Lab 4 Solutions

Lambda

Lambda expressions are one-line functions that specify two things: the parameters and the return value.

lambda <parameters>: <return value>

While both lambda and def statements are related to functions, there are some differences.

lambda x: x * x
           

def square(x):
    return x * x

A lambda expression by itself is not very interesting. As with any objects such as numbers, booleans, strings, we usually:

• assign lambda to variables (foo = lambda x: x)
• pass them in to other functions (bar(lambda x: x))
• return them as the results of other functions (return lambda x: x)
• return them as the results of other lambdas (lambda x: lambda y: x + y)

In the final example above, the outer lambda (lambda x) takes in a value x, and it returns another lambda (lambda y) that takes an argument y and returns x+y.

Environment Diagrams

Environment diagrams are one of the best learning tools for understanding lambda expressions because you're able to keep track of all the different names, function objects, and arguments to functions. We highly recommend drawing environment diagrams or using Python tutor if you get stuck doing the WWPD problems below. For examples of what environment diagrams should look like, try running some code in Python tutor. Here are the rules:

Lambdas

Note: As we saw in the lambda expression section above, lambda functions have no intrinsic name. When drawing lambda functions in environment diagrams, they are labeled with the name lambda or with the lowercase Greek letter λ. This can get confusing when there are multiple lambda functions in an environment diagram, so you can distinguish them by numbering them or by writing the line number on which they were defined.

1. Draw the lambda function object and label it with λ, its formal parameters, and its parent frame. A function's parent frame is the frame in which the function was defined.

This is the only step. We are including this section to emphasize the fact that the difference between lambda expressions and def statements is that lambda expressions do not create any new bindings in the environment.

WWPD

Question 1: WWPD: Lambda the Free

Use Ok to test your knowledge with the following "What Would Python Display?" questions:

python3 ok -q lambda -u

For all WWPD questions, type Function if you believe the answer is <function...>, Error if it errors, and Nothing if nothing is displayed. As a reminder, the following two lines of code will not display anything in the Python interpreter when executed:

>>> x = None
>>> x

>>> lambda x: x  # A lambda expression with one parameter x
______
<function <lambda> at ...>
>>> a = lambda x: x  # Assigning the lambda function to the name a
>>> a(5)
______
5
>>> (lambda: 3)()  # Using a lambda expression as an operator in a call exp.
______
3
>>> b = lambda x: lambda: x  # Lambdas can return other lambdas!
>>> c = b(88)
>>> c
______
<function <lambda> at ...
>>> c()
______
88
>>> d = lambda f: f(4)  # They can have functions as arguments as well.
>>> def square(x):
...     return x * x
>>> d(square)
______
16

>>> z = 3
>>> e = lambda x: lambda y: lambda: x + y + z
>>> e(0)(1)()
______
4
>>> f = lambda z: x + z
>>> f(3)
______
NameError: name 'x' is not defined

>>> higher_order_lambda = lambda f: lambda x: f(x)
>>> g = lambda x: x * x
>>> higher_order_lambda(2)(g)  # Which argument belongs to which function call?
______
Error
>>> higher_order_lambda(g)(2)
______
4
>>> call_thrice = lambda f: lambda x: f(f(f(x)))
>>> call_thrice(lambda y: y + 1)(0)
______
3
>>> print_lambda = lambda z: print(z)  # When is the return expression of a lambda expression executed?
>>> print_lambda
______
Function
>>> one_thousand = print_lambda(1000)
______
1000
>>> one_thousand
______
# print_lambda returned None, so nothing gets displayed

Lambdas

Question 2: Exponents Are Fun

Using a lambda expression, complete the exponent_fun function. This function should take an argument exponent and returns the base raised to that exponent. The body of the function must be one line long!

def exponent_fun(exponent):
    """
    Returns a function that takes one argument and returns the 
    base raised to that exponent.
    >>> square = exponent_fun(2)
    >>> square(5)
    25
    >>> cubed = exponent_fun(3)
    >>> cubed(2)
    8
    """
    "*** YOUR CODE HERE ***"
    
    return lambda base: base ** exponent

Use OK to test your code:

python3 ok -q exponent_fun

Question 3: Compare Lambda

Write a function that returns a subtraction lambda function or addition lambda function depending on the operator passed into compare_lambda. The lambda functions you create should take in two arguments. If a user passes in an invalid operator, use a lambda function to return "Remember to only use + or -!".

def compare_lambda(operator):
    """
    Write a function that returns a subtraction lambda 
    function or addition lambda function depending on 
    the operator passed into compare lambda. Both lambda 
    functions take in two arguments.

    >>> adding = compare_lambda("+")
    >>> adding(3,2)
    5
    >>> subtracting = compare_lambda("-")
    >>> subtracting(6,2)
    4
    >>> operator_not_supported = compare_lambda("*")
    >>> operator_not_supported(2,3)
    'Remember to only use + or -!'
    """
    "*** YOUR CODE HERE ***"
    if operator == "-":
        return lambda x, y: x - y
    elif operator == "+":
        return lambda x, y: x + y
    else:
        return lambda x, y: 'Remember to only use + or -!'

Use OK to test your code:

python3 ok -q compare_lambda

Dictionaries

Question 4: Flip Dictionary

Implement the function flip_dict which takes in a dictionary and returns a similar dictionary where the values have become the keys and the keys have become the values.

In this problem, you can assume that each key value pair is unique, and no key or value will be repeated or used more than once.

def flip_dict(dictionary):
    """Returns a flipped version of the original dictionary.

    >>> TAs = {"12pm-2pm": "sean", "4pm-6pm": "rebecca", "2pm-4pm": "lily"}
    >>> flipped_TAs = flip_dict(TAs)
    >>> flipped_TAs 
    {'sean': '12pm-2pm', 'rebecca': '4pm-6pm', 'lily': '2pm-4pm'}
    """
    "*** YOUR CODE HERE ***"
    
    result_dict = {}
    for key in dictionary:
        value = dictionary[key]
        result_dict[value] = key
    return result_dict

Use OK to test your code:

python3 ok -q flip_dict

Question 5: Build the Full Roster

Implement the function common_players. The common_players function takes in a roster dictionary and identifies which keys share the same values. The function returns a new dictionary of this structure:

• Keys: The values from the roster dictionary
• Values: A list of keys from roster that share that same value.

def common_players(roster):
    """Returns a dictionary containing values along with a corresponding
    list of keys that had that value from the original dictionary.
    >>> full_roster = {"bob": "Team A", "barnum": "Team B", "beatrice": "Team C", "bernice": "Team B", "ben": "Team D", "belle": "Team A", "bill": "Team B", "bernie": "Team B", "baxter": "Team A"}
    >>> player_dict = common_players(full_roster)
    >>> dict(sorted(player_dict.items()))
    {'Team A': ['bob', 'belle', 'baxter'], 'Team B': ['barnum', 'bernice', 'bill', 'bernie'], 'Team C': ['beatrice'], 'Team D': ['ben']}
    """
    "*** YOUR CODE HERE ***"
    
    result_dict = {}
    for player in roster:
        team = roster[player]
        if team in result_dict:
            result_dict[team] += [player]
        else:
            result_dict[team] = [player]
    return result_dict

Use OK to test your code:

python3 ok -q common_players