Triathlon Competitor Scheduling You are trying to schedule triathlon contestants so that the triathlon completes as early in the day as possible. (The triathlon completes when all the contestants are done.) Each contestant has a projected swimming time, running time, and biking time. Since the pool is very small only one contestant can be in the pool at a time. Any number of contestants can be biking and running at the same time. The contestants first swim, then bike, and finally run. Assuming that each contestant will complete each event in their projected time, what is the best order to send the people out, if you want the whole competition to be over as soon as possible? That is, give and efficient algorithm that produces a schedule whose completion time is as early as possible. A. Specify an efficient greedy algorithm to achieve the goal of earliest completion of the competition. B. Prove your algorithm always finds the optimal solution. C. Analyze your algorithm's complexity.

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

You need a reliable network for about twenty-five computers that will be distributed across a large building. it is important that the network be relatively cheap. which topology should you use?

Dave has to create animations for a game. which tool can dave use?