Suppose we are comparing implementations of insertion sort and merge sort on the same machine. for inputs of size n, insertion sort runs in 8ð2 steps, while merge sort runs in 64ð log2 ð steps. for which values of ndoes insertion sort beat merge sort?

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.

Ihave a music player on my phone. i can buy songs, add them to playlists and play them. obviously it would be redundant to store each song in each playlist; each playlist is just a list of pointers to the songs. for this lab you will simulate this behavior. your program will need to have options to: add songs to the system library (you will store the text of the first line of the song, rather than the audio) add playlists add songs to a playlist list playlists play a playlist list all of the songs in the library with a count of how many times each song has been played remove a song from a playlist remove a playlist remove a song from the library (and thus from all playlists that contain it) note that we will not be checking many error cases. in real programming this would be bad, you should usually try to recognize and respond to as many types of errors as you can. in the context of class we are trying to acquaint you with as many concepts as possible, so for the sake of educational efficiency we will not be checking most errors in this lab, you may assume that your user provides correct input. you may add all appropriate error testing if you wish, but we will not be testing for it.

1. which of the following is a search engine? a) mozilla firefox b)internet explorer c)google d)safari 2. which of the following statements is true? a) all search engines will provide the same results when you enter the same query. b) all search engines use the same amount of advertisements. c) some search engines are also browsers. d) search engines often provide different results, even when you enter the same query.