python coding test course, finding the direction of line segments

Hello! In this post, we will examine one of the coding test problems using Python, titled “Finding the Direction of a Line Segment.” Through this problem, we will develop practical problem-solving skills and practice geometric problems that are often encountered in coding tests.

Problem Description

Given two points A(x1, y1) and B(x2, y2), this problem asks to determine the direction of line segment AB in relation to line segment CD. Based on line segment AB, find the direction of line segment CD and output the following values:

  • 1: When line segment CD is to the left of line segment AB
  • -1: When line segment CD is to the right of line segment AB
  • 0: When line segment CD is parallel to line segment AB

Input Format

The first line contains the coordinates of points A and B separated by a space, and the second line contains the coordinates of points C and D also separated by a space.

A's x y coordinates: x1 y1
B's x y coordinates: x2 y2
C's x y coordinates: x3 y3
D's x y coordinates: x4 y4

Output Format

Output an integer indicating the direction of line segment CD.

Problem-Solving Approach

To solve this problem, we first need to compute the direction vectors of line segments AB and CD. The direction vector can be calculated as follows:

  • AB vector = (x2 – x1, y2 – y1)
  • CD vector = (x4 – x3, y4 – y3)

Next, we determine the direction by calculating the cross product of the two vectors. The direction of the line segment can be decided based on the result of the cross product.

Cross Product Calculation

The cross product of two vectors (x1, y1) and (x2, y2) is calculated as follows:

cross_product = x1 * y2 - y1 * x2

If this value is > 0, then it is to the left; < 0 means it is to the right; and 0 means it is parallel.

Example

For instance, given A(1, 1), B(4, 4), C(4, 1), D(1, 4), the direction vector of AB is (3, 3). The direction vector of CD is (-3, 3). Calculating the cross product gives:

cross_product = (3 * 3) - (3 * -3) = 9 + 9 = 18 (therefore, line segment CD is located to the left of AB.)

Code Implementation

Now, let’s write a Python code based on the above process:

def direction(a, b, c, d):
    # Vector AB
    ab = (b[0] - a[0], b[1] - a[1])
    # Vector CD
    cd = (d[0] - c[0], d[1] - c[1])
    
    # Cross product calculation
    cross_product = ab[0] * cd[1] - ab[1] * cd[0]
    
    if cross_product > 0:
        return 1    # Left
    elif cross_product < 0:
        return -1   # Right
    else:
        return 0    # Parallel

# Sample input
a = (1, 1)
b = (4, 4)
c = (4, 1)
d = (1, 4)

# Function call
result = direction(a, b, c, d)
print(result)

Result

By executing the code above, since line segment CD is located to the left of AB, the result will be 1.

Conclusion

In this post, we solved an algorithm problem to find the direction of a line segment. This problem requires geometric thinking, and understanding vector cross products is crucial. As you solve more problems, familiarize yourself with such geometric problems, and I hope you achieve good results in coding tests!

Additional Tips

  • Be sure to test sufficiently with various inputs.
  • Utilizing visual diagrams can be helpful in understanding the problem.
  • Debug visually through the results of the cross product.