help in solving these assignments

Write the code for the data type, as well as the poplast and last functions. You may also need to write a function norm that ensures amortised constant time under all conditions. [8 markings] (c) Consider the complexity of your winning diff technique for Part (a). Assume that the three auxiliary functions compute in constant time for this question. | For the running time of your method, give the recurrence relation T(n), where n is the number of coins in the row. (ii) State the algorithm's complexity in Olevel (a) a perfect number The sieve algorithm is used to locate all prime integers up to a certain limit of n. The algorithm keeps track of a list of integers ranging from 2 to n. The next step is to Write a Java program that adds the provided values to a defined array for each of the n (as entered) and n integer inputs. (a) Demonstrate how you'll make a Java array with 1,000 integer values. [1 mark] (b) An array's values could be utilized to represent decimal digits. a visual representation of a large number For instance, the number one 7 contains decimal value60 = 24d 602 = (V24d)2 3600 = 24d 24 24 150 = d you agree or disagree with the investigator's equation? Why or why not?As you solve the following square root equations, determine the most efficient way to check for extraneous solutions. a. x+8 = -5 b. V4x = -2 c. V3x = x d. 2x + 10 = 6 e. x = v6 -x