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      1 tutorial_tests = """
      2 Let's try a simple generator:
      3 
      4     >>> def f():
      5     ...    yield 1
      6     ...    yield 2
      7 
      8     >>> for i in f():
      9     ...     print i
     10     1
     11     2
     12     >>> g = f()
     13     >>> g.next()
     14     1
     15     >>> g.next()
     16     2
     17 
     18 "Falling off the end" stops the generator:
     19 
     20     >>> g.next()
     21     Traceback (most recent call last):
     22       File "<stdin>", line 1, in ?
     23       File "<stdin>", line 2, in g
     24     StopIteration
     25 
     26 "return" also stops the generator:
     27 
     28     >>> def f():
     29     ...     yield 1
     30     ...     return
     31     ...     yield 2 # never reached
     32     ...
     33     >>> g = f()
     34     >>> g.next()
     35     1
     36     >>> g.next()
     37     Traceback (most recent call last):
     38       File "<stdin>", line 1, in ?
     39       File "<stdin>", line 3, in f
     40     StopIteration
     41     >>> g.next() # once stopped, can't be resumed
     42     Traceback (most recent call last):
     43       File "<stdin>", line 1, in ?
     44     StopIteration
     45 
     46 "raise StopIteration" stops the generator too:
     47 
     48     >>> def f():
     49     ...     yield 1
     50     ...     raise StopIteration
     51     ...     yield 2 # never reached
     52     ...
     53     >>> g = f()
     54     >>> g.next()
     55     1
     56     >>> g.next()
     57     Traceback (most recent call last):
     58       File "<stdin>", line 1, in ?
     59     StopIteration
     60     >>> g.next()
     61     Traceback (most recent call last):
     62       File "<stdin>", line 1, in ?
     63     StopIteration
     64 
     65 However, they are not exactly equivalent:
     66 
     67     >>> def g1():
     68     ...     try:
     69     ...         return
     70     ...     except:
     71     ...         yield 1
     72     ...
     73     >>> list(g1())
     74     []
     75 
     76     >>> def g2():
     77     ...     try:
     78     ...         raise StopIteration
     79     ...     except:
     80     ...         yield 42
     81     >>> print list(g2())
     82     [42]
     83 
     84 This may be surprising at first:
     85 
     86     >>> def g3():
     87     ...     try:
     88     ...         return
     89     ...     finally:
     90     ...         yield 1
     91     ...
     92     >>> list(g3())
     93     [1]
     94 
     95 Let's create an alternate range() function implemented as a generator:
     96 
     97     >>> def yrange(n):
     98     ...     for i in range(n):
     99     ...         yield i
    100     ...
    101     >>> list(yrange(5))
    102     [0, 1, 2, 3, 4]
    103 
    104 Generators always return to the most recent caller:
    105 
    106     >>> def creator():
    107     ...     r = yrange(5)
    108     ...     print "creator", r.next()
    109     ...     return r
    110     ...
    111     >>> def caller():
    112     ...     r = creator()
    113     ...     for i in r:
    114     ...             print "caller", i
    115     ...
    116     >>> caller()
    117     creator 0
    118     caller 1
    119     caller 2
    120     caller 3
    121     caller 4
    122 
    123 Generators can call other generators:
    124 
    125     >>> def zrange(n):
    126     ...     for i in yrange(n):
    127     ...         yield i
    128     ...
    129     >>> list(zrange(5))
    130     [0, 1, 2, 3, 4]
    131 
    132 """
    133 
    134 # The examples from PEP 255.
    135 
    136 pep_tests = """
    137 
    138 Specification:  Yield
    139 
    140     Restriction:  A generator cannot be resumed while it is actively
    141     running:
    142 
    143     >>> def g():
    144     ...     i = me.next()
    145     ...     yield i
    146     >>> me = g()
    147     >>> me.next()
    148     Traceback (most recent call last):
    149      ...
    150       File "<string>", line 2, in g
    151     ValueError: generator already executing
    152 
    153 Specification: Return
    154 
    155     Note that return isn't always equivalent to raising StopIteration:  the
    156     difference lies in how enclosing try/except constructs are treated.
    157     For example,
    158 
    159         >>> def f1():
    160         ...     try:
    161         ...         return
    162         ...     except:
    163         ...        yield 1
    164         >>> print list(f1())
    165         []
    166 
    167     because, as in any function, return simply exits, but
    168 
    169         >>> def f2():
    170         ...     try:
    171         ...         raise StopIteration
    172         ...     except:
    173         ...         yield 42
    174         >>> print list(f2())
    175         [42]
    176 
    177     because StopIteration is captured by a bare "except", as is any
    178     exception.
