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)
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