I found Hen Hanna's "packing" problem to be an intriguing one: Given a
list of words:
['APPLE', 'PIE', 'APRICOT', 'BANANA', 'CANDY']
find a string (in general non-unique) as short as possible which
contains the letters of each of these words, in order, as a subsequence.
It struck me as being rather hard for a homework problem, unless I'm
missing something blindingly obvious.
Here is what I came up with (I could have done with
removeprefix/removesuffix but I'm stuck on Python 3.8 for now 🙁):
# Pack.py
def Pack(Words):
if not Words:
return ''
# The method is to build up the result by adding letters at the
beginning
# and working forward, and by adding letters at the end, working
backwards,
# meanwhile shrinking the words in the list.
Words = list(Words) # Don't mutate the original
Initial = ''
Final = ''
while True:
AnyProgress = False
# It is safe to add an initial letter (of one or more of the
words) if
# EITHER There is no word that contains it as
# a non-initial letter but not as an initial letter.
# OR All words start with it.
while True:
FirstLetters = ''.join(w[0] for w in Words)
FirstLetters = [ ch for ch in FirstLetters if
all(w[0]==ch for w in Words)
or not any(ch in w[1:] and w[0]!=ch for w in Words) ]
if not FirstLetters:
break
AnyProgress = True
ch = FirstLetters[0] # Pick one
Initial += ch # Build up the answer from the
beginning
Words = [ (w[1:] if w[0]==ch else w) for w in Words ]
Words = [ w for w in Words if w != '']
if not Words:
return Initial + Final
# It is safe to add a final letter (of one or more of the words) of
# EITHER There is no word that contains it as
# a non-final letter but not as a final letter.
# OR All words end with it.
while True:
LastLetters = ''.join(w[-1] for w in Words)
LastLetters = [ ch for ch in LastLetters if
all(w[-1]==ch for w in Words)
or not any(ch in w[:-1] and w[-1]!=ch for w in Words) ]
if not LastLetters:
break
AnyProgress = True
ch = LastLetters[0] # Pick one
Final = ch + Final # Build up the answer from the end
Words = [ (w[:-1] if w[-1]==ch else w) for w in Words ]
Words = [ w for w in Words if w != '']
if not Words:
return Initial + Final
if not AnyProgress:
break
# Try all the possibilities for the next letter to add at the
beginning,
# with recursive calls, and pick one that gives a shortest answer:
BestResult = None
for ch in set(w[0] for w in Words):
Words2 = list( (w[1:] if w[0] == ch else w) for w in Words )
Words2 = [ w for w in Words2 if w != '' ]
res = ch + Pack(Words2)
if BestResult is None or len(res) < len(BestResult):
BestResult = res
return Initial + BestResult + Final
print(Pack(['APPLE', 'PIE', 'APRICOT', 'BANANA', 'CANDY']))
The output:
BAPPRICNANADYOTLE
which has the same length as the answer I came up with trying to solve
it with my unaided brain, which may or may not be reassuring 😂,
and also contains a much-needed BRANDY.
I expect there are simpler and more efficient solutions.
Best wishes
Rob Cliffe
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