Big-O of list slicing

Getting a slice is O(i_2 - i_1). This is because Python's internal representation of a list is an array, so you can start at i_1 and iterate to i_2.

For more information, see the Python Time Complexity wiki entry

You can also look at the implementation in the CPython source if you want to.

For a list of size N, and a slice of size M, the iteration is actually only O(M), not O(N). Since M is often << N, this makes a big difference.

In fact, if you think about your explanation, you can see why. You're only iterating from i_1 to i_2, not from 0 to i_1, then I_1 to i_2.

according to http://wiki.python.org/moin/TimeComplexity

it is O(k) where k is the slice size