Jugs (This is a variation on Exercise 14 in Chapter 10.1 of the textbook) Two jugs A and B have capacities of 3 and 5 cups respectively, but no measuring markings. You are working in a sink and you can perform as many of the following actions as you want in any order: filling a jug to capacity from the tap. completely emptying a jug into the drain. pouring as much water as possible from one jug into the other (any water left over stays in the first jug). You will now draw two transition diagrams (see lecture 2.1 on munchkins and monsters) to show sequences of steps that can be taken to measure out one cup of water in one of the jugs. In these graphs, • the vertices represent the state of the two jugs, i.e. the quantity of liquid in each jug. 00 is the name of the vertex representing the state where both jugs are empty, and 35 the name of the vertex for the state where both jugs are full • each transition (arrow) represents a single action that changes the states of the jugs. Each arrow is labelled with that action. a) The first graph should show the smallest sequence of actions you can take to measure out one cup of water in one of the jugs. b) The second graph shows a sequence of actions you can take to measure out one cup of water in one of the jugs if the jugs can never in the state where A is full and B is empty.

Question 5 Please answer them correctly by choosing one of the following answer

q6) Which of the following asymptotic notation is used for representing the lower bound of an algorithm with respective space and time complexity? a. Big Alpha (α)​ b. Big Oh(O) c. Big Omega (Ω)​ d. Big Theta (Θ)

Let the universe of discourse be the set of positive integers. By selecting True or False, give the truth value of the following: ThereExistsUnique x (x = 2x + 1). True ○ False

ATTEMPT ONLY IF YOU ARE 100% SURE    DO NOT COPY FROM OTHER WEBSITES

What is the difference between Transform and Conquer & Divide and Conquer?  Justify your answer by providing at one example for each algorithm in solving a problem.

computes and returns the smallest positive integer n for which 1+2+3+...+n equals or exceeds the value of "goal".