This is data structures, please help.

Students will be able todetermine the relation between the growth rate of functions, use asymptotic notations, determine the time complexity of programs, and create array-based implementations of an abstract data type.

Students will be able to determine the relation between the growth rate of functions, use asymptotic notations, determine the time complexity of programs, and create array-based implementations of an abstract data type. Assignment Questions 1. (This exercise is a variation of Exercise 2.1 in Chapter 2 of the textbook) Order the following functions according to their growth rates from slowest to fastest: n, vn,n log? n, 2, n, 37, nalogn,n", nlogn 2. Using the definition of Big-Oh discussed in class, to prove that 10n = O(n) we can select (a) c = 0, no = 1 (b) c = 1, no = 1 (c) c = 2, no = 5 (d) c = 1, no = 9 3. (This exercise is a variation of Exercise 2.7 in Chapter 2 of the textbook) For each of the following program fragments, determine the time complexity: O(n), 012"), O(n%), O(nxi), (i?), O(n xi?), or O(n). Size of the input is n in each case. (1) sum =0; for(i = 0; i