Week 5: Lists

Week 5: Lists#

Important

First, download_week05.py and run the script in VSCode. You may need to confirm the download in your browser.

The script should end with Successfully completed!. If you encounter an error, follow the instructions in the error message. If needed, you can proceed with the exercises and seek assistance from a TA later.

Note

Many of the following exercises can also be solved with NumPy arrays. This has some advantages, but also some disadvantages compared to lists. We will cover NumPy arrays in a later lecture. For this exercise, please use lists.

Exercise 5.1: Warm-up with lists#

Before you start with the exercises, try out some simple list operations:

Create a list of numbers and print it.
Reverse the list
Sort the list
Add a number to the list
Remove a number from the list (try the last number, the first number, and a number in the middle)
Create a list of strings and print it.
Only keep the first three elements of the list
Assign a new value to the second element of the list
Try out what happens when you assign the same list to two different variables and then modify one of the variables. Why is this important to keep in mind?

Tip

If you want to create a copy of a list and assign it to a new variable, you can use the list.copy() function. This can be useful if you want to modify a list but also keep the original list.

Video 5.1: Warmup on list and common list operations

Exercise 5.2: Average of a list#

Exercise 5.2

In this first exercise, you will write a function that calculates the average of a list of numbers. You can assume that the input list contains one or more numbers.

Test your function on a few examples. For instance, the average of the list [4, 2, 1, 3] should be 2.5.

cp.ex05.average.calculate_average(nums)#

Return the average of a list of numbers.

Parameters: nums (list) – list of numbers
Return type: float
Returns: average of list

You can run the provided tests by inserting the function into cp/ex05/average.py.

Exercise 5.3: Conditional maximum#

Exercise 5.3

In this exercise, you are given a list of numbers and a threshold. You want to find the largest number that is strictly smaller than the threshold. If no number is smaller than the threshold, your function should return 0.

Try a few examples:

>>> a = [1, 2, 3, 4, 5]
>>> conditioned_maximum(a, 3)
2
>>> conditioned_maximum(a, 0)
0
>>> conditioned_maximum(a, 10)
5

cp.ex05.conditioned_maximum.conditioned_maximum(nums, threshold)#

Return the maximum of a list of numbers, that is strictly smaller than the given threshold.

Parameters

nums (list) – list of numbers
threshold (float) – limit for maximum value

Return type

float

Returns

maximum of list thats smaller than the threshold

Insert your function into cp/ex05/conditioned_maximum.py to test it.

Exercise 5.4: Find the tallest animal#

Exercise 5.4

Imagine you are given a list of heights of animals, and you want to find the name of the tallest animal that’s still smaller than a given animal. You can use your function from the previous exercise and extend it so it tells you the name of the largest animal that’s smaller than a given height. You can assume that the list of heights and the list of names have the same length, and there is always a number smaller than the threshold.

You can use these lists to test your function:

>>> heights = [1.5, 1.6, 5.5, 3.0, 2.5, 1.0, 1.4]
>>> names = ['cow', 'horse', 'giraffe', 'elephant', 'dinosaur', 'dog', 'deer']
>>> conditioned_maximum_name(heights, names, 2.0)
'horse'
>>> conditioned_maximum_name(heights, names, 3.0)
'dinosaur'

Optional: try writing a new function that takes the name of an animal as input and returns the name of the largest animal that’s smaller than the given animal.

cp.ex05.conditioned_maximum.conditioned_maximum_name(nums, names, threshold)#

Return the name of the maximum of a list of numbers, that is smaller than the given threshold.

Parameters

nums (list) – list of numbers with animal heights.
names (list) – list of animal names
threshold (float) – limit for maximum value

Return type

str

Returns

animal name with the corresponding maximum height, which is shorter than the threshold height.

You can run the provided tests by inserting your functions into cp/ex05/conditioned_maximum.py. (Note: If you solve the optional exercise, the tests will fail.)

Exercise 5.5: Short words#

Exercise 5.5

In this exercise, you are given a string of words, and you want to find all words that are shorter than a given length. Your function should return a string of all shorter words separated by a whitespace ' '.

Try a few examples:

>>> s = 'This is a sentence with some short and some longlonglong words.'
>>> short_words(s, 4)
'is a and'
>>> short_words(s, 2)
'a'
>>> short_words(s, 10)
'This is a sentence with some short and some words.'

