Problem 1 In one of the national parks the park administration wants to set up warning signs to inform tourists that they should check themselves for ticks after their hike. The park has a number of recommended routes, each of which touch some points of interest (POI). Different routes may contain the same POI. The signs will be placed at the POIs. The park wants to put up as few signs as possible, but in such a way that each route contains at least one sign. There are a total of n POIs and m routes.

(a) (5 points) Assume that you are given a "black-box" machine that can answer certain questions instantaneously. You can post to it the routes (as POI sequences) and a number k, and then the machine will output "yes" if there is a set of k locations for the signs so that each route contains some. Otherwise it returns "no". (It will not tell you the exact locations though.) Show an algorithm that can use polynomial number of calls to this machine and finds the minimum number k of signs required.

(b) (10 points) In class, you have learned about a problem called the set cover problem. Show that the sign placement problem is equivalent to the set cover problem, in the following way. Give a reduction of the sign placement problem to the set cover problem, and also a reduction from of the set cover problem to the sign placement problem.

Write a program that takes in 3 inputs [players (int type), expected game time (double type), team (char type)] and calculates actual game time (double) based on the following conditions: if the number of players or the expected game time is less than or equal to zero, it should output wrong input if the number of players is greater than 0 and less than or equal to 6 and if they are on the â€r’ or â€r’ team, their game time will be 10% faster. and if they are on the â€b’ or â€b’ team, their game time will be 15% faster. and if they are on the â€y’ or â€y’ team, their game time will be 20% faster. and if they are on any other team, they will play 0% faster. if the number of players is greater than 6 but less than or equal to 12 and if they are on the â€r’ or â€r’ team, their game time will be 20% faster. and if they are on the â€b’ or â€b’ team, their game time will be 25% faster. and if they are on the â€y’ or â€y’ team their game time will be 30% faster. and if they are on any other team, they will play 0% faster. if the number of players is greater than 12 but less than or equal to 18 and if they are on the â€r’ or â€r’ team, their game time will be 30% faster. and if they are on the â€b’ or â€b’ team, their game time will be 35% faster. and if they are on the â€y’ or â€y’ team, their game time will

Kyle, a receptionist for a building supply company, recently won an award for saving his company money on their phone system. after being presented with kyle's research, the company changed the way in which it made long-distance phone calls and cut their expenses in this area by 75 percent. the new system the kyle's company most likely adopted was wired communications switching stations voip hdtv

Iam a bacterium. i cause stomach cramps and diarrhea. i am caused by eating rotten foodssuch as chicken, fish, or eggs. sometimes turtles carry my bacteria.what am i?