    179 
    180 Specification: Generators and Exception Propagation
    181 
    182     >>> def f():
    183     ...     return 1//0
    184     >>> def g():
    185     ...     yield f()  # the zero division exception propagates
    186     ...     yield 42   # and we'll never get here
    187     >>> k = g()
    188     >>> k.next()
    189     Traceback (most recent call last):
    190       File "<stdin>", line 1, in ?
    191       File "<stdin>", line 2, in g
    192       File "<stdin>", line 2, in f
    193     ZeroDivisionError: integer division or modulo by zero
    194     >>> k.next()  # and the generator cannot be resumed
    195     Traceback (most recent call last):
    196       File "<stdin>", line 1, in ?
    197     StopIteration
    198     >>>
    199 
    200 Specification: Try/Except/Finally
    201 
    202     >>> def f():
    203     ...     try:
    204     ...         yield 1
    205     ...         try:
    206     ...             yield 2
    207     ...             1//0
    208     ...             yield 3  # never get here
    209     ...         except ZeroDivisionError:
    210     ...             yield 4
    211     ...             yield 5
    212     ...             raise
    213     ...         except:
    214     ...             yield 6
    215     ...         yield 7     # the "raise" above stops this
    216     ...     except:
    217     ...         yield 8
    218     ...     yield 9
    219     ...     try:
    220     ...         x = 12
    221     ...     finally:
    222     ...         yield 10
    223     ...     yield 11
    224     >>> print list(f())
    225     [1, 2, 4, 5, 8, 9, 10, 11]
    226     >>>
    227 
    228 Guido's binary tree example.
    229 
    230     >>> # A binary tree class.
    231     >>> class Tree:
    232     ...
    233     ...     def __init__(self, label, left=None, right=None):
    234     ...         self.label = label
    235     ...         self.left = left
    236     ...         self.right = right
    237     ...
    238     ...     def __repr__(self, level=0, indent="    "):
    239     ...         s = level*indent + repr(self.label)
    240     ...         if self.left:
    241     ...             s = s + "\\n" + self.left.__repr__(level+1, indent)
    242     ...         if self.right:
    243     ...             s = s + "\\n" + self.right.__repr__(level+1, indent)
    244     ...         return s
    245     ...
    246     ...     def __iter__(self):
    247     ...         return inorder(self)
    248 
    249     >>> # Create a Tree from a list.
    250     >>> def tree(list):
    251     ...     n = len(list)
    252     ...     if n == 0:
    253     ...         return []
    254     ...     i = n // 2
    255     ...     return Tree(list[i], tree(list[:i]), tree(list[i+1:]))
    256 
    257     >>> # Show it off: create a tree.
    258     >>> t = tree("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
    259 
    260     >>> # A recursive generator that generates Tree labels in in-order.
    261     >>> def inorder(t):
    262     ...     if t:
    263     ...         for x in inorder(t.left):
    264     ...             yield x
    265     ...         yield t.label
    266     ...         for x in inorder(t.right):
    267     ...             yield x
    268 
    269     >>> # Show it off: create a tree.
    270     >>> t = tree("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
    271     >>> # Print the nodes of the tree in in-order.
    272     >>> for x in t:
    273     ...     print x,
    274     A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
    275 
    276     >>> # A non-recursive generator.
    277     >>> def inorder(node):
    278     ...     stack = []
    279     ...     while node:
    280     ...         while node.left:
    281     ...             stack.append(node)
    282     ...             node = node.left
    283     ...         yield node.label
    284     ...         while not node.right:
    285     ...             try:
    286     ...                 node = stack.pop()
    287     ...             except IndexError:
    288     ...                 return
    289     ...             yield node.label
    290     ...         node = node.right
    291 
    292     >>> # Exercise the non-recursive generator.
    293     >>> for x in t:
    294     ...     print x,
    295     A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
    296 
    297 """
    298 
    299 # Examples from Iterator-List and Python-Dev and c.l.py.
    300 
    301 email_tests = """
    302 
    303 The difference between yielding None and returning it.
    304 
    305 >>> def g():
    306 ...     for i in range(3):
    307 ...         yield None
    308 ...     yield None
    309 ...     return
    310 >>> list(g())
    311 [None, None, None, None]
    312 
    313 Ensure that explicitly raising StopIteration acts like any other exception
    314 in try/except, not like a return.
    315 
    316 >>> def g():
    317 ...     yield 1
    318 ...     try:
    319 ...         raise StopIteration
    320 ...     except:
    321 ...         yield 2
    322 ...     yield 3
    323 >>> list(g())
    324 [1, 2, 3]
    325 
    326 Next one was posted to c.l.py.
    327 
    328 >>> def gcomb(x, k):
    329 ...     "Generate all combinations of k elements from list x."
    330 ...
    331 ...     if k > len(x):
    332 ...         return
    333 ...     if k == 0:
    334 ...         yield []
    335 ...     else:
    336 ...         first, rest = x[0], x[1:]
    337 ...         # A combination does or doesn't contain first.
    338 ...         # If it does, the remainder is a k-1 comb of rest.
