"Dive Into Python 3" is a fantastic book. For instance, chapter 8 "Advanced Iterators" introduces a cool alphametic puzzle solver. Unfortunately, it has a hidden crashing bug (Google searching result on 12th Jul. 2012 implies that I'm the first one reporting this bug on Internet ;-). Besides bug, it can be even cooler with following improvements.
At the beginning of solve(), it converts puzzle to upper case, which implies it also accepts lower case input string.
words = re.findall('[A-Z]+', puzzle.upper())
However at the end of solve(), it assumes puzzle must be in upper case. Otherwise, following eval() would crash because of invalid equation.
equation = puzzle.translate(dict(zip(characters, guess)))
if eval(equation):
We can insert upper() between puzzle. and translate(. But that seems duplicate. So, my suggestion is that caller should make sure input string is always in upper case (line 40 in my revision).
To be honest, I spent 5 minutes to read following codes.
first_letters = {word[0] for word in words}
n = len(first_letters)
sorted_characters = ''.join(first_letters) + \
''.join(unique_characters - first_letters)
characters = tuple(ord(c) for c in sorted_characters)
...
if zero not in guess[:n]:
Finally, I figured out those codes just want to make sure leading digit for each word is not 0. In my opinion, a regular expression '(\D|^)0\d*' is more straight forward (line 23 and 27 in my revision).
But, would regular expression slow down the code significantly? cProfiler answered no.
Surprisingly, bottle neck actually is eval() that accounts for 60% time. Meanwhile, translate() accounts for 8%. re.search() only accounts for 10%.
It takes around 40 seconds to calculate "SEND + MORE == MONEY" on my computer. That is long enough to make people suspect the code is running into dead loop. Therefore a command line based animated progress is added. Probably you want to try my alphametic.py on your terminal. That progress animation is cool.
On implementation side, this trick actually is simple if you are aware of the difference between carriage return "\r" and line feed "\n". Just insert end='\r' into print() (line 26 in my revision). However, do not forget to overwrite the progress at the end of the function because '\r' only move cursor but delete nothing.
The cost for progress animation is performance. It takes extra 20 seconds roughly for "SEND + MORE == MONEY" on my computer. But I believe that is worth in term of overall user experience (slower but more responsive).
Thanks powerful eval(). This alphametic solver actually can support -, *, /, ** in addition to +. So, you can play with "MONEY - MORE == SEND", too.
If you think about input equation (e.g. "MONEY - MORE == SEND") further, you might realize that essentially is an abstract pattern, which is not necessary in alphabet! Equation "A * B == B" should perform as same as equation "1 * 2 == 2" because "A" and "1" represent same dynamic operand. With a tiny change (line 13 in my revision), pattern in digit is supported easily. Now, you are able to check whether there is any solution for pattern "11 * 11 == 121".