Added a simple but general backtracking generator (conjoin), and a couple
examples of use. These poke stuff not specifically targeted before, incl. recursive local generators relying on nested scopes, ditto but also inside class methods and rebinding instance vars, and anonymous partially-evaluated generators (the N-Queens solver creates a different column-generator for each row -- AFAIK this is my invention, and it's really pretty <wink>). No problems, not even a new leak.
This commit is contained in:
Tim Peters
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@ -1,3 +1,5 @@
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from __future__ import nested_scopes
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tutorial_tests = """
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Let's try a simple generator:
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@ -739,11 +741,170 @@ Traceback (most recent call last):
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SyntaxError: 'return' with argument inside generator (<string>, line 8)
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"""
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# conjoin is a simple backtracking generator, named in honor of Icon's
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# "conjunction" control structure. Pass a list of no-argument functions
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# that return iterable objects. Easiest to explain by example: assume the
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# function list [x, y, z] is passed. Then conjoin acts like:
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#
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# def g():
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# values = [None] * 3
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# for values[0] in x():
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# for values[1] in y():
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# for values[2] in z():
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# yield values
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#
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# So some 3-lists of values *may* be generated, each time we successfully
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# get into the innermost loop. If an iterator fails (is exhausted) before
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# then, it "backtracks" to get the next value from the nearest enclosing
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# iterator (the one "to the left"), and starts all over again at the next
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# slot (pumps a fresh iterator). Of course this is most useful when the
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# iterators have side-effects, so that which values *can* be generated at
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# each slot depend on the values iterated at previous slots.
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def conjoin(gs):
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values = [None] * len(gs)
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def gen(i, values=values):
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if i >= len(gs):
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yield values
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else:
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for values[i] in gs[i]():
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for x in gen(i+1):
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yield x
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for x in gen(0):
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yield x
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# A conjoin-based N-Queens solver.
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class Queens:
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def __init__(self, n):
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self.n = n
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rangen = range(n)
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# Assign a unique int to each column and diagonal.
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# columns: n of those, range(n).
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# NW-SE diagonals: 2n-1 of these, i-j unique and invariant along
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# each, smallest i-j is 0-(n-1) = 1-n, so add n-1 to shift to 0-
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# based.
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# NE-SW diagonals: 2n-1 of these, i+j unique and invariant along
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# each, smallest i+j is 0, largest is 2n-2.
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# For each square, compute a bit vector of the columns and
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# diagonals it covers, and for each row compute a function that
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# generates the possiblities for the columns in that row.
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self.rowgenerators = []
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for i in rangen:
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rowuses = [(1L << j) | # column ordinal
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(1L << (n + i-j + n-1)) | # NW-SE ordinal
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(1L << (n + 2*n-1 + i+j)) # NE-SW ordinal
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for j in rangen]
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def rowgen(rowuses=rowuses):
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for j in rangen:
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uses = rowuses[j]
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if uses & self.used:
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continue
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self.used |= uses
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yield j
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self.used &= ~uses
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self.rowgenerators.append(rowgen)
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# Generate solutions.
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def solve(self):
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self.used = 0
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for row2col in conjoin(self.rowgenerators):
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yield row2col
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def printsolution(self, row2col):
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n = self.n
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assert n == len(row2col)
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sep = "+" + "-+" * n
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print sep
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for i in range(n):
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squares = [" " for j in range(n)]
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squares[row2col[i]] = "Q"
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print "|" + "|".join(squares) + "|"
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print sep
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conjoin_tests = """
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Generate the 3-bit binary numbers in order. This illustrates dumbest-
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possible use of conjoin, just to generate the full cross-product.
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>>> def g():
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... return [0, 1]
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>>> for c in conjoin([g] * 3):
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... print c
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[0, 0, 0]
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[0, 0, 1]
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[0, 1, 0]
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[0, 1, 1]
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[1, 0, 0]
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[1, 0, 1]
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[1, 1, 0]
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[1, 1, 1]
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And run an 8-queens solver.
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>>> q = Queens(8)
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>>> LIMIT = 2
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>>> count = 0
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>>> for row2col in q.solve():
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... count += 1
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... if count <= LIMIT:
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... print "Solution", count
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... q.printsolution(row2col)
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Solution 1
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+-+-+-+-+-+-+-+-+
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|Q| | | | | | | |
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+-+-+-+-+-+-+-+-+
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| | | | |Q| | | |
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+-+-+-+-+-+-+-+-+
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| | | | | | | |Q|
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+-+-+-+-+-+-+-+-+
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| | | | | |Q| | |
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+-+-+-+-+-+-+-+-+
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| | |Q| | | | | |
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+-+-+-+-+-+-+-+-+
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| | | | | | |Q| |
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+-+-+-+-+-+-+-+-+
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| |Q| | | | | | |
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+-+-+-+-+-+-+-+-+
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| | | |Q| | | | |
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+-+-+-+-+-+-+-+-+
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Solution 2
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+-+-+-+-+-+-+-+-+
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|Q| | | | | | | |
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+-+-+-+-+-+-+-+-+
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| | | | | |Q| | |
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+-+-+-+-+-+-+-+-+
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| | | | | | | |Q|
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+-+-+-+-+-+-+-+-+
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| | |Q| | | | | |
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+-+-+-+-+-+-+-+-+
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| | | | | | |Q| |
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+-+-+-+-+-+-+-+-+
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| | | |Q| | | | |
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+-+-+-+-+-+-+-+-+
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| |Q| | | | | | |
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+-+-+-+-+-+-+-+-+
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| | | | |Q| | | |
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+-+-+-+-+-+-+-+-+
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>>> print count, "solutions in all."
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92 solutions in all.
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"""
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__test__ = {"tut": tutorial_tests,
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"pep": pep_tests,
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"email": email_tests,
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"fun": fun_tests,
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"syntax": syntax_tests}
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"syntax": syntax_tests,
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"conjoin": conjoin_tests}
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# Magic test name that regrtest.py invokes *after* importing this module.
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# This worms around a bootstrap problem.
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