Maximum number of line intersections formed through intersection of N planes
Given N planes. The task is to find the maximum number of line intersections that can be formed through the intersections of N planes.
Input: N = 3
Input: N = 5
Let there be N planes such that no 3 planes intersect in a single line of intersection and no 2 planes are parallel to each other. Adding ‘N+1’th plane to this space should be possible while retaining the above two conditions. In that case, this plane would intersect each of the N planes in ‘N’ distinct lines.
Thus, the ‘N+1’th plane could atmost add ‘N’ new lines to the total count of lines of intersection. Similarly, the Nth plane could add at most “N-1′ distinct lines of intersection. It is easy therefore to see that, for ‘N’ planes, the maximum number of lines of intersection could be:
(N-1) + (N-2) +...+ 1 = N*(N-1)/2
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)