wildcard exclusion in cartesian products

[wkehowski]

The python code below is adapted from a Haskell program written by
Tomasz
Wielonka on the comp.lang.functional group. It's more verbose than his
since I wanted to make sure I got it right.

http://groups.google.com/group/comp.lang.functional/browse_frm/thread...

Does anyone know how to turn it into a module (or whatever it's called)
so that I can put it in a
loop and not have to generate the whole list? I've already tried
without success.

The program solves the following problem: generate the subset X of the
cartesian product S^n that excludes n-tuples defined by wildcards. For
example, if I want to exclude from [1,2,3]^3 the wc's [1,"*",2] and
["*",3,"*",3,"*"], where "*" stands for a sequence of zero or more
elements of [1,2,3], then I just type

for x in generateNotMatching([1,2,3,4],4,[[1,'*',2],[3,'*',4]]): print
x

and get the output

[1, 1, 1]
[1, 1, 3]
[1, 2, 1]
[1, 2, 3]
[1, 3, 1]
[2, 1, 1]
[2, 1, 2]
[2, 1, 3]
[2, 2, 1]
[2, 2, 2]
[2, 2, 3]
[2, 3, 1]
[2, 3, 2]
[3, 1, 1]
[3, 1, 2]
[3, 2, 1]
[3, 2, 2]

This is nice! But all elements are generated before they are printed.

##----------------------------
import sys, os, string

def imap(function, source):
for element in source:
yield function(element)

def any(iterable):
'''True iff at least one element of the iterable is True'''
for element in iterable:
if element:
return True # or element and change the definition
return False

def all(iterable):
'''True iff no element of the iterable is True'''
'''SHOULD BE?: True iff all element of the iterable are True'''
for element in iterable:
if not element:
return False
return True

def rev(L):
rL=[]
for x in L: rL=[x]+rL
return rL

def advancePattern(x,p):
if p==[]: return []
else:
h=p[0]
t=p[1:]
if h != '*':
if h == x: return [t]
else: return []
else: return [p] + [t] + advancePattern(x,t)

def advancePatterns(x,P):
aP=[]
for p in P:
aP += advancePattern(x,p)
return aP

# return [advancePattern(x,p) for p in P]

def allStar(p):
return all( imap((lambda x: x=='*'),p) )

def notNullOrZero(p,n):
return p !=[] or n==0

def generateNotMatching(A,n,P):
return gen(A,n,P,[])

def gen(A,n,P,acc):
if any(imap((lambda p: allStar(p) and notNullOrZero(p,n)), P)):
return []
else:
if n==0:
return map(rev,[acc])
else:
aG=[]
for a in A:
aG += gen(A,n-1,advancePatterns(a,P),[a]+acc)
return aG

##----------------------------

 

[Michael Spencer]

The python code below is adapted from a Haskell program written by
Tomasz
Wielonka on the comp.lang.functional group. It's more verbose than his
since I wanted to make sure I got it right.

http://groups.google.com/group/comp.lang.functional/browse_frm/thread...

Does anyone know how to turn it into a module (or whatever it's called)
so that I can put it in a
loop and not have to generate the whole list? I've already tried
without success.

I know next to nothing about Haskell, but I believe that it evaluates sequences
lazily by default. Python can certainly do lazy evaluation, but you'll have to
ask for it explicitly.

The program solves the following problem: generate the subset X of the
cartesian product S^n that excludes n-tuples defined by wildcards. For
example, if I want to exclude from [1,2,3]^3 the wc's [1,"*",2] and
["*",3,"*",3,"*"], where "*" stands for a sequence of zero or more
elements of [1,2,3], then I just type

[I think your example and test case may have become mixed up]
....