Tip

You can use the str.split() function to split a string into a list of words.
You can use the delimiter.join(list)() function to join a list of words into a string. (Remember to define the delimiter.)

cp.ex05.short_words.short_words(words, max_len)#

Return a string of words that are shorter than max_len.

Parameters

words (str) – string of words
max_len (int) – maximum length of words

Return type

str

Returns

string of words that are shorter than max_len

You can run the provided tests by inserting your functions into cp/ex05/short_words.py.

Exercise 5.6: Check if the list is rectangular#

Exercise 5.6

In this exercise, you want to check whether a nested list is rectangular. A nested list is rectangular if all sublists have the same length. Your function should return True if the nested list is rectangular and False otherwise.

Try a few examples:

>>> is_rectangular([[1, 2, 3], ['cat', 'dog', 'mouse']]  )
True
>>> is_rectangular([[1, 2, 3], [1, 2, 3, 4]])
False
>>> is_rectangular([[1, 2, 3], ['cat', 'dog', 'mouse'], [3, 4, 3]])
True
>>> is_rectangular([[1, 2, 3], ['cat', 'dog', 'mouse'], []])
False

You can test your function by inserting it into cp/ex05/rectangular.py.

cp.ex05.rectangular.is_rectangular(nested_list)#

Check if a list is rectangular.

Parameters: nested_list (list) – nested list
Return type: bool
Returns: True if list is rectangular, False otherwise

Exercise 5.7: Vector addition#

Exercise 5.7

In this exercise, you will add two lists elementwise. You can assume that the two lists have the same length. Make sure that you define a new list for the result and that you’re not modifying the input lists.

Note

This corresponds to adding two vectors in linear algebra. Here, we represent the vectors as lists of numbers. Here is a simple example:

\[\begin{split}\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} + \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix} = \begin{pmatrix} 5 \\ 7 \\ 9 \end{pmatrix}\end{split}\]

Test your function on a few examples and make sure to check if your input vectors are still the same.

Test a few examples to see if your function works as expected:

>>> a = [1, 2, 3]
>>> b = [4, 5, 6]
>>> print(a,'+',b,'=',vector_add(a, b))
[1, 2, 3] + [4, 5, 6] = [5, 7, 9]

Optional: What happens if you have two lists of different lengths? Try including a check for length and print an error message if the lists have different lengths.

cp.ex05.vector_add.vector_add(v, w)#

Add two vectors.

Parameters

v (list) – vector 1 (list of numbers)
w (list) – vector 2 (list of numbers, same length as v)

Return type

list

Returns

sum of v and w (list of number)

You can test your function by inserting it into cp/ex05/vector_add.py.

Exercise 5.8: Count Multiples#

Exercise 5.8

In this exercise, you will write a function that counts how many multiples of a given number “m” are in a list of numbers. A multiple of a number “m” is any number that can be divided by m with a remainder of 0. You should return the count of multiples within the list. You can assume that the list contains only numbers.

Test a few examples to see if your function works as expected:

>>> a = [1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> count_multiples(a, 2)
4
>>> count_multiples(a, 3)
3
>>> count_multiples(a, 5)
1
>>> count_multiples(a, 10)
0

cp.ex05.multiples.count_multiples(numbers, m)#

Count the number of numbers that are divisible by m.

Parameters

numbers (list) – list of numbers
m (int) – number to divide by

Return type

int

Returns

number of numbers that are divisible by m

You can test your function by inserting it into cp/ex05/multiples.py.

Exercise 5.9: Create list containing multiples#

Exercise 5.9

Now, you are not interested in the number of multiples, but in the multiples themselves. Write a function that returns a list of all multiples of a given number in a list. You can assume that the list contains one or more numbers.

Test a few examples to see if your function works as expected:

>>> a = [1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> multiples_list(a, 2)
[2, 4, 6, 8]
>>> multiples_list(a, 3)
[3, 6, 9]
>>> multiples_list(a, 5)
[5]
>>> multiples_list(a, 10)
[]

cp.ex05.multiples.multiples_list(numbers, m)#

Make a list with all numbers from a list that are divisible by m.

Parameters

numbers (list) – list of numbers
m (int) – number to divide by

Return type

list

Returns

list of numbers that are divisible by m

You can test your function by inserting it into cp/ex05/multiples.py.

Note

The following exercises are part of Project 3: Lists and dictionaries. The link contains additional details, including how to hand in your results.

