Problem: Given a set of tasks and a dependency list between tasks. Output: Ordered list of tasks such that each task is only started once the tasks it depends on are completed. Analyze your algorithm.

Consider the following multiplication problem: Given an integer list (an array) of size n, we want to calculate the product of all numbers in the list and display the result. (a) Define an instance of a problem in general. (b) Specify two different instances of the multiplication problem defined above. (c) What is the solution for each instance in part (b). How did you come up with that solution?

OZ PROGRAMMING LANGUAGE    Exercise 1. (Efficient Recurrence Relations Calculation) At slide 54 of Lecture 10, we have seen aconcurrent implementation of classical Fibonacci recurrence. This is: fun {Fib X} if X==0 then 0 elseif X==1 then 1 else thread {Fib X-1} end + {Fib X-2} end end By calling Fib for actual parameter value 6, we get the following execution containing several calls ofthe same actual parameters.For example, F3, that stands for {Fib 3}, is calculated independently three times (although it providesthe same value every time). Write an efficient Oz implementation that is doing a function call for a givenactual parameter only once.Consider a more general recurrence relation, e.g.:F0, F1, ..., Fm-1 are known as initial values.Fn = g(Fn-1, ..., Fn-m), for any n ≥ m.For example, Fibonacci recurrence has m=2, g(x, y) = x+y, F0=F1=1

Exercise 2.3. What is wrong with this procedure, which is supposed to return True if the element x occurs in the list items, and False otherwise? def member (x, items): for i in items: if x == 1: return True else: return False