Given two integers X and Y, the task is to find the maximum number of points of intersection possible among X circles and Y straight lines.
Input: X = 4, Y = 4
4 lines intersect each other at 6 points and 4 circles intersect each other at maximum of 12 points.
Each line intersects 4 circles at 8 points.
Hence, 4 lines intersect four circles at a maximum of 32 points.
Thus, required number of intersections = 6 + 12 + 32 = 50.
Input: X = 3, Y = 4
It can be observed that there are three types of intersections:
- The number of ways to choose a pair of points from X circles is . Each such pair intersect at most two points.
- The number of ways to choose a pair of points from Y lines is . Each such pair intersect in at most one point.
- The number of ways to choose one circle and one line from X circles and Y lines is is . Each such pair intersect in at most two points.
So, the maximum number of point of intersection can be calculated as:
Thus, formula to find maximum number of point of intersection of X circles and Y straight lines is:
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
- Puzzle | Connect 9 circles each arranged at center of a Matrix using 3 straight lines
- Count of different straight lines with total n points with m collinear
- Count of intersections of M line segments with N vertical lines in XY plane
- Count of rectangles possible from N and M straight lines parallel to X and Y axis respectively
- Ratio of the distance between the centers of the circles and the point of intersection of two direct common tangents to the circles
- Ratio of the distance between the centers of the circles and the point of intersection of two transverse common tangents to the circles
- Represent a given set of points by the best possible straight line
- Maximum XOR value of maximum and second maximum element among all possible subarrays
- Check if three straight lines are concurrent or not
- Check whether two straight lines are orthogonal or not
- Check if given two straight lines are identical or not
- Count straight lines intersecting at a given point
- Maximum number of line intersections formed through intersection of N planes
- Maximum points of intersection n circles
- Check whether a straight line can be formed using N co-ordinate points
- Maximum points of intersection n lines
- Python - Find the maximum number of triangles with given points on three lines
- Minimum LCM and GCD possible among all possible sub-arrays
- Number of intersections between two ranges
- Print N lines of 4 numbers such that every pair among 4 numbers has a GCD K
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.