this is the pdf link, see p2 (mobiles).
SOLUTION : binsrch on answer and check. however my code is giving error (WA). its quite small, so hopefully it will be readable.
Any help is appreciated.
PS: main function only has the binary search part. Check function checks if the dist chosen will cover the entire line. i have removed the redundant segments using deque using the fact that the points are already sorted by x coordinate
code