Big O of min and max in Python

To find the maximum or minimum of a sequence, you must look at each element once, thus you can't get better than O(n).

Of course, Python min and max have O(n) too: docs.

You can write your own min/max function with a for loop and it will have the same complexity, but will be slower because it is not optimized in C.

For time complexity O(1) You can use this:

minimum = y ^ ((x ^ y) & -(x < y)); // min(x, y)

maximum = x ^ ((x ^ y) & -(x < y)); // max(x, y)

It's O(n). It's a general algorithm, you can't find the max/min in the general case without checking all of them. Python doesn't even have a built-in sorted collection type that would make the check easy to specialize.

A for loop would have the same algorithmic complexity, but would run slower in the typical case, since min/max (on CPython anyway) are running an equivalent loop at the C layer, avoiding bytecode interpreter overhead, which the for loop would incur.