3. Exercises

Exercise 3.1

Only one of the following cases is possible. For that case, write the function increase_by_one. For the other cases, explain why it is not possible to write such a function.

a.

>>> val = 5.0
>>> increase_by_one(val)
>>> print(val)
6.0

b.

>>> val = "hello"
>>> increase_by_one(val)
>>> print(val)
hello1

c.

>>> val = [0, 0, 0]
>>> increase_by_one(val)
>>> print(val)
[0, 0, 0, 1]

d.

>>> val = np.array([0, 0, 0])
>>> increase_by_one(val)
>>> print(val)
[0 0 0 1]

Exercise 3.2 (Functions and Mutable Variables)

The method list.reverse() performs an in-place reversal of a list (i.e. it reverses the elements of a list without creating a new list).

>>> a = [1, 2, 3, 4, 5]
>>> a.reverse()
>>> print(a)
[5, 4, 3, 2, 1]

Write a function reverse_array(x) which reverses a Numpy array in place (ie without creating a new array).

def reverse_array(x):
    # your code here

Test your code works as below:

>>> import numpy as np
>>> x = np.array([1, 2, 3, 4, 5])
>>> reverse_array(x)
>>> print(x)
[5 4 3 2 1]

Exercise 3.3 (Nested Lists)

A nested list is a list whose elements are also list. For example,

x = [[1, 2], [3, 4], [5, 6, 7]]

1. What is the type and value of each of the following expressions?

a. x[2] b. x[0][1]

Lists are mutable, which can have some rather surprising consequences when they are nested inside each other.

2. What is the value of x and y after executing the following code? Explain why.

a.

x = [1, 2, 3]
y = [x, x]
x.append(4)

b.

x = [1, 2]
y = []
for i in range(5):
    y.append(x)
x[0] = 100

c.

x = [1]
for z in x:
    x.append(z)

d.

x = []
y = []
x.append(y)
y.append(x)

3. Write a function which flattens a list-of-lists. That is, given the array

[[1, 2, 3], [4, 5, 6], [7], [8, 9]]

your function should return

[1, 2, 3, 4, 5, 6, 7, 8, 9]

Exercise 3.4

Write a function which transposes a list of list. That is, if

[[1, 2, 3, 4, 5],
 [2, 3, 4, 5, 6],
 [3, 4, 5, 6, 7]]

Then your function should return

[[1, 2, 3],
 [2, 3, 4],
 [3, 4, 5],
 [4, 5, 6],
 [5, 6, 7]]

[There are many ways to do this. You should try to find a solution that uses only loops and lists.]