After the tree is populated as described immediately above, execute a set of 10 contains operations 1,000 times, timing how long it takes to complete all 10,000 contains calls. Report out the execution time. Rebalance the tree and repeat the 10,000 calls, and report out how long it takes after the tree has been rebalanced. Be sure to avoid including any I/O in the execution times. Use these values as the actual parameters for the contains calls: 2, 7, 1117, 22307, 33331, 45533, 48611, 4, 24000, 50000

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.

How can a user open a blank presentation? 1.on the file menu, click new, and then click recent templates 2.on the file menu, click new, and then click blank presentation 3. on the view menu, click templates, and then click recent templates 4. on the view menu, click samples, and then click blank presentation

Atool that matches persoal skills qualities interests and talets to a career is called a