Exercise 5.10: Water height#

The height of the water in a pond changes daily, governed by two contributions: the constant decrease of height due to the water outflow and the variable increase of height due to the rain. Given the water height for one day and the rain value \(r\), the water height for the next day can be computed as

\[h_{today} = h_{yesterday} + r - 2\]

If the computed value is negative, it should be replaced by 0, indicating that the pond is empty. The computation can be repeated for any number of days as long as we have rain values.

Write a function that takes a list of rain values and a starting water height and returns the final water height. The list of rain values can be of any length, including zero length.

Does your function return the correct value for the following examples?

>>> water_height(0, [1])
0
>>> water_height(0, [4, 2, 3])
3
>>> water_height(5, [1, 0, 2, 1])
1

Add your solution to cp/ex05/water_height.py to get it graded for the project.

cp.ex05.water_height.water_height(h0, r)#

Calculate the water height after multiple days of rain.

Param: h0: initial height of the water
Param: r: list of rain showers
Return type: int
Returns: height of water after days of rain

Exercise 5.11: Best buy#

You are given a list of prices for items you want to buy and some money. How many items can you buy?

You should be able to start at any index in the list and work your way forwards. You buy the first item you can afford, then the second, and so on. If you run out of money or reach the end of the list, you stop. You should also be able to go through the list backwards in the same manner, stopping if you reach the start of the list.

Tip

To change your starting index, you can define a new index and assign it to the starting index. Use this index to access the list.
To go backwards you can either reverse the list (but remember to adapt your starting index), or you can decrease the index each time you buy an item.

Write a function that takes a list of prices and the amount of money you have and returns the number of items you can buy. Your function should be able to handle all three scenarios.

Test a few examples to see if your function works as expected:

>>> prices = [3, 2, 1, 3, 5]
>>> best_buy(prices, 10, 0, False)
4
>>> best_buy(prices, 3, 1, False)
2
>>> best_buy(prices, 8, 4, True)
2
>>> best_buy(prices, 10, 4, True)
3

Add your solution to cp/ex05/best_buy.py to get it graded for the project.

cp.ex05.best_buy.best_buy(prices, money, start_index, reverse)#

Return the number of items that can be bought with the given amount of money. The function should be able to handle arbitrary starting points and to run the list in reverse.

Parameters

prices (list) – list of prices
money (int) – amount of money
start_index (int) – starting index in list
reverse (bool) – boolean to indicate if list should be run in reverse

Return type

int

Returns

number of items that can be bought with the given amount of money

Exercise 5.12: Tic Tac Toe - Printing the board#

Starting from this exercise and continuing through the exercises for the week, you will be tasked with writing multiple functions to create a Python implementation of the game Tic Tac Toe using lists. The rules of Tic Tac Toe are straightforward:

There are two players, 'X' and 'O'.
The game is played on a \(3\times3\) board.
The players take turns placing their symbol on the board.
The first player to get three of their symbols in a row wins.
If no player succeeds in getting three of their symbols in a row, and there are no empty spaces, the game is a draw.

For this implementation, you can assume that the game board is represented as a nested list (a list of lists) of strings. Each string in the nested list can be one of three values: 'X', 'O', or '-' indicating an empty position.

The moves in the game are specified using a list of two integer indices, referred to as position. The first integer indicates index of the row, and the second integer indicates the index of the column where the player wants to make their move on the board.

Start by implementing a function print_board() that takes as input a board and prints the current game board.

>>> board = [['X', 'X', 'X'], ['-', 'O', '-'], ['-', 'O', '-']]
>>> print_board(board)
XXX
-O-
-O-

cp.ex05.tictactoe.print_board(board)#

Print the current state of the game board.

Parameters: board (list) – List of lists of strings representing the game board.

Add your solution to cp/ex05/tictactoe.py.

Exercise 5.13: Tic Tac Toe - Update board#

Now, let’s create a function called update_board() that allows a player to make a move in the game of Tic-Tac-Toe. This function should take three inputs:

The current state of the game board.
The player who is making the move (either 'X' or 'O').
The position where the player wants to make their move.

The primary purpose of this function is to update the game board with the player’s move, but it should also check that the intended player position is empty so that the board is updated consistently, for a fair game of Tic-Tac-Toe. The function should return the updated game board with the last move played by the specified player. If an invalid move is played, the function should print 'Invalid move!' and not update the board.

