C# Coding Test Course, Finding the Intersection of Line Segments

Hello! In this post, we will discuss the coding test problem ‘Determining whether line segments intersect’ using C#.
This problem is a geometric problem, which determines whether the two given line segments intersect.
It is a fundamental problem that is utilized in various fields, making it useful for improving algorithm problem-solving skills and mathematical reasoning.

Problem Description

Given line segment 1 with two points A(x1, y1) and B(x2, y2), and line segment 2 with two points C(x3, y3) and D(x4, y4),
write a program to determine whether the two segments intersect.

Input

• Coordinates of the two points A and B of the first segment: (x1, y1), (x2, y2)
• Coordinates of the two points C and D of the second segment: (x3, y3), (x4, y4)

Output

Output true if the two segments intersect, otherwise output false.

Approach to Solution

To solve this problem, it is necessary to understand the position relationships of the segments. For the segments to intersect, both of the following conditions must be satisfied:

1. The endpoints of segment AB must lie on opposite sides of segment CD.
2. The endpoints of segment CD must lie on opposite sides of segment AB.

Mathematical Background

Given the points, we can determine if two points are on opposite sides using the cross product of the vectors.
If the signs of the cross product of the two vectors v1 = B - A and v2 = C - A are different, it means point C is on one side of segment AB,
and point D is on the opposite side. This method can be used to determine the intersection of the segments.

Implementation Method

The basic logic to solve the problem is as follows:

1. Define the direction of each segment using the four given points A, B, C, and D.
2. Create a cross product function to calculate the cross product of the two vectors.
3. Compare the signs of the cross product based on the two cases and return whether they intersect.

C# Code Implementation

using System;

class Program
{
    static void Main()
    {
        // Input coordinates of points A, B, C, D
        int[] A = { 1, 1 }; // (x1, y1)
        int[] B = { 4, 4 }; // (x2, y2)
        int[] C = { 1, 4 }; // (x3, y3)
        int[] D = { 4, 1 }; // (x4, y4)

        // Check intersection
        bool isCross = DoSegmentsIntersect(A, B, C, D);
        Console.WriteLine(isCross ? "true" : "false");
    }

    static bool DoSegmentsIntersect(int[] A, int[] B, int[] C, int[] D)
    {
        // Check intersection using cross product
        int d1 = CrossProduct(A, B, C);
        int d2 = CrossProduct(A, B, D);
        int d3 = CrossProduct(C, D, A);
        int d4 = CrossProduct(C, D, B);

        // Must be on opposite sides to intersect
        if (d1 * d2 < 0 && d3 * d4 < 0)
            return true;

        // Also consider the case where the segments touch at endpoints
        if (d1 == 0 && IsOnSegment(A, B, C)) return true;
        if (d2 == 0 && IsOnSegment(A, B, D)) return true;
        if (d3 == 0 && IsOnSegment(C, D, A)) return true;
        if (d4 == 0 && IsOnSegment(C, D, B)) return true;

        return false;
    }

    static int CrossProduct(int[] A, int[] B, int[] C)
    {
        // Calculate cross product
        return (B[0] - A[0]) * (C[1] - A[1]) - (B[1] - A[1]) * (C[0] - A[0]);
    }

    static bool IsOnSegment(int[] A, int[] B, int[] P)
    {
        // Check if point P lies on segment AB
        return Math.Min(A[0], B[0]) <= P[0] && P[0] <= Math.Max(A[0], B[0]) &&
               Math.Min(A[1], B[1]) <= P[1] && P[1] <= Math.Max(A[1], B[1]);
    }
}

Code Explanation

The above code can solve the line segment intersection problem. The detailed explanation of each function is as follows.

• Main: The entry point of the program, which sets the points of each segment and checks for intersection.
• DoSegmentsIntersect: The core logic to determine whether the two segments intersect is implemented in this function.
• CrossProduct: This function calculates the cross product using the given three points. The result of the cross product is used to determine the direction.
• IsOnSegment: This function checks whether a specific point lies on the segment.

Test Cases

To test the given code, several test cases can be considered.

Conclusion

In this article, we implemented an algorithm to determine whether line segments intersect using C#.
Understanding geometric problems helps in grasping these problem-solving techniques and lays the foundation for learning advanced algorithms.
Let’s continue solving various algorithm problems together. Thank you!