Problem 3 (20 points). A minor league baseball team tracks statistics for all of its pitchers during a season, looking for players that can throw perfect games. (A perfect game is when a pitcher does not allow a single player from the opposing team to reach a base.) For a given pitcher, their record records 1 if they pitched a perfect game, 0 if they pitched but allowed players on base, and -1 if they did not play for each of the n games in the season. For example, their record may look like (0,0,1,-1,0,-1,1,-1,1,0,...). (a) Write pseudocode that reports if a pitcher ever threw a perfect game during the season. (b) What pitching record gives the best case running time for your algorithm? How many games need to be checked? (c) What pitching record gives the worst case running time for your algorithm? How many games need to be checked? (d) The team's corporate sponsor "Crazy Coffee is offering a year's worth of free coffee to any season ticket holder if the same pitcher throws two perfect games in a row, without any breaks between them. At the end of the season, they need to identify if any of the pitchers threw two consecutive perfect games. Write pseudocode that can determine if pitcher P earned free coffee for a year for all the season ticket holders by looking at fewer than n entries in P's record. Assume that n%3= 1. Hint: Start by looking at the first even game.]