    339 ...         for c in gcomb(rest, k-1):
    340 ...             c.insert(0, first)
    341 ...             yield c
    342 ...         # If it doesn't contain first, it's a k comb of rest.
    343 ...         for c in gcomb(rest, k):
    344 ...             yield c
    345 
    346 >>> seq = range(1, 5)
    347 >>> for k in range(len(seq) + 2):
    348 ...     print "%d-combs of %s:" % (k, seq)
    349 ...     for c in gcomb(seq, k):
    350 ...         print "   ", c
    351 0-combs of [1, 2, 3, 4]:
    352     []
    353 1-combs of [1, 2, 3, 4]:
    354     [1]
    355     [2]
    356     [3]
    357     [4]
    358 2-combs of [1, 2, 3, 4]:
    359     [1, 2]
    360     [1, 3]
    361     [1, 4]
    362     [2, 3]
    363     [2, 4]
    364     [3, 4]
    365 3-combs of [1, 2, 3, 4]:
    366     [1, 2, 3]
    367     [1, 2, 4]
    368     [1, 3, 4]
    369     [2, 3, 4]
    370 4-combs of [1, 2, 3, 4]:
    371     [1, 2, 3, 4]
    372 5-combs of [1, 2, 3, 4]:
    373 
    374 From the Iterators list, about the types of these things.
    375 
    376 >>> def g():
    377 ...     yield 1
    378 ...
    379 >>> type(g)
    380 <type 'function'>
    381 >>> i = g()
    382 >>> type(i)
    383 <type 'generator'>
    384 >>> [s for s in dir(i) if not s.startswith('_')]
    385 ['close', 'gi_code', 'gi_frame', 'gi_running', 'next', 'send', 'throw']
    386 >>> from test.test_support import HAVE_DOCSTRINGS
    387 >>> print(i.next.__doc__ if HAVE_DOCSTRINGS else 'x.next() -> the next value, or raise StopIteration')
    388 x.next() -> the next value, or raise StopIteration
    389 >>> iter(i) is i
    390 True
    391 >>> import types
    392 >>> isinstance(i, types.GeneratorType)
    393 True
    394 
    395 And more, added later.
    396 
    397 >>> i.gi_running
    398 0
    399 >>> type(i.gi_frame)
    400 <type 'frame'>
    401 >>> i.gi_running = 42
    402 Traceback (most recent call last):
    403   ...
    404 TypeError: readonly attribute
    405 >>> def g():
    406 ...     yield me.gi_running
    407 >>> me = g()
    408 >>> me.gi_running
    409 0
    410 >>> me.next()
    411 1
    412 >>> me.gi_running
    413 0
    414 
    415 A clever union-find implementation from c.l.py, due to David Eppstein.
    416 Sent: Friday, June 29, 2001 12:16 PM
    417 To: python-list (at] python.org
    418 Subject: Re: PEP 255: Simple Generators
    419 
    420 >>> class disjointSet:
    421 ...     def __init__(self, name):
    422 ...         self.name = name
    423 ...         self.parent = None
    424 ...         self.generator = self.generate()
    425 ...
    426 ...     def generate(self):
    427 ...         while not self.parent:
    428 ...             yield self
    429 ...         for x in self.parent.generator:
    430 ...             yield x
    431 ...
    432 ...     def find(self):
    433 ...         return self.generator.next()
    434 ...
    435 ...     def union(self, parent):
    436 ...         if self.parent:
    437 ...             raise ValueError("Sorry, I'm not a root!")
    438 ...         self.parent = parent
    439 ...
    440 ...     def __str__(self):
    441 ...         return self.name
    442 
    443 >>> names = "ABCDEFGHIJKLM"
    444 >>> sets = [disjointSet(name) for name in names]
    445 >>> roots = sets[:]
    446 
    447 >>> import random
    448 >>> gen = random.WichmannHill(42)
    449 >>> while 1:
    450 ...     for s in sets:
    451 ...         print "%s->%s" % (s, s.find()),
    452 ...     print
    453 ...     if len(roots) > 1:
    454 ...         s1 = gen.choice(roots)
    455 ...         roots.remove(s1)
    456 ...         s2 = gen.choice(roots)
    457 ...         s1.union(s2)
    458 ...         print "merged", s1, "into", s2
    459 ...     else:
    460 ...         break
    461 A->A B->B C->C D->D E->E F->F G->G H->H I->I J->J K->K L->L M->M
    462 merged D into G
    463 A->A B->B C->C D->G E->E F->F G->G H->H I->I J->J K->K L->L M->M
    464 merged C into F
    465 A->A B->B C->F D->G E->E F->F G->G H->H I->I J->J K->K L->L M->M
    466 merged L into A
    467 A->A B->B C->F D->G E->E F->F G->G H->H I->I J->J K->K L->A M->M
    468 merged H into E
    469 A->A B->B C->F D->G E->E F->F G->G H->E I->I J->J K->K L->A M->M
    470 merged B into E
    471 A->A B->E C->F D->G E->E F->F G->G H->E I->I J->J K->K L->A M->M
    472 merged J into G
    473 A->A B->E C->F D->G E->E F->F G->G H->E I->I J->G K->K L->A M->M
    474 merged E into G
    475 A->A B->G C->F D->G E->G F->F G->G H->G I->I J->G K->K L->A M->M
    476 merged M into G
    477 A->A B->G C->F D->G E->G F->F G->G H->G I->I J->G K->K L->A M->G
    478 merged I into K
    479 A->A B->G C->F D->G E->G F->F G->G H->G I->K J->G K->K L->A M->G
    480 merged K into A
    481 A->A B->G C->F D->G E->G F->F G->G H->G I->A J->G K->A L->A M->G
    482 merged F into A
    483 A->A B->G C->A D->G E->G F->A G->G H->G I->A J->G K->A L->A M->G
    484 merged A into G
    485 A->G B->G C->G D->G E->G F->G G->G H->G I->G J->G K->G L->G M->G
    486 
    487 """
    488 # Emacs turd '
    489 
    490 # Fun tests (for sufficiently warped notions of "fun").
