Time Complexity of String Operations

David Wahler dwahler at gmail.com
Tue Jul 22 06:39:58 CEST 2008


On Mon, Jul 21, 2008 at 10:31 PM, youtoo <you2000too at gmail.com> wrote:
> It has been extensively discussed the time complexity (quadratic) of
> string concatenation (due to string's immutability).

Actually, it is roughly linear, at least for reasonable string lengths:

$ python -V
Python 2.5.2
$ python -mtimeit -s "n=1000; a='#'*n" "a+a"
1000000 loops, best of 3: 1 usec per loop
$ python -mtimeit -s "n=10000; a='#'*n" "a+a"
100000 loops, best of 3: 5.88 usec per loop
$ python -mtimeit -s "n=100000; a='#'*n" "a+a"
10000 loops, best of 3: 59.8 usec per loop

Repeatedly constructing a string by appending a constant number of
characters at a time, however, is quadratic in the final string length
(although VM optimizations may affect this).

> But what is:
>
> == the time complexity of string indexing? Is it constant?

Yes.

> == the time complexity of string slicing? Is it O(K) with K the
> slice's length?

I suspect so, since the time is dominated by the time taken to copy
the data into a new string object.

> How are strings stored in Python? As arrays? As linked lists?

Arrays; see Include/stringobject.h in the Python source distribution.

-- David



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