Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in AŒ1. Then find the second smallest element of A, and exchange it with AŒ2. Continue in this manner for the first n1 elements of A. Write pseudocode for this algorithm, which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n 1 elements, rather than for all n elements? Give the best-case and worst-case running times of selection sort in ‚-notation.

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.

1)consider the following code snippet: #ifndef book_h#define book_hconst double max_cost = 1000.0; class book{public: book(); book(double new_cost); void set_cost(double new_cost); double get_cost() const; private: double cost; }; double calculate_terms(book bk); #endifwhich of the following is correct? a)the header file is correct as given. b)the definition of max_cost should be removed since header files should not contain constants. c)the definition of book should be removed since header files should not contain class definitions. d)the body of the calculate_terms function should be added to the header file.

What is a programming method that provides for interactive modules to a website?