Jeśli masz tylko jedno odniesienie do łańcucha i połączysz inny łańcuch do końca, CPython teraz specjalne przypadki to i próbuje rozszerzyć łańcuch w miejscu.

Wynikiem końcowym jest to, że operacja jest amortyzowana O (n).

Np.

s = ""
for i in range(n):
    s+=str(i)

Kiedyś było O (N^2), ale teraz jest O (n).

Ze źródła (bytesobject.c):

void
PyBytes_ConcatAndDel(register PyObject **pv, register PyObject *w)
{
    PyBytes_Concat(pv, w);
    Py_XDECREF(w);
}


/* The following function breaks the notion that strings are immutable:
   it changes the size of a string.  We get away with this only if there
   is only one module referencing the object.  You can also think of it
   as creating a new string object and destroying the old one, only
   more efficiently.  In any case, don't use this if the string may
   already be known to some other part of the code...
   Note that if there's not enough memory to resize the string, the original
   string object at *pv is deallocated, *pv is set to NULL, an "out of
   memory" exception is set, and -1 is returned.  Else (on success) 0 is
   returned, and the value in *pv may or may not be the same as on input.
   As always, an extra byte is allocated for a trailing \0 byte (newsize
   does *not* include that), and a trailing \0 byte is stored.
*/

int
_PyBytes_Resize(PyObject **pv, Py_ssize_t newsize)
{
    register PyObject *v;
    register PyBytesObject *sv;
    v = *pv;
    if (!PyBytes_Check(v) || Py_REFCNT(v) != 1 || newsize < 0) {
        *pv = 0;
        Py_DECREF(v);
        PyErr_BadInternalCall();
        return -1;
    }
    /* XXX UNREF/NEWREF interface should be more symmetrical */
    _Py_DEC_REFTOTAL;
    _Py_ForgetReference(v);
    *pv = (PyObject *)
        PyObject_REALLOC((char *)v, PyBytesObject_SIZE + newsize);
    if (*pv == NULL) {
        PyObject_Del(v);
        PyErr_NoMemory();
        return -1;
    }
    _Py_NewReference(*pv);
    sv = (PyBytesObject *) *pv;
    Py_SIZE(sv) = newsize;
    sv->ob_sval[newsize] = '\0';
    sv->ob_shash = -1;          /* invalidate cached hash value */
    return 0;
}

$ python -m timeit -s"s=''" "for i in xrange(10):s+='a'"
1000000 loops, best of 3: 1.85 usec per loop
$ python -m timeit -s"s=''" "for i in xrange(100):s+='a'"
10000 loops, best of 3: 16.8 usec per loop
$ python -m timeit -s"s=''" "for i in xrange(1000):s+='a'"
10000 loops, best of 3: 158 usec per loop
$ python -m timeit -s"s=''" "for i in xrange(10000):s+='a'"
1000 loops, best of 3: 1.71 msec per loop
$ python -m timeit -s"s=''" "for i in xrange(100000):s+='a'"
10 loops, best of 3: 14.6 msec per loop
$ python -m timeit -s"s=''" "for i in xrange(1000000):s+='a'"
10 loops, best of 3: 173 msec per loop

Ważne jest jednak, aby pamiętać, że ta optymalizacja nie jest częścią specyfikacji Pythona. Z tego co wiem to tylko w implementacji cpythona. Te same badania empiryczne na przykład pypy lub jython mogą pokazać starszą wydajność O (n * * 2).

$ pypy -m timeit -s"s=''" "for i in xrange(10):s+='a'"
10000 loops, best of 3: 90.8 usec per loop
$ pypy -m timeit -s"s=''" "for i in xrange(100):s+='a'"
1000 loops, best of 3: 896 usec per loop
$ pypy -m timeit -s"s=''" "for i in xrange(1000):s+='a'"
100 loops, best of 3: 9.03 msec per loop
$ pypy -m timeit -s"s=''" "for i in xrange(10000):s+='a'"
10 loops, best of 3: 89.5 msec per loop

$ pypy -m timeit -s"s=''" "for i in xrange(100000):s+='a'"
10 loops, best of 3: 12.8 sec per loop