python max function using 'key' and lambda expression

I come from OOP background and trying to learn python. I am using the max function which uses a lambda expression to return the instance of type Player having maximum totalScore among the list players.

def winner():
    w = max(players, key=lambda p: p.totalScore)

The function correctly returns instance of type Player having maximum totalScore. I am confused about the following three things:

1. How does the max function work? What are the arguments it is taking? I looked at the documentation but failed to understand.
2. What is use of the keyword key in max function? I know it is also used in context of sort function
3. Meaning of the lambda expression? How to read them? How do they work?

These are all very noobish conceptual questions but will help me understand the language. It would help if you could give examples to explain. Thanks

lambda is an anonymous function, it is equivalent to:

def func(p):
   return p.totalScore     

Now max becomes:

max(players, key=func)

But as def statements are compound statements they can't be used where an expression is required, that's why sometimes lambda's are used.

Note that lambda is equivalent to what you'd put in a return statement of a def. Thus, you can't use statements inside a lambda, only expressions are allowed.

What does max do?

max(a, b, c, ...[, key=func]) -> value

With a single iterable argument, return its largest item. With two or more arguments, return the largest argument.

So, it simply returns the object that is the largest.

How does key work?

By default in Python 2 key compares items based on a set of rules based on the type of the objects (for example a string is always greater than an integer).

To modify the object before comparison, or to compare based on a particular attribute/index, you've to use the key argument.

Example 1:

A simple example, suppose you have a list of numbers in string form, but you want to compare those items by their integer value.

>>> lis = ['1', '100', '111', '2']

Here max compares the items using their original values (strings are compared lexicographically so you'd get '2' as output) :

>>> max(lis)
'2'

To compare the items by their integer value use key with a simple lambda:

>>> max(lis, key=lambda x:int(x))  # compare `int` version of each item
'111'

Example 2: Applying max to a list of tuples.

>>> lis = [(1,'a'), (3,'c'), (4,'e'), (-1,'z')]

By default max will compare the items by the first index. If the first index is the same then it'll compare the second index. As in my example, all items have a unique first index, so you'd get this as the answer:

>>> max(lis)
(4, 'e')

But, what if you wanted to compare each item by the value at index 1? Simple: use lambda:

>>> max(lis, key = lambda x: x[1])
(-1, 'z')

Comparing items in an iterable that contains objects of different type:

List with mixed items:

lis = ['1','100','111','2', 2, 2.57]

In Python 2 it is possible to compare items of two different types:

>>> max(lis)  # works in Python 2
'2'
>>> max(lis, key=lambda x: int(x))  # compare integer version of each item
'111'

But in Python 3 you can't do that any more:

>>> lis = ['1', '100', '111', '2', 2, 2.57]
>>> max(lis)
Traceback (most recent call last):
  File "<ipython-input-2-0ce0a02693e4>", line 1, in <module>
    max(lis)
TypeError: unorderable types: int() > str()

But this works, as we are comparing integer version of each object:

>>> max(lis, key=lambda x: int(x))  # or simply `max(lis, key=int)`
'111'

Strongly simplified version of max:

def max(items, key=lambda x: x):
    current = item[0]
    for item in items:
        if key(item) > key(current):
            current = item
    return current

Regarding lambda:

>>> ident = lambda x: x
>>> ident(3)
3
>>> ident(5)
5

>>> times_two = lambda x: 2*x
>>> times_two(2)
4

How does the max function work?

It looks for the "largest" item in an iterable. I'll assume that you can look up what that is, but if not, it's something you can loop over, i.e. a list or string.

What is use of the keyword key in max function? I know it is also used in context of sort function

Key is a lambda function that will tell max which objects in the iterable are larger than others. Say if you were sorting some object that you created yourself, and not something obvious, like integers.

Meaning of the lambda expression? How to read them? How do they work?

That's sort of a larger question. In simple terms, a lambda is a function you can pass around, and have other pieces of code use it. Take this for example:

def sum(a, b, f):
    return (f(a) + f(b))

This takes two objects, a and b, and a function f. It calls f() on each object, then adds them together. So look at this call:

>>> sum(2, 2, lambda a:  a * 2)
8

sum() takes 2, and calls the lambda expression on it. So f(a) becomes 2 * 2, which becomes 4. It then does this for b, and adds the two together.

In not so simple terms, lambdas come from lambda calculus, which is the idea of a function that returns a function; a very cool math concept for expressing computation. You can read about that here, and then actually understand it here.

It's probably better to read about this a little more, as lambdas can be confusing, and it's not immediately obvious how useful they are. Check here.

max function is used to get the maximum out of an iterable.

The iterators may be lists, tuples, dict objects, etc. Or even custom objects as in the example you provided.

max(iterable[, key=func]) -> value
max(a, b, c, ...[, key=func]) -> value

With a single iterable argument, return its largest item.
With two or more arguments, return the largest argument.

So, the key=func basically allows us to pass an optional argument key to the function on whose basis is the given iterator/arguments are sorted & the maximum is returned.

lambda is a python keyword that acts as a pseudo function. So, when you pass player object to it, it will return player.totalScore. Thus, the iterable passed over to function max will sort according to the key totalScore of the player objects given to it & will return the player who has maximum totalScore.

If no key argument is provided, the maximum is returned according to default Python orderings.

Examples -

max(1, 3, 5, 7)
>>>7
max([1, 3, 5, 7])
>>>7

people = [('Barack', 'Obama'), ('Oprah', 'Winfrey'), ('Mahatma', 'Gandhi')]
max(people, key=lambda x: x[1])
>>>('Oprah', 'Winfrey')

According to the documentation:

max(iterable[, key])
max(arg1, arg2, *args[, key])
Return the largest item in an iterable or the largest of two or more arguments.

If one positional argument is provided, iterable must be a non-empty iterable (such as a non-empty string, tuple or list). The largest item in the iterable is returned. If two or more positional arguments are provided, the largest of the positional arguments is returned.

The optional key argument specifies a one-argument ordering function like that used for list.sort(). The key argument, if supplied, must be in keyword form (for example, max(a,b,c,key=func)).

What this is saying is that in your case, you are providing a list, in this case players. Then the max function will iterate over all the items in the list and compare them to each other to get a "maximum".

As you can imagine, with a complex object like a player determining its value for comparison is tricky, so you are given the key argument to determine how the max function will decide the value of each player. In this case, you are using a lambda function to say "for each p in players get p.totalscore and use that as his value for comparison".