    491 
    492 fun_tests = """
    493 
    494 Build up to a recursive Sieve of Eratosthenes generator.
    495 
    496 >>> def firstn(g, n):
    497 ...     return [g.next() for i in range(n)]
    498 
    499 >>> def intsfrom(i):
    500 ...     while 1:
    501 ...         yield i
    502 ...         i += 1
    503 
    504 >>> firstn(intsfrom(5), 7)
    505 [5, 6, 7, 8, 9, 10, 11]
    506 
    507 >>> def exclude_multiples(n, ints):
    508 ...     for i in ints:
    509 ...         if i % n:
    510 ...             yield i
    511 
    512 >>> firstn(exclude_multiples(3, intsfrom(1)), 6)
    513 [1, 2, 4, 5, 7, 8]
    514 
    515 >>> def sieve(ints):
    516 ...     prime = ints.next()
    517 ...     yield prime
    518 ...     not_divisible_by_prime = exclude_multiples(prime, ints)
    519 ...     for p in sieve(not_divisible_by_prime):
    520 ...         yield p
    521 
    522 >>> primes = sieve(intsfrom(2))
    523 >>> firstn(primes, 20)
    524 [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
    525 
    526 
    527 Another famous problem:  generate all integers of the form
    528     2**i * 3**j  * 5**k
    529 in increasing order, where i,j,k >= 0.  Trickier than it may look at first!
    530 Try writing it without generators, and correctly, and without generating
    531 3 internal results for each result output.
    532 
    533 >>> def times(n, g):
    534 ...     for i in g:
    535 ...         yield n * i
    536 >>> firstn(times(10, intsfrom(1)), 10)
    537 [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
    538 
    539 >>> def merge(g, h):
    540 ...     ng = g.next()
    541 ...     nh = h.next()
    542 ...     while 1:
    543 ...         if ng < nh:
    544 ...             yield ng
    545 ...             ng = g.next()
    546 ...         elif ng > nh:
    547 ...             yield nh
    548 ...             nh = h.next()
    549 ...         else:
    550 ...             yield ng
    551 ...             ng = g.next()
    552 ...             nh = h.next()
    553 
    554 The following works, but is doing a whale of a lot of redundant work --
    555 it's not clear how to get the internal uses of m235 to share a single
    556 generator.  Note that me_times2 (etc) each need to see every element in the
    557 result sequence.  So this is an example where lazy lists are more natural
    558 (you can look at the head of a lazy list any number of times).
    559 
    560 >>> def m235():
    561 ...     yield 1
    562 ...     me_times2 = times(2, m235())
    563 ...     me_times3 = times(3, m235())
    564 ...     me_times5 = times(5, m235())
    565 ...     for i in merge(merge(me_times2,
    566 ...                          me_times3),
    567 ...                    me_times5):
    568 ...         yield i
    569 
    570 Don't print "too many" of these -- the implementation above is extremely
    571 inefficient:  each call of m235() leads to 3 recursive calls, and in
    572 turn each of those 3 more, and so on, and so on, until we've descended
    573 enough levels to satisfy the print stmts.  Very odd:  when I printed 5
    574 lines of results below, this managed to screw up Win98's malloc in "the
    575 usual" way, i.e. the heap grew over 4Mb so Win98 started fragmenting
    576 address space, and it *looked* like a very slow leak.
    577 
    578 >>> result = m235()
    579 >>> for i in range(3):
    580 ...     print firstn(result, 15)
    581 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
    582 [25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
    583 [81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
    584 
    585 Heh.  Here's one way to get a shared list, complete with an excruciating
    586 namespace renaming trick.  The *pretty* part is that the times() and merge()
    587 functions can be reused as-is, because they only assume their stream
    588 arguments are iterable -- a LazyList is the same as a generator to times().
