sudoku solver in Python ...
Boris Borcic
bborcic at gmail.com
Thu Jan 24 14:09:34 CET 2008
Shawn Milochik wrote:
> On Jan 23, 2008, at 10:02 PM, Derek Marshall wrote:
>
>> This is just for fun, in case someone would be interested and because
>> I haven't had the pleasure of posting anything here in many years ...
>>
>> http://derek.marshall.googlepages.com/pythonsudokusolver
>>
>> Appreciate any feedback anyone who takes the time to have a look would
>> want to give ...
>>
>> Yours with-too-much-time-to-kill-on-the-train'ly,
>> Derek
>> --
>> http://mail.python.org/mailman/listinfo/python-list
>
> For those interested in this topic, here's another (much shorter) one:
>
> http://norvig.com/sudoku.html
>
> I'm not making any judgements here, though. If anyone takes the time
> to actually review them, I'd be interested in hearing any educated
> comparisons.
>
> Shawn
So would I. Below is the "winner" of my hacking for an as fast as possible 110%
pure python (no imports at all!) comprehensive sudoku solver under 50 LOCs, back
in 2006. Performance is comparable to the solver you advertize - numbers are
slightly better, but platform differences could easily absorb that - eg (not
counting module initialization and not using psyco) it takes 9.3 ms average on
the "AI escargot" problem linked to in Norwig's page, 5.6 ms/problem on some
standard "top1465" list of hard problems, and 3.4 ms/problem on the first 1000
on some other "top50000" list of relatively hard problems. This on my 2GHz Intel
Centrino '05 laptop. Psyco reduces times by about 50%. Dropping performance
requirements by half allows reducing LOC count in proportion.
OTOH, the code although short is nearly unreadable, sorry; should probably
feature/comment it on some web page, like the two already proposed in the
thread. Will do if/for reviewer. Interface is calling sudoku99(problem) with
'problem' a standard 81 character string with '0' or '.' placeholder for
unknowns. Returns same with values filled in.
Beware that although in practice it solved all well-formed human-solvable
problems I could find, it is not guaranteed to deal properly (or even
terminate?) for underdetermined problems or determined problems that would
require exploring choicepoints with more than 2 possibilities (if such exist).
Cheers, Boris
w2q = [[n/9,n/81*9+n%9+243,n%81+162,n%9*9+n/243*3+n/27%3+81]
for n in range(729)]
q2w = (z[1] for z in sorted((x,y) for y,s in enumerate(w2q) for x in s))
q2w = map(set,zip(*9*[q2w]))
w2q2w = [set(w for q in qL for w in q2w[q] if w!=w0) for w0,qL in enumerate(w2q)]
empty = set(range(729)).copy
def sudoku99(problem) :
givens = set(9*j+int(k)-1 for j,k in enumerate(problem) if '0'<k)
ws=search(givens,[9]*len(q2w),empty())
return ''.join(str(w%9+1) for w in sorted(ws))
def search(w0s,q2nw,free) :
while 1 :
while w0s:
w0 = w0s.pop()
for q in w2q[w0] : q2nw[q]=100
wz = w2q2w[w0]&free
free-=wz
for w in wz :
for q in w2q[w] :
n = q2nw[q] = q2nw[q]-1
if n<2 :
ww,=q2w[q]&free
w0s.add(ww)
if len(free)==81 : return free
thres = int((len(free)+52.85)/27.5)
ix,vmax = -1,0
try :
while 1 :
ix=q2nw.index(2,ix+1)
for w0 in (q2w[ix]&free)-w0s :
v = len(w2q2w[w0]&free)
if v > vmax :
ixmax = ix
if v >=thres : break
vmax = v
w0s.add(w0)
else : continue
break
except : pass
w0,w1 = q2w[ixmax]&free
try :
w0s.clear()
w0s.add(w0)
return search(w0s,q2nw[:],free.copy())
except ValueError :
w0s.clear()
w0s.add(w1)
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