Statement

In an unspecified zoo, there are N walruses" in Romanian sitting neatly in a line. The walruses are numbered from 0 to N-1. The state of the walruses are denoted by a string of N characters \overlinec_0c_1… c_N-1, where: (1) c_i=`.', if walrus i is sleeping; or (2) c_i=`-', if walrus i is awake. In each second, the following two things happen: (1) you can choose to wake up a walrus yourself; and (2) every walrus that was awakened in the previous second wakes up its neighbours. The walruses which were awake at the start will never wake up their neighbours. Since waking up the walruses yourself is dangerous, you ask yourself the following questions: (1) What is the smallest number of walruses you need to wake up yourself to guarantee that every walrus will be awake eventually? (2) When waking up as few walruses yourself as possible, what is the earliest possible time (in seconds) when all the walruses will be awake?