Task 1: Iterators & Generators – Fibonacci Numbers *(20 Points)*

First, write an iterator class (**FibonnaciNumberIterator**) which allows to iterate over the Fibonnacci numbers (possibly infinitely many …). Fibonacci numbers fib(n) for n=1,2, … are defined as follows: fib(1)=fib(2)=1, fib(n)=fib(n-1)+fib(n-2), for n greater or equal to 3.

Second, write a generator class (**FibonacciNumberGenerator**) which generates (also possibly infinitely many) Fibonnaci numbers.

Write unit tests for both the iterator and the generator implementations, testing the Fibonnacci numbers for n=1,2,…,10. The tests should, of course, finish in finite time. The tests should assess all methods of the two classes, and should of course test for the correctness of the implementation.

**Task 2: Recursion & Decorators (20 Points)**

First provide a recursive implementation of a function which returns the **nth **fibonnacci number. This function should be named **fib**, then **fib**(1) should return 1, **fib**(2) should return 1, **fib**(3) should return 2, and so on (see the definition of the Fibonnaci numbers in Task 1).

Then, implement a decorator function **trace **(hint: a “higher order function”) which takes a function **fun **as an argument, calls the function, and both prints the arguments the function **fun **is called with as well as the value that function **fun **returns. To make the output more readable, add indentation levels to (recursive) function calls, such that an indented “|-- “ is printed for each recursive call, while increasing the “indentation depth” level by level of the recursion. As a test, use your decorator function, for tracing the function **fib.**

Then, as an example, **fib(5) **would result in something like the following output:

|-- fib 5

| |-- fib 4

| | |-- fib 3

| | | |-- fib 2

| | | | |-- return 1

| | | |-- fib 1

| | | | |-- return 1

| | | |-- return 2

| | |-- fib 2

| | | |-- return 1

| | |-- return 3

| |-- fib 3

| | |-- fib 2

| | | |-- return 1

| | |-- fib 1

| | | |-- return 1

| | |-- return 2

| |-- return 5 5

In the file that you submit, provide some example output, calling the ** decorated **function

Task 3: OOP Design: Graphs and a simple Graph Generator *(20 Points)*

A graph generator is a program for generating random graphs (also known as random networks, or social networks) according to some models. A **graph **consists of **nodes **and **edges**. Edges can be undirected and directed. Implement the specific classes in good object-oriented fashion.

A simple strategy for generating graphs is the Erdos-Renyi model. In the Erdos-Renyi model, the number of nodes ** n **is specified, in addition to an edge probability

For the implementation, you are *not *allowed to use any graph-/network-specific packages like NetworkX, etc. Numpy and SciPy are allowed.

**Task 4: Optimization – Graph Generation (20 Points)**

Another model for graph generation is the Barabasi-Albert model: Here, the network begins with an initial connected network of *m’ *nodes (initially 1). Then, new nodes are added to the network one at a time, until a maximum number of nodes *max_nodes *is reached. Each new node is connected to ** m **<=

for each node *i *with a probability p_{i} as follows:

where *k _{i} *is the degree of node

Implement a Graph-Generator according to the model above which returns the generated graph using the ** generate **method, i.e. implement this in an OOP design using the

For the implementation, you are *not *allowed to use any graph-/network-specific packages like NetworkX, etc. Numpy and SciPy are allowed.

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