We wish to keep track of all 5-character substrings that occur in a given string, using a trie. show the trie that results when we insert the 14 substrings of length five of the string abcdabacdebacadeba.

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.

Read the code below. what will the computer print if the input for year_variable is 1700? if year_variable == 1776: print("your answer is correct. the declaration of independence was signed in “year_variable”.") elif year_variable < 1776: compute_variable = 1776 - year_variable. print("add “compute_variable“ years to your answer for the correct answer.") elif year_variable > 1776: compute_variable = year_variable - 1776 print("subtract “compute_variable” years from your answer for the correct answer.")

Consider the following code snippet: #ifndef cashregister_h#define cashregister_hconst double max_balance = 6000000.0; class cashregister{public: cashregister(); cashregister(double new_balance); void set_balance(double new_balance); double get_balance() const; private: double balance[12]; }; double get_monthly_balance(cashregister bk, int month); #endifwhich of the following is correct? a)the header file is correct as given.b)the definition of max_balance should be removed since header files should not contain constants.c)the definition of cashregister should be removed since header files should not contain class definitions.d)the body of the get_monthly_balance function should be added to the header file.