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 q 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 largest.

    How `key` works?

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've 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)

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

Example 2: Applying max to a list of lists.

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

By default max will will compare the items by the first index, if the first index is same then it'd compare the second index. As in my example all items have 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
    >>> max(lis, key=lambda x: int(x)) #compare integer version of each item

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>
    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)`


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