Lecture 2, Part 2 Advanced Exercises

Before starting, please run the following cell

In [ ]:
from __future__ import division, print_function 

Question 12

12.1

Write a function called invertBool(l) that takes in a list of lists called l, and returns a list of lists that represents all the booleans in the matrix, inverted.

For example:

invertBool(
[[True, False, True], [False, True, True], [False, False, False]]) =>

[[False, True, False], [True, False, False], [True, True, True]]

In [11]:
# write code here 

Run the following cell to test your invertBool(l) function.

In [10]:
def test(): 
    lsts = [[[True, False, True, True],
            [False, False, False, True],
            [True, True, True, True],
            [False, True, False, True]],
            
            [[False, True, False],
             [True, True, True],
             [False, False, False]]]
    ans = [[[False, True, False, False],
            [True, True, True, False],
            [False, False, False, False],
            [True, False, True, False]],
            
            [[True, False, True],
             [False, False, False],
             [True, True, True]]]
    
    for i in range(2):
        if invertBool(lsts[i]) != ans[i]: 
            return "Test Failed :'("
    return "All Tests Passed!"

test()
Out[10]:
'All Tests Passed!'

12.2

Write a function called diagProd(l) that takes in a list of integer or float lists where each nested list are the same length, and returns the product of a matrix's diagonal. You may assume the list is non-empty.

For example:

diagProd(
[[12, 5, 3], [2, 1, 3], [35, 23, 2]] )

will return 24.

In [20]:
# Write your function here

Run the following cell to test your diagProd(l) function.

In [21]:
def test(): 
    lst = [
           [[12, 5, 3],
            [2, 1, 3],  
            [35, 23, 2]], 
           [[54, 345, 23, 25],
            [135, 43, 3, 5],
            [75, 46, 63, 15],
            [16, 10, 9, 2]],
            [[1]], 
            [[2, 4],
             [4, 2]]
          ]
    ans = [24,292572, 1, 4]
    for i in range(2):
        if diagProd(lst[i]) != ans[i]: 
            return "Test Failed :'("
    return "All Tests Passed!"

test()
Out[21]:
'All Tests Passed!'

12.3

Write a function called symmetric(l) that takes in a list of integer lists called l, and returns a boolean on whether or not the matrix is symmetric. Recall that a matrix is symmetric if and only if when the ith columm becomes the ith row, it is still the same matrix.

Hint: You can do this without looking at the elements more than once.

For example:

symmetric(
[[12, 5, 3], [2, 1, 3], [35, 23, 2]] ) will return False.

symmetric(
[[1, 4, 5], [4, 2, 6], [5, 6, 3]] ) will return True.

In [34]:
# Write your code here

Run the following cell to test your symmetric(l) function.

In [33]:
def test(): 
    lst = [[[12, 5, 3],
            [2, 1, 3],  
            [35, 23, 2]],
           
            [[1, 4, 5],
            [4, 2, 6],  
            [5, 6, 3]], 
           
            [[2, 4], 
             [4, 2]],
           
           [[54, 345, 23, 25],
            [135, 43, 3, 5],
            [75, 46, 63, 15],
            [16, 10, 9, 2]]
          ]
    ans = [False, True, True, False]
    
    for i in range(4):
        if symmetric(lst[i]) != ans[i]:
            return f'Test Case #{i +1} Failed'
    return "All Test Cases Passed!"

test()
Out[33]:
'All Test Cases Passed!'

Question 13

13.1

Write the function advancedCheckered(x) that takes in an integer s and prints a s by s checkerboard that has hashtags starting on even lines, and has percent signs starting on the odd lines, and they alternate during the line.

For example:

advancedCheckered(4)  
#%#%
%#%#
#%#%
%#%#
In [1]:
# Write code here

Question 14

14.1

An image is usually represented as a 2D array, but let's say we only have access to a 1D array. Is there a way that we can represent a 2D array using a 1D array? Here's a picture that describes how we can store an image as a 1D array.

<img src = "2D.png" width = "800px"> <img src = "1D.png" width = "800px">

Write a function called getPixel(lst, h, w, i, j) where lst is a 1D array, h is the height of the image, w is the width of image, i is the row that the pixel is on, and j is the column that the pixel is on. Then, this function will return the value that the pixel holds.

14.2

Write a function called 1Dto2D that takes in a list of integer pixels lst, height h, and width w and returns the 2D array representation of the image.

For example:

1Dto2D([34, 234, 23, 255, 98, 23, 155, 87], 2, 4)  
[[34, 234, 23, 255],
  [98, 23, 155, 87]]