$ mkdir ~/cs170/tests $ mkdir ~/cs170/tests/final $ cd ~/cs170/test/final
This portion of the test is worth 28 total points. You may only access this webpage, the Python documentation website, and the tkinter documentation website. NO OTHER WEBSITES ARE PERMITTED. As usual, you are not allowed to directly copy any code from the Internet or another individual. You should also follow all coding standards discussed thus far.
Create a file called question_10.py in your directory.
Inside this file, write a function
called cartesian_square(a_list)
. This function takes a
list of values, and returns a list of tuples which represents the
cartesian product of a_list with itself.
Cartesian Product of a list A with itself is defined as the list of ALL ordered pairs of the elements from A.
my_list = [0, 1, 2, 3] print(cartesian_square(my_list)) # [(3, 3), (2, 2), (2, 3), (3, 2), (1, 1), (1, 2), (2, 1), (1, 3), # (3, 1), (0, 0), (0, 1), (1, 0), (0, 2), (2, 0), (0, 3), (3, 0)]
(9 points)
Download the file linked_list.py, and save it into
your test directory. Write a method
called delete_duplicates(self)
, which removes all
duplicates from the linked list. You may write any additional
functions and methods as necessary.
#Test Case 1: No duplicates test_list = linked_list.LinkedList() for i in range(10): test_list.append(i) print(test_list) #head -> 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> None test_list.delete_duplicates() print(test_list) #head -> 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> None #Test Case 2: duplicates side by side test_list = linked_list.LinkedList() for i in range(5): test_list.append(i) test_list.append(i) print(test_list) #head -> 0 -> 0 -> 1 -> 1 -> 2 -> 2 -> 3 -> 3 -> 4 -> 4 -> None test_list.delete_duplicates() print(test_list) #head -> 0 -> 1 -> 2 -> 3 -> 4 -> None #Test Case 3: duplicates elsewhere in the list test_list = linked_list.LinkedList() for i in range(5): test_list.append(i) for i in range(4, -1, -1): test_list.append(i) print(test_list) #head -> 0 -> 1 -> 2 -> 3 -> 4 -> 4 -> 3 -> 2 -> 1 -> 0 -> None test_list.delete_duplicates() print(test_list) #head -> 0 -> 1 -> 2 -> 3 -> 4 -> None
(10 points)
Download the graph.py file into your test
directory. In a file called question_12.py, write a
function called is_connected(a_graph)
, which
returns True if the specified undirected graph is
connected.
An undirected graph is connected if every vertex
appears in a depth first traversal of the graph, irrelevant of the
starting position. Write a function
called depth_first(a_graph, curr_vertex,
visited_list)
, which adds all of the verticies that can be
reached from curr_vertex to the visited list.
my_graph = graph.Graph("exam_sample.in") print(is_connected(my_graph)) # True my_graph.adjacency_matrix[2][4] = 0 print(is_connected(my_graph)) # False
(9 points)
For this bonus question, you will be adding to the graph.py class.
In graph theory, a hamiltonian cycle is a set of edges that visits
each vertex exactly once, and the start vertex and end vertex are
connected by an edge. Add a method to the graph class
called has_hamiltonian
, which returns True if a
hamiltonian cycle exists in the graph. You may need to write a
helper function.
Note: You will likely need to use backtracking to solve this problem.
A collection of test cases can be found here.
import graph my_graph = graph.Graph("sample_graphs/simple_graph") print(my_graph.has_hamiltonian()) #True my_graph = graph.Graph("sample_graphs/line_graph") print(my_graph.has_hamiltonian()) #False my_graph = graph.Graph("sample_graphs/cycle_graph") print(my_graph.has_hamiltonian()) #True my_graph = graph.Graph("sample_graphs/simple_non_path") print(my_graph.has_hamiltonian()) #False my_graph = graph.Graph("sample_graphs/complex_non") print(my_graph.has_hamiltonian()) #False my_graph = graph.Graph("sample_graphs/dodecahedron") print(my_graph.has_hamiltonian()) #True
(8 points)
In a file called bonus.py, write a function
called draw_recursive_tree(curr_point, curr_length,
curr_angle)
. This method takes a tuple of integers (x,
y), a positive integer, and an angle in radians. This
method should use Tk to draw a fractal tree.
A fractal tree can be drawn by drawing a line from curr_point to the point curr_length distance away at angle curr_angle. from this new point, recursively draw a line at angle \( \pm \frac{\pi}{4} \)from the current angle, with half the length. Continue doing this until the curr_length is 1.
The following image is what a tree looks like, if DIMS = 400, and the following statement is executed:
draw_recursive_tree((DIMS // 2, DIMS), DIMS // 2, math.pi / 2)
(5 points)
When you have finished, create a tar file of your final
directory. To create a tar file, execute the following commands:
cd ~/cs170/tests tar czvf final.tgz final/
To submit your activity, go to inquire.roanoke.edu. You should
see an available assignment called Final Exam
.