups' using C++. Through this problem, we experienced the process of designing algorithms and learned the fundamental concepts of sorting and group classification. Such problems are frequently encountered in real coding tests, so it is essential to practice these kinds of problems repeatedly. I hope you continue to build your skills by practicing various algorithm problems in the future.