kotlin coding test course, determining the intersection of line segments

Problems regarding the intersection of line segments are frequently presented in programming competitions and coding tests. In this course, we will learn how to determine whether line segments intersect using the Kotlin language. This course will help you develop geometric techniques and mathematical thinking. Additionally, we will validate the accuracy of the algorithm through various test cases.

Problem Description

The problem is to determine whether two given line segments intersect. Line segment A is defined by points P1(x1, y1) and P2(x2, y2), and line segment B is defined by points Q1(x3, y3) and Q2(x4, y4). If they intersect, output “YES”, and if they do not, output “NO”.

Input Format

  • The first line contains four integers x1, y1, x2, y2 separated by spaces, representing the two points P1 and P2 of line segment A.
  • The second line contains four integers x3, y3, x4, y4 separated by spaces, representing the two points Q1 and Q2 of line segment B.

Output Format

Output “YES” or “NO” depending on whether they intersect.

Approach to the Problem

To determine the intersection of the line segments, we follow these steps:

  1. We must consider the directionality of each line segment for them to intersect.
  2. We use the endpoints of each segment and the two points of the other segment to determine the direction.
  3. The intersection of the segments can be judged through intervals and positions.

Specifically, we can determine whether points P1 and P2 of segment A are oriented counterclockwise or clockwise with respect to points Q1 and Q2 of segment B. This can be used to discern their intersection.

Kotlin Code Implementation

Now let’s look at the code implemented in Kotlin. The code below is a simple example to determine whether line segments A and B intersect.


fun main() {
    val (x1, y1, x2, y2) = readLine()!!.split(" ").map { it.toInt() }
    val (x3, y3, x4, y4) = readLine()!!.split(" ").map { it.toInt() }

    if (doIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) {
        println("YES")
    } else {
        println("NO")
    }
}

// Calculate the direction of two points
fun orientation(px: Int, py: Int, qx: Int, qy: Int, rx: Int, ry: Int): Int {
    val value = (qy - py) * (rx - qx) - (qx - px) * (ry - qy)
    return when {
        value == 0 -> 0 // Collinear
        value > 0 -> 1  // Counterclockwise
        else -> 2       // Clockwise
    }
}

// Function to determine if two segments intersect
fun doIntersect(x1: Int, y1: Int, x2: Int, y2: Int, x3: Int, y3: Int, x4: Int, y4: Int): Boolean {
    val o1 = orientation(x1, y1, x2, y2, x3, y3)
    val o2 = orientation(x1, y1, x2, y2, x4, y4)
    val o3 = orientation(x3, y3, x4, y4, x1, y1)
    val o4 = orientation(x3, y3, x4, y4, x2, y2)

    // Standard case
    if (o1 != o2 && o3 != o4) return true

    // Exception handling for when segments are on the same line
    if (o1 == 0 && onSegment(x1, y1, x3, y3, x2, y2)) return true
    if (o2 == 0 && onSegment(x1, y1, x4, y4, x2, y2)) return true
    if (o3 == 0 && onSegment(x3, y3, x1, y1, x4, y4)) return true
    if (o4 == 0 && onSegment(x3, y3, x2, y2, x4, y4)) return true

    return false
}

// Function to determine if a given point lies on the segment
fun onSegment(px: Int, py: Int, qx: Int, qy: Int, rx: Int, ry: Int): Boolean {
    return (rx <= maxOf(px, qx) && rx >= minOf(px, qx) &&
            ry <= maxOf(py, qy) && ry >= minOf(py, qy))
}

Code Explanation

The code above implements the process of determining the intersection of line segments A and B.

  • orientation function: This function calculates the orientation of the given three points (P, Q, R). Based on the orientation, the values are classified as 0 (collinear), 1 (counterclockwise), and 2 (clockwise). This value is used to determine the intersection.
  • doIntersect function: This function calculates the directionality of each segment and evaluates the standard and exceptional cases to return the result.
  • onSegment function: This function determines whether point R lies on segment PQ by comparing R’s position with the endpoints of the segment.

Test Cases

Now we will verify the accuracy of the code through various test cases.

  • Test Case 1: 0 0 2 2 0 2 2 0 → Result: YES
  • Test Case 2: 1 1 10 1 1 2 10 2 → Result: NO
  • Test Case 3: 10 0 0 10 0 0 10 10 → Result: YES
  • Test Case 4: 1 1 3 3 1 3 3 1 → Result: YES
  • Test Case 5: 0 0 0 10 0 5 10 5 → Result: NO

Conclusion

In this course, we implemented an efficient algorithm to determine the intersection of line segments using Kotlin. This problem, based on geometric concepts, can be effectively utilized in various situations. Gaining experience in solving diverse problems through applicable algorithms and techniques is important.

It is crucial to implement and execute the code and test cases to clearly understand the functioning of the algorithm. Continuous practice will enhance your problem-solving abilities in geometry.