reduce()--what is it good for?
Alex Martelli
aleaxit at yahoo.com
Sat Nov 8 00:49:30 CET 2003
JCM wrote:
> Alex Martelli <aleax at aleax.it> wrote:
> ...various good points...
>
>> if one is in a hurry, recursion and
>> memoization are obviously preferable:
>
>> def facto(n, _memo={1:1}):
>> try: return _memo[n]
>> except KeyError:
>> result = _memo[n] = (n-1) * facto(n-1)
>> return result
...
>> [alex at lancelot bo]$ timeit.py -c -s'import facs' 'facs.facto(13)'
>> 1000000 loops, best of 3: 1.26 usec per loop
>
> I'm going off topic, but it's really not fair to compare a memoized
> function to non-memoized implementations using a "best of 3" timing
> test.
The best-of-3 is irrelevant, it's the million loops that help:-).
Of course you can memoize any pure function of hashable args. But
memoizing a recursive implementation of factorial has a nice property,
shared by other int functions implemented recursively in terms of their
values on other ints, such as fibonacci numbers: the memoization you do for
any value _helps_ the speed of computation for other values. This nice
property doesn't apply to non-recursive implementations.
Once you run timeit.py, with its million loops (and the best-of-3, but
that's not crucial:-), this effect disappears. But on smaller tests it is
more easily seen. You can for example define the memoized functions
by a def nested inside another, so each call of the outer function will undo
the memoization, and exercise them that way even with timeit.py. E.g.:
import operator
def wireduce(N=23):
def factorial(x, _memo={0:1, 1:1}):
try: return _memo[x]
except KeyError:
result = _memo[x] = reduce(operator.mul, xrange(2,x+1), 1)
return result
for x in range(N, 0, -1): factorial(x)
def wirecurse(N=23):
def factorial(x, _memo={0:1, 1:1}):
try: return _memo[x]
except KeyError:
result = _memo[x] = x * factorial(x-1)
return result
for x in range(N, 0, -1): factorial(x)
[alex at lancelot bo]$ timeit.py -c -s'import aa' 'aa.wireduce()'
1000 loops, best of 3: 710 usec per loop
[alex at lancelot bo]$ timeit.py -c -s'import aa' 'aa.wirecurse()'
1000 loops, best of 3: 280 usec per loop
Alex
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