    589 
    590 >>> class LazyList:
    591 ...     def __init__(self, g):
    592 ...         self.sofar = []
    593 ...         self.fetch = g.next
    594 ...
    595 ...     def __getitem__(self, i):
    596 ...         sofar, fetch = self.sofar, self.fetch
    597 ...         while i >= len(sofar):
    598 ...             sofar.append(fetch())
    599 ...         return sofar[i]
    600 
    601 >>> def m235():
    602 ...     yield 1
    603 ...     # Gack:  m235 below actually refers to a LazyList.
    604 ...     me_times2 = times(2, m235)
    605 ...     me_times3 = times(3, m235)
    606 ...     me_times5 = times(5, m235)
    607 ...     for i in merge(merge(me_times2,
    608 ...                          me_times3),
    609 ...                    me_times5):
    610 ...         yield i
    611 
    612 Print as many of these as you like -- *this* implementation is memory-
    613 efficient.
    614 
    615 >>> m235 = LazyList(m235())
    616 >>> for i in range(5):
    617 ...     print [m235[j] for j in range(15*i, 15*(i+1))]
    618 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
    619 [25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
    620 [81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
    621 [200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384]
    622 [400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675]
    623 
    624 Ye olde Fibonacci generator, LazyList style.
    625 
    626 >>> def fibgen(a, b):
    627 ...
    628 ...     def sum(g, h):
    629 ...         while 1:
    630 ...             yield g.next() + h.next()
    631 ...
    632 ...     def tail(g):
    633 ...         g.next()    # throw first away
    634 ...         for x in g:
    635 ...             yield x
    636 ...
    637 ...     yield a
    638 ...     yield b
    639 ...     for s in sum(iter(fib),
    640 ...                  tail(iter(fib))):
    641 ...         yield s
    642 
    643 >>> fib = LazyList(fibgen(1, 2))
    644 >>> firstn(iter(fib), 17)
    645 [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
    646 
    647 
    648 Running after your tail with itertools.tee (new in version 2.4)
    649 
    650 The algorithms "m235" (Hamming) and Fibonacci presented above are both
    651 examples of a whole family of FP (functional programming) algorithms
    652 where a function produces and returns a list while the production algorithm
    653 suppose the list as already produced by recursively calling itself.
    654 For these algorithms to work, they must:
    655 
    656 - produce at least a first element without presupposing the existence of
    657   the rest of the list
    658 - produce their elements in a lazy manner
    659 
    660 To work efficiently, the beginning of the list must not be recomputed over
    661 and over again. This is ensured in most FP languages as a built-in feature.
    662 In python, we have to explicitly maintain a list of already computed results
    663 and abandon genuine recursivity.
    664 
    665 This is what had been attempted above with the LazyList class. One problem
    666 with that class is that it keeps a list of all of the generated results and
    667 therefore continually grows. This partially defeats the goal of the generator
    668 concept, viz. produce the results only as needed instead of producing them
    669 all and thereby wasting memory.
    670 
    671 Thanks to itertools.tee, it is now clear "how to get the internal uses of
    672 m235 to share a single generator".
    673 
    674 >>> from itertools import tee
    675 >>> def m235():
    676 ...     def _m235():
    677 ...         yield 1
    678 ...         for n in merge(times(2, m2),
    679 ...                        merge(times(3, m3),
    680 ...                              times(5, m5))):
    681 ...             yield n
    682 ...     m1 = _m235()
    683 ...     m2, m3, m5, mRes = tee(m1, 4)
    684 ...     return mRes
    685 
    686 >>> it = m235()
    687 >>> for i in range(5):
    688 ...     print firstn(it, 15)
    689 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
    690 [25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
    691 [81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
    692 [200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384]
    693 [400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675]
    694 
    695 The "tee" function does just what we want. It internally keeps a generated
    696 result for as long as it has not been "consumed" from all of the duplicated
    697 iterators, whereupon it is deleted. You can therefore print the hamming
    698 sequence during hours without increasing memory usage, or very little.
    699 
    700 The beauty of it is that recursive running-after-their-tail FP algorithms
    701 are quite straightforwardly expressed with this Python idiom.
    702 
    703 Ye olde Fibonacci generator, tee style.
    704 
    705 >>> def fib():
    706 ...
    707 ...     def _isum(g, h):
    708 ...         while 1:
    709 ...             yield g.next() + h.next()
    710 ...
    711 ...     def _fib():
    712 ...         yield 1
    713 ...         yield 2
    714 ...         fibTail.next() # throw first away
    715 ...         for res in _isum(fibHead, fibTail):
    716 ...             yield res
    717 ...
    718 ...     realfib = _fib()
    719 ...     fibHead, fibTail, fibRes = tee(realfib, 3)
    720 ...     return fibRes
    721 
    722 >>> firstn(fib(), 17)
    723 [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
    724 
    725 """
    726 
    727 # syntax_tests mostly provokes SyntaxErrors.  Also fiddling with #if 0
    728 # hackery.
