Hello! Today, we will solve algorithm problems related to geometry in the Java coding test course. Geometric problems are often covered in algorithm exams and help in understanding basic shapes like plane geometry, triangles, circles, and polygons. These problems usually provide an opportunity to develop mathematical thinking skills based on the theoretical properties of shapes.<\/p>\n
Let’s solve the following geometric problem:<\/p>\n
The length of the line segment is defined as the distance between the two points, and the distance between two points P1(x1, y1) and P2(x2, y2) can be calculated using the following formula:<\/p>\n
distance = \u221a((x2 - x1)\u00b2 + (y2 - y1)\u00b2)<\/code><\/pre>\nProblem Solving Process<\/h2>\n1. Problem Analysis<\/h3>\n
Analyzing the problem, the coordinates of the two points P1 and P2 are fixed, and the goal is to find the distance between these two points. The mathematical concept that can be used here is the Pythagorean theorem. We can calculate the Euclidean distance using the coordinates of the given two points.<\/p>\n
2. Mathematical Judgment<\/h3>\n
We are given two points P1(1, 3) and P2(4, 6). Based on this, we can calculate the differences in the x-coordinate and y-coordinate to apply the distance formula.<\/p>\n
– Difference in x-coordinates: (x2 - x1) = (4 - 1) = 3<\/code>
\n– Difference in y-coordinates: (y2 - y1) = (6 - 3) = 3<\/code><\/p>\n3. Distance Calculation<\/h3>\n
Substituting the calculated differences into the distance formula:<\/p>\n
distance = \u221a(3\u00b2 + 3\u00b2) = \u221a(9 + 9) = \u221a18 = 3\u221a2 \u2248 4.24<\/code><\/pre>\n4. Writing Java Code<\/h3>\n
Now let’s implement this algorithm in Java code. The flow of the algorithm is as follows:<\/p>\n
\npublic class DistanceCalculator {\n public static void main(String[] args) {\n double x1 = 1, y1 = 3; \/\/ Coordinates of the first point P1\n double x2 = 4, y2 = 6; \/\/ Coordinates of the second point P2\n \n double distance = calculateDistance(x1, y1, x2, y2);\n System.out.println(\"Distance between points P1 and P2: \" + distance);\n }\n\n \/\/ Method to calculate the distance between two points\n public static double calculateDistance(double x1, double y1, double x2, double y2) {\n return Math.sqrt(Math.pow((x2 - x1), 2) + Math.pow((y2 - y1), 2));\n }\n}\n<\/code><\/pre>\n5. Output Result<\/h3>\n
When the above code is run, the program calculates and outputs the distance between the two points P1 and P2. The result is approximately 4.24.<\/p>\n
Conclusion<\/h2>\n
Through this lecture, we have understood how to calculate the distance between points in plane geometry. The problem-solving process proceeded as follows: problem analysis, mathematical judgment, distance calculation, writing Java code, and outputting the result. These geometric problems can be applied to various algorithm problems, and it is important to solidify the basic concepts.<\/p>\n
We look forward to covering more geometric problems and algorithms in the future! Thank you.<\/p>\n
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