Computer Science

You wish to drive from point A to point B along a highway minimizing the time that you are stopped for gas. You are told beforehand the capacity C of you gas tank in liters, your rate F of fuel consumption in liters/kilometer, the rate r in liters/minute at which you can fill your tank at a gas station, and the locations A = x1, ··· , B = xn of the gas stations along the highway. So if you stop to fill your tank from 2 liters to 8 liters, you would have to stop for 6/r minutes. Consider the following two algorithms: (a) Stop at every gas station, and fill the tank with just enough gas to make it to the next gas station. (b) Stop if and only if you don’t have enough gas to make it to the next gas station, and if you stop,fill the tank up all the way. For each algorithm either prove or disprove that this algorithm correctly solves the problem. Your proof of correctness must use an exchange argument.

No hand written solution

Sam is a competitive swimmer that competes in the 100 m freestyle and 100 m backstroke.  High school swimming state averages are as follows: Freestyle:  mean time 72.39 seconds, standard deviation 3.7 seconds Backstroke:  mean time 81.09 seconds, standard deviation 4.1 seconds   If Sam's times were 71.1 seconds in freestyle and 80.1 seconds in backstroke, select the correct words to describe how his times compare to each other. Since the z-score in freestyle is       ["", ""]  than the z-score in backstroke, his time in freestyle is       ["", ""]  when compared to the rest of the swimmers in that event.