    729 
    730 syntax_tests = """
    731 
    732 >>> def f():
    733 ...     return 22
    734 ...     yield 1
    735 Traceback (most recent call last):
    736   ..
    737 SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[0]>, line 3)
    738 
    739 >>> def f():
    740 ...     yield 1
    741 ...     return 22
    742 Traceback (most recent call last):
    743   ..
    744 SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[1]>, line 3)
    745 
    746 "return None" is not the same as "return" in a generator:
    747 
    748 >>> def f():
    749 ...     yield 1
    750 ...     return None
    751 Traceback (most recent call last):
    752   ..
    753 SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[2]>, line 3)
    754 
    755 These are fine:
    756 
    757 >>> def f():
    758 ...     yield 1
    759 ...     return
    760 
    761 >>> def f():
    762 ...     try:
    763 ...         yield 1
    764 ...     finally:
    765 ...         pass
    766 
    767 >>> def f():
    768 ...     try:
    769 ...         try:
    770 ...             1//0
    771 ...         except ZeroDivisionError:
    772 ...             yield 666
    773 ...         except:
    774 ...             pass
    775 ...     finally:
    776 ...         pass
    777 
    778 >>> def f():
    779 ...     try:
    780 ...         try:
    781 ...             yield 12
    782 ...             1//0
    783 ...         except ZeroDivisionError:
    784 ...             yield 666
    785 ...         except:
    786 ...             try:
    787 ...                 x = 12
    788 ...             finally:
    789 ...                 yield 12
    790 ...     except:
    791 ...         return
    792 >>> list(f())
    793 [12, 666]
    794 
    795 >>> def f():
    796 ...    yield
    797 >>> type(f())
    798 <type 'generator'>
    799 
    800 
    801 >>> def f():
    802 ...    if 0:
    803 ...        yield
    804 >>> type(f())
    805 <type 'generator'>
    806 
    807 
    808 >>> def f():
    809 ...     if 0:
    810 ...         yield 1
    811 >>> type(f())
    812 <type 'generator'>
    813 
    814 >>> def f():
    815 ...    if "":
    816 ...        yield None
    817 >>> type(f())
    818 <type 'generator'>
    819 
    820 >>> def f():
    821 ...     return
    822 ...     try:
    823 ...         if x==4:
    824 ...             pass
    825 ...         elif 0:
    826 ...             try:
    827 ...                 1//0
    828 ...             except SyntaxError:
    829 ...                 pass
    830 ...             else:
    831 ...                 if 0:
    832 ...                     while 12:
    833 ...                         x += 1
    834 ...                         yield 2 # don't blink
    835 ...                         f(a, b, c, d, e)
    836 ...         else:
    837 ...             pass
    838 ...     except:
    839 ...         x = 1
    840 ...     return
    841 >>> type(f())
    842 <type 'generator'>
    843 
    844 >>> def f():
    845 ...     if 0:
    846 ...         def g():
    847 ...             yield 1
    848 ...
    849 >>> type(f())
    850 <type 'NoneType'>
    851 
    852 >>> def f():
    853 ...     if 0:
    854 ...         class C:
    855 ...             def __init__(self):
    856 ...                 yield 1
    857 ...             def f(self):
    858 ...                 yield 2
    859 >>> type(f())
    860 <type 'NoneType'>
    861 
    862 >>> def f():
    863 ...     if 0:
    864 ...         return
    865 ...     if 0:
    866 ...         yield 2
    867 >>> type(f())
    868 <type 'generator'>
    869 
    870 
    871 >>> def f():
    872 ...     if 0:
    873 ...         lambda x:  x        # shouldn't trigger here
    874 ...         return              # or here
    875 ...         def f(i):
    876 ...             return 2*i      # or here
    877 ...         if 0:
    878 ...             return 3        # but *this* sucks (line 8)
    879 ...     if 0:
    880 ...         yield 2             # because it's a generator (line 10)
    881 Traceback (most recent call last):
    882 SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.syntax[24]>, line 10)
    883 
    884 This one caused a crash (see SF bug 567538):
    885 
    886 >>> def f():
    887 ...     for i in range(3):
    888 ...         try:
    889 ...             continue
    890 ...         finally:
    891 ...             yield i
    892 ...
    893 >>> g = f()
    894 >>> print g.next()
    895 0
    896 >>> print g.next()
    897 1
    898 >>> print g.next()
    899 2
    900 >>> print g.next()
    901 Traceback (most recent call last):
    902 StopIteration
    903 
    904 
    905 Test the gi_code attribute
    906 
    907 >>> def f():
    908 ...     yield 5
    909 ...
