JavaScript Coding Test Course, Finding the Direction of a Line Segment

Problem Description

This is a problem of determining the direction of the line segment AB defined by two given points A(x1, y1) and B(x2, y2). The result of the direction must be one of the following three:

• “UP”: If the line segment is directed upwards
• “DOWN”: If the line segment is directed downwards
• “HORIZONTAL”: If the line segment is horizontal

Input Format

The coordinates of the two points A(x1, y1) and B(x2, y2) are provided as input. Each coordinate is given as an integer.

Output Format

A string indicating the direction of the line segment AB is output.

Example

Solution Process

1. Understanding the Problem

To understand the problem, we need to determine the direction of line segment AB when two points A and B are given. The direction of the line segment is determined by the difference in y-coordinates (Δy) and the difference in x-coordinates (Δx). By evaluating these differences, we can deduce if the line segment is horizontal, upward, or downward.

2. Building the Logic to Determine the Direction of the Line Segment

The basic formulas needed to determine the direction of the line segment are as follows:

• Δy = y2 – y1
• Δx = x2 – x1

Now, we can determine the direction through three cases:

• If Δy > 0, the line segment is pointing upwards, so we return “UP”.
• If Δy < 0, the line segment is pointing downwards, so we return “DOWN”.
• If Δy == 0, the line segment is horizontal, so we return “HORIZONTAL”.

3. Implementing in JavaScript

The required JavaScript code to solve the problem is as follows:

function getDirection(x1, y1, x2, y2) {
    const deltaY = y2 - y1;
    
    if (deltaY > 0) {
        return "UP";
    } else if (deltaY < 0) {
        return "DOWN";
    } else {
        return "HORIZONTAL";
    }
}

// Example calls
console.log(getDirection(1, 2, 3, 5)); // "UP"
console.log(getDirection(1, 3, 4, 2)); // "DOWN"
console.log(getDirection(1, 3, 4, 3)); // "HORIZONTAL"

4. Complexity Analysis

The time complexity of this algorithm is O(1). Since it reads the coordinates of the two given points and determines the direction through simple operations, it is optimal for resolving within a fixed time.

5. Additional Improvements

The current algorithm is optimized for calculating the direction between two points in a 2D plane, but some improvements can be made:

• Exception handling can be added to handle various inputs. For example, we need to deal with cases where the input points are identical.
• A logic can be added to validate that the values of the input points are numeric to enhance stability.

Conclusion

In this tutorial, we implemented an algorithm to determine the direction of the line segment between two points using JavaScript. By utilizing simple mathematical principles and condition statements, we demonstrated that the problem can be effectively solved. We hope you will enhance your coding skills by solving more algorithmic problems in the future.