Peter Norvig has an essay describing a program to solve sudoku puzzles, even the hardest ones, by combining deterministic logical operations and smart traversal of the possible solutions. The latter is done recursively; here's that function (source):
def search(values):
"Using depth-first search and propagation, try all possible values."
if values is False:
return False ## Failed earlier
if all( len( values[s]) == 1 for s in squares):
return values ## Solved!
## Chose the unfilled square s with the fewest possibilities
_,s = min( (len( values[s]), s)
for s in squares
if len(values[s]) > 1
)
return some( search( assign( values.copy(), s, d))
for d in values[s]
)
(I've added some spaces, CRs, and tabs for the sake of my eyes; apologies to Dr. Norvig.)
Right below the comment there's a line starting with "_,s". That seems to be the unpacked tuple (len(values[s]),s) with the minimal value of s. Is Dr. Norvig using "_" as a variable name just to indicate it's a "don't care" result, or is something else going on? Are there times when "_" is recommended as a variable name? In interactive mode, "_" holds the answer of the previous operation; is there a similar function in non-interactive code?
Thanks for the good answers. I guess The Answer goes to Alex Martelli for "value added"; he points out that the "_, vbl_of_interest" idiom is often a side effect of the DSU idiom, which itself has been made largely unnecessary.
Yep, _ is a traditional name for "don't care" (which unfortunately clashes with its use in I18N, but that's a separate issue;-). BTW, in today's Python, instead of:
_, s = min(
(len(values[s]), s)
for s in squares
if len(values[s]) > 1
)
you might code
s = min(
(s for s in squares if len(values[s]) > 1),
key=lambda s: len(values[s]),
)
(not sure what release of Python Peter was writing for, but the idiom he's using is an example of "decorate-sort-undecorate" [[DSU]] except with min instead of sort, and in today's Python the key= optional parameter is generally the best way to do DSU;-).