    910 >>> g = f()
    911 >>> g.gi_code is f.func_code
    912 True
    913 >>> g.next()
    914 5
    915 >>> g.next()
    916 Traceback (most recent call last):
    917 StopIteration
    918 >>> g.gi_code is f.func_code
    919 True
    920 
    921 
    922 Test the __name__ attribute and the repr()
    923 
    924 >>> def f():
    925 ...    yield 5
    926 ...
    927 >>> g = f()
    928 >>> g.__name__
    929 'f'
    930 >>> repr(g)  # doctest: +ELLIPSIS
    931 '<generator object f at ...>'
    932 
    933 Lambdas shouldn't have their usual return behavior.
    934 
    935 >>> x = lambda: (yield 1)
    936 >>> list(x())
    937 [1]
    938 
    939 >>> x = lambda: ((yield 1), (yield 2))
    940 >>> list(x())
    941 [1, 2]
    942 """
    943 
    944 # conjoin is a simple backtracking generator, named in honor of Icon's
    945 # "conjunction" control structure.  Pass a list of no-argument functions
    946 # that return iterable objects.  Easiest to explain by example:  assume the
    947 # function list [x, y, z] is passed.  Then conjoin acts like:
    948 #
    949 # def g():
    950 #     values = [None] * 3
    951 #     for values[0] in x():
    952 #         for values[1] in y():
    953 #             for values[2] in z():
    954 #                 yield values
    955 #
    956 # So some 3-lists of values *may* be generated, each time we successfully
    957 # get into the innermost loop.  If an iterator fails (is exhausted) before
    958 # then, it "backtracks" to get the next value from the nearest enclosing
    959 # iterator (the one "to the left"), and starts all over again at the next
    960 # slot (pumps a fresh iterator).  Of course this is most useful when the
    961 # iterators have side-effects, so that which values *can* be generated at
    962 # each slot depend on the values iterated at previous slots.
    963 
    964 def simple_conjoin(gs):
    965 
    966     values = [None] * len(gs)
    967 
    968     def gen(i):
    969         if i >= len(gs):
    970             yield values
    971         else:
    972             for values[i] in gs[i]():
    973                 for x in gen(i+1):
    974                     yield x
    975 
    976     for x in gen(0):
    977         yield x
    978 
    979 # That works fine, but recursing a level and checking i against len(gs) for
    980 # each item produced is inefficient.  By doing manual loop unrolling across
    981 # generator boundaries, it's possible to eliminate most of that overhead.
    982 # This isn't worth the bother *in general* for generators, but conjoin() is
    983 # a core building block for some CPU-intensive generator applications.
    984 
    985 def conjoin(gs):
    986 
    987     n = len(gs)
    988     values = [None] * n
    989 
    990     # Do one loop nest at time recursively, until the # of loop nests
    991     # remaining is divisible by 3.
    992 
    993     def gen(i):
    994         if i >= n:
    995             yield values
    996 
    997         elif (n-i) % 3:
    998             ip1 = i+1
    999             for values[i] in gs[i]():
   1000                 for x in gen(ip1):
   1001                     yield x
   1002 
   1003         else:
   1004             for x in _gen3(i):
   1005                 yield x
   1006 
   1007     # Do three loop nests at a time, recursing only if at least three more
   1008     # remain.  Don't call directly:  this is an internal optimization for
   1009     # gen's use.
   1010 
   1011     def _gen3(i):
   1012         assert i < n and (n-i) % 3 == 0
   1013         ip1, ip2, ip3 = i+1, i+2, i+3
   1014         g, g1, g2 = gs[i : ip3]
   1015 
   1016         if ip3 >= n:
   1017             # These are the last three, so we can yield values directly.
   1018             for values[i] in g():
   1019                 for values[ip1] in g1():
   1020                     for values[ip2] in g2():
   1021                         yield values
   1022 
   1023         else:
   1024             # At least 6 loop nests remain; peel off 3 and recurse for the
   1025             # rest.
   1026             for values[i] in g():
   1027                 for values[ip1] in g1():
   1028                     for values[ip2] in g2():
   1029                         for x in _gen3(ip3):
   1030                             yield x
   1031 
   1032     for x in gen(0):
   1033         yield x
   1034 
   1035 # And one more approach:  For backtracking apps like the Knight's Tour
   1036 # solver below, the number of backtracking levels can be enormous (one
   1037 # level per square, for the Knight's Tour, so that e.g. a 100x100 board
   1038 # needs 10,000 levels).  In such cases Python is likely to run out of
   1039 # stack space due to recursion.  So here's a recursion-free version of
   1040 # conjoin too.
   1041 # NOTE WELL:  This allows large problems to be solved with only trivial
   1042 # demands on stack space.  Without explicitly resumable generators, this is
   1043 # much harder to achieve.  OTOH, this is much slower (up to a factor of 2)
   1044 # than the fancy unrolled recursive conjoin.
   1045 
   1046 def flat_conjoin(gs):  # rename to conjoin to run tests with this instead
   1047     n = len(gs)
   1048     values = [None] * n
   1049     iters  = [None] * n
   1050     _StopIteration = StopIteration  # make local because caught a *lot*
   1051     i = 0
   1052     while 1:
   1053         # Descend.