Here's an iterative "lazy" solution. While we're at it, why not use re for
pattern matching, rather than rolling our own matcher (this does restrict the
set members to characters, maybe that's OK):

import re

def cp_excl_wc(alpha, N, *exclusions):
RE0, RE1 = compile_re(exclusions)
def add_one(outer, RE_PATTS):
if RE_PATTS:
for partial in outer:
for a in alpha:
next = partial + a
if not RE_PATTS.match(next):
yield next
else: # if there's no pattern to match at this length
# don't waste time trying
for partial in outer:
for a in alpha:
yield partial+a
cpgen = "",
# RE0 holds the patterns that match at the beginning, so are tested
# against all iterations less than full length
for n in range(N-1):
cpgen = add_one(cpgen, RE0)
# For the last place, test the full-length patterns
cpgen = add_one(cpgen, RE1)
return cpgen


def compile_re(exclusions):
re0 = [] # patterns that can be matched anywhere
re1 = [] # patterns that match only the full-length
for pattern in exclusions:
pattern = pattern.replace("*", ".*")
if pattern.endswith(".*"):
re0.append(pattern)
re1.append(pattern+"$")

re0 = re0 and re.compile("|".join(re0)) or None
re1 = re1 and re.compile("|".join(re1)) or None
return re0, re1
['131', '133', '211', '212', '213', '221', '222', '223', '231', '232', '233',
'312', '313', '322', '323', '332', '333']
Is this the sort of thing you had in mind?

Michael

 

[wkehowski]

Michael,

Yes! That is precisely what I had in mind!

Thanks,

Walter Kehowski

 

[John Zenger]

A quick fix: change your last two functions to:

def generateNotMatching(A,n,P):
for g in gen(A,n,P,[]):
for x in g:
yield x

def gen(A,n,P,acc):
if any(imap((lambda p: allStar(p) and notNullOrZero(p,n)), P)):
yield []
else:
if n==0:
yield map(rev,[acc])
else:
for a in A:
for xx in gen(A,n-1,advancePatterns(a,P),[a]+acc):
yield xx

For the most part, just replace return with yield.

By the way: you are reinventing the wheel with imap and rev. imap is
itertools.imap. rev(L) is the same as L[:-1].

The python code below is adapted from a Haskell program written by
Tomasz
Wielonka on the comp.lang.functional group. It's more verbose than his
since I wanted to make sure I got it right.

http://groups.google.com/group/comp.lang.functional/browse_frm/thread...

Does anyone know how to turn it into a module (or whatever it's called)
so that I can put it in a
loop and not have to generate the whole list? I've already tried
without success.

The program solves the following problem: generate the subset X of the
cartesian product S^n that excludes n-tuples defined by wildcards. For
example, if I want to exclude from [1,2,3]^3 the wc's [1,"*",2] and
["*",3,"*",3,"*"], where "*" stands for a sequence of zero or more
elements of [1,2,3], then I just type

for x in generateNotMatching([1,2,3,4],4,[[1,'*',2],[3,'*',4]]): print
x

and get the output

[1, 1, 1]
[1, 1, 3]
[1, 2, 1]
[1, 2, 3]
[1, 3, 1]
[2, 1, 1]
[2, 1, 2]
[2, 1, 3]
[2, 2, 1]
[2, 2, 2]
[2, 2, 3]
[2, 3, 1]
[2, 3, 2]
[3, 1, 1]
[3, 1, 2]
[3, 2, 1]
[3, 2, 2]

This is nice! But all elements are generated before they are printed.

##----------------------------
import sys, os, string

def imap(function, source):
for element in source:
yield function(element)

def any(iterable):
'''True iff at least one element of the iterable is True'''
for element in iterable:
if element:
return True # or element and change the definition
return False

def all(iterable):
'''True iff no element of the iterable is True'''
'''SHOULD BE?: True iff all element of the iterable are True'''
for element in iterable:
if not element:
return False
return True

def rev(L):
rL=[]
for x in L: rL=[x]+rL
return rL

def advancePattern(x,p):
if p==[]: return []
else:
h=p[0]
t=p[1:]
if h != '*':
if h == x: return [t]
else: return []
else: return [p] + [t] + advancePattern(x,t)

def advancePatterns(x,P):
aP=[]
for p in P:
aP += advancePattern(x,p)
return aP

# return [advancePattern(x,p) for p in P]

def allStar(p):
return all( imap((lambda x: x=='*'),p) )

def notNullOrZero(p,n):
return p !=[] or n==0

def generateNotMatching(A,n,P):
return gen(A,n,P,[])

def gen(A,n,P,acc):
if any(imap((lambda p: allStar(p) and notNullOrZero(p,n)), P)):
return []
else:
if n==0:
return map(rev,[acc])
else:
aG=[]
for a in A:
aG += gen(A,n-1,advancePatterns(a,P),[a]+acc)
return aG

##----------------------------