Hello! Today, we will learn how to solve geometric problems that are frequently asked in Python coding tests. Geometric problems mainly include calculations of areas, perimeters, intersections, distances, etc., and are an important part of algorithm problem-solving. In this course, we will explain commonly asked problems based on basic geometric concepts and look at step-by-step approaches to successfully solve them.<\/p>\n
This problem involves determining whether two given line segments intersect.<\/p>\n
Determine whether the given two line segments Four integers If the segments intersect, print “YES”. Otherwise, print “NO”.<\/p>\n To determine whether two line segments intersect, we must use the geometric concept of ‘direction of the segments’. By calculating the direction for each point of the two segments, we can verify whether they intersect.<\/p>\n To calculate the direction for line segments This function calculates the direction for points We can determine that line segments These conditions can be combined to integrate the entire logic into one function.<\/p>\n Let’s implement the entire code based on what we have explained so far.<\/p>\n In this lecture, we implemented an algorithm to determine whether two line segments intersect. Geometric problems are based on basic mathematical theories, and understanding algorithms is necessary. By practicing with various examples, you will gain confidence in solving geometric problems. I hope you will encounter more algorithm problems in the future and improve your coding skills through them.<\/p>\n Thank you!<\/p>\n <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"AB<\/code> and CD<\/code> intersect. Each line segment is defined by two points as follows:<\/p>\n\n
AB<\/code>: Point A(x1, y1)<\/code>, Point B(x2, y2)<\/code><\/li>\nCD<\/code>: Point C(x3, y3)<\/code>, Point D(x4, y4)<\/code><\/li>\n<\/ul>\nInput Format<\/h3>\n
x1, y1, x2, y2, x3, y3, x4, y4<\/code> are given.<\/p>\nOutput Format<\/h3>\n
Problem Approach<\/h2>\n
1. Direction Calculation<\/h3>\n
AB<\/code> and CD<\/code>, we use the following formula:<\/p>\ndef direction(px, py, qx, qy, rx, ry):\n return (qx - px) * (ry - py) - (qy - py) * (rx - px)<\/code><\/pre>\nP<\/code>, Q<\/code>, R<\/code> and returns a positive, negative, or zero value.<\/p>\n2. Intersection Determination<\/h3>\n
AB<\/code> and CD<\/code> intersect when the endpoints have different directions. That is, the following conditions must be satisfied:<\/p>\n\n
A, B, C<\/code>) and direction(A, B, D<\/code>) is greater than 0, and the product of direction(C, D, A<\/code>) and direction(C, D, B<\/code>) is also greater than 0.<\/li>\n<\/ul>\n3. Code Implementation<\/h3>\n
def ccw(px, py, qx, qy, rx, ry):\n return (qx - px) * (ry - py) - (qy - py) * (rx - px) > 0\n\ndef is_intersect(x1, y1, x2, y2, x3, y3, x4, y4):\n d1 = ccw(x1, y1, x2, y2, x3, y3)\n d2 = ccw(x1, y1, x2, y2, x4, y4)\n d3 = ccw(x3, y3, x4, y4, x1, y1)\n d4 = ccw(x3, y3, x4, y4, x2, y2)\n\n if d1 != d2 and d3 != d4:\n return \"YES\"\n\n return \"NO\"\n\n# Example input\nx1, y1, x2, y2 = map(int, input().split())\nx3, y3, x4, y4 = map(int, input().split())\n\nprint(is_intersect(x1, y1, x2, y2, x3, y3, x4, y4))<\/code><\/pre>\nConclusion<\/h2>\n