I think their analysis is assuming that you have precomputed all values of p and in that case the runtime of the method is indeed O(n). Computing the values of p though will take O(n log n).
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.