Complexity of list.index(x) in Python

It's O(n), also check out: http://wiki.python.org/moin/TimeComplexity

This page documents the time-complexity (aka "Big O" or "Big Oh") of various operations in current CPython. Other Python implementations (or older or still-under development versions of CPython) may have slightly different performance characteristics. However, it is generally safe to assume that they are not slower by more than a factor of O(log n)...

According to said documentation:

list.index(x)

Return the index in the list of the first item whose value is x. It is an error if there is no such item.

Which implies searching. You're effectively doing x in s but rather than returning True or False you're returning the index of x. As such, I'd go with the listed time complexity of O(n).

Any list implementation is going to have an O(n) complexity for a linear search (e.g., list.index). Although maybe there are some wacky implementations out there that do worse...

You can improve lookup complexity by using different data structures, such as ordered lists or sets. These are usually implemented with binary trees. However, these data structures put constraints on the elements they contain. In the case of a binary tree, the elements need to be orderable, but the lookup cost goes down to O(log n).

As mentioned previously, look here for run time costs of standard Python data structures: http://wiki.python.org/moin/TimeComplexity