>>> board = [['X', 'X', 'X'], ['-', 'O', '-'], ['-', 'O', '-']]
>>> update_board(board, 'O', [2, 2])
[['X', 'X', 'X'], ['-', 'O', '-'], ['-', 'O', 'O']]
>>> update_board(board, 'O', [0, 0])
Invalid move!
[['X', 'X', 'X'], ['-', 'O', '-'], ['-', 'O', 'O']]

cp.ex05.tictactoe.update_board(board, player, position)#

Update the game board with the player’s move.

Parameters

board (list) – List of lists of strings representing the game board.
player (str) – Player making the move (‘X’ or ‘O’).
position (list) – List containing two integer indices [row, column] indicating the position to make a move.

Return type

list

Returns

Updated game board after the move.

Add your solution to cp/ex05/tictactoe.py.

Exercise 5.14: Tic Tac Toe - Get game state!#

Let’s proceed by implementing a function named get_game_state() to determine the game state of the Tic-Tac-Toe game. This function should take the game board as input and assess whether the game has been won by one of the players, if it has resulted in a draw, or if it is still ongoing.

To achieve this, the function will examine the board to check if any player has achieved three symbols in a row, either horizontally, vertically, or diagonally. The function should return:

'X' if player 'X' has won,
'O' if player 'O' has won,
'Draw' if the game is a draw (all positions are filled by players’ symbols),
'-' if the game is still ongoing.

>>> winning_board = [['X', 'X', 'X'], ['-', 'O', '-'], ['-', 'O', '-']]
>>> get_game_state(winning_board)
'X'
>>> ongoing_board = [['X', 'O', '-'], ['-', '-', '-'], ['-', '-', '-']]
>>> get_game_state(ongoing_board)
'-'

cp.ex05.tictactoe.get_game_state(board)#

Check if a player has won the game, if it’s a draw, or if it’s ongoing.

Parameters: board (list) – List of lists of strings representing the game board.
Return type: str
Returns: A string which is ‘X’ if player ‘X’ won, ‘O’ if player ‘O’ has won, ‘Draw’ if the game is a draw, or ‘-’ if the game is ongoing.

Add your solution to cp/ex05/tictactoe.py.

Exercise 5.15: Tic Tac Toe - Putting everything together!#

Finally, implement a function tictactoe() that combines the functions above. Your function should take the board (list of lists), the player ('X', 'O') and the position (list) of the next move as input. It should return and print the updated board. In the case that there is a winner it should print 'Player X won!' or 'Player O won!'. You can use the function iteratively to play Tic-Tac-Toe as in the following example:

>>> board = [['-', '-', '-'], ['-', '-', '-'], ['-', '-', '-']]
>>> board = tictactoe(board, 'X', [0, 1])
-X-
---
---
>>> board = tictactoe(board, 'O', [0, 2])
-XO
---
---
>>> board = tictactoe(board, 'X', [1, 0])
-XO
X--
---
>>> board = tictactoe(board, 'O', [1, 1])
-XO
XO-
---
>>> board = tictactoe(board, 'X', [1, 1])
Invalid move!
-XO
XO-
---
>>> board = tictactoe(board, 'X', [1, 2])
-XO
XOX
---
>>> board = tictactoe(board, 'O', [2, 0])
-XO
XOX
O--
Player O won!

Add your solution to cp/ex05/tictactoe.py to get it graded for the project.

cp.ex05.tictactoe.tictactoe(board, player, position)#

Play a move in the Tic-Tac-Toe game and determine the winner.

Parameters

board (list) – List of lists of strings representing the game board.
player (str) – Player making the move (‘X’ or ‘O’).
position (list) – List containing two integer indices [row, column] indicating the position to make a move.

Return type

list

Returns

Updated game board after the move.

Week 5: Lists

Contents

Week 5: Lists#

Exercise 5.1: Warm-up with lists#

Exercise 5.2: Average of a list#

Exercise 5.3: Conditional maximum#

Exercise 5.4: Find the tallest animal#

Exercise 5.5: Short words#

Exercise 5.6: Check if the list is rectangular#

Exercise 5.7: Vector addition#

Exercise 5.8: Count Multiples#

Exercise 5.9: Create list containing multiples#

Exercise 5.10: Water height#

Exercise 5.11: Best buy#

Exercise 5.12: Tic Tac Toe - Printing the board#

Exercise 5.13: Tic Tac Toe - Update board#

Exercise 5.14: Tic Tac Toe - Get game state!#

Exercise 5.15: Tic Tac Toe - Putting everything together!#