   1054         try:
   1055             while i < n:
   1056                 it = iters[i] = gs[i]().next
   1057                 values[i] = it()
   1058                 i += 1
   1059         except _StopIteration:
   1060             pass
   1061         else:
   1062             assert i == n
   1063             yield values
   1064 
   1065         # Backtrack until an older iterator can be resumed.
   1066         i -= 1
   1067         while i >= 0:
   1068             try:
   1069                 values[i] = iters[i]()
   1070                 # Success!  Start fresh at next level.
   1071                 i += 1
   1072                 break
   1073             except _StopIteration:
   1074                 # Continue backtracking.
   1075                 i -= 1
   1076         else:
   1077             assert i < 0
   1078             break
   1079 
   1080 # A conjoin-based N-Queens solver.
   1081 
   1082 class Queens:
   1083     def __init__(self, n):
   1084         self.n = n
   1085         rangen = range(n)
   1086 
   1087         # Assign a unique int to each column and diagonal.
   1088         # columns:  n of those, range(n).
   1089         # NW-SE diagonals: 2n-1 of these, i-j unique and invariant along
   1090         # each, smallest i-j is 0-(n-1) = 1-n, so add n-1 to shift to 0-
   1091         # based.
   1092         # NE-SW diagonals: 2n-1 of these, i+j unique and invariant along
   1093         # each, smallest i+j is 0, largest is 2n-2.
   1094 
   1095         # For each square, compute a bit vector of the columns and
   1096         # diagonals it covers, and for each row compute a function that
   1097         # generates the possibilities for the columns in that row.
   1098         self.rowgenerators = []
   1099         for i in rangen:
   1100             rowuses = [(1L << j) |                  # column ordinal
   1101                        (1L << (n + i-j + n-1)) |    # NW-SE ordinal
   1102                        (1L << (n + 2*n-1 + i+j))    # NE-SW ordinal
   1103                             for j in rangen]
   1104 
   1105             def rowgen(rowuses=rowuses):
   1106                 for j in rangen:
   1107                     uses = rowuses[j]
   1108                     if uses & self.used == 0:
   1109                         self.used |= uses
   1110                         yield j
   1111                         self.used &= ~uses
   1112 
   1113             self.rowgenerators.append(rowgen)
   1114 
   1115     # Generate solutions.
   1116     def solve(self):
   1117         self.used = 0
   1118         for row2col in conjoin(self.rowgenerators):
   1119             yield row2col
   1120 
   1121     def printsolution(self, row2col):
   1122         n = self.n
   1123         assert n == len(row2col)
   1124         sep = "+" + "-+" * n
   1125         print sep
   1126         for i in range(n):
   1127             squares = [" " for j in range(n)]
   1128             squares[row2col[i]] = "Q"
   1129             print "|" + "|".join(squares) + "|"
   1130             print sep
   1131 
   1132 # A conjoin-based Knight's Tour solver.  This is pretty sophisticated
   1133 # (e.g., when used with flat_conjoin above, and passing hard=1 to the
   1134 # constructor, a 200x200 Knight's Tour was found quickly -- note that we're
   1135 # creating 10s of thousands of generators then!), and is lengthy.
   1136 
   1137 class Knights:
   1138     def __init__(self, m, n, hard=0):
   1139         self.m, self.n = m, n
   1140 
   1141         # solve() will set up succs[i] to be a list of square #i's
   1142         # successors.
   1143         succs = self.succs = []
   1144 
   1145         # Remove i0 from each of its successor's successor lists, i.e.
   1146         # successors can't go back to i0 again.  Return 0 if we can
   1147         # detect this makes a solution impossible, else return 1.
   1148 
   1149         def remove_from_successors(i0, len=len):
   1150             # If we remove all exits from a free square, we're dead:
   1151             # even if we move to it next, we can't leave it again.
   1152             # If we create a square with one exit, we must visit it next;
   1153             # else somebody else will have to visit it, and since there's
   1154             # only one adjacent, there won't be a way to leave it again.
   1155             # Finelly, if we create more than one free square with a
   1156             # single exit, we can only move to one of them next, leaving
   1157             # the other one a dead end.
   1158             ne0 = ne1 = 0
   1159             for i in succs[i0]:
   1160                 s = succs[i]
   1161                 s.remove(i0)
   1162                 e = len(s)
   1163                 if e == 0:
   1164                     ne0 += 1
   1165                 elif e == 1:
   1166                     ne1 += 1
   1167             return ne0 == 0 and ne1 < 2
   1168 
   1169         # Put i0 back in each of its successor's successor lists.
   1170 
   1171         def add_to_successors(i0):
   1172             for i in succs[i0]:
   1173                 succs[i].append(i0)
   1174 
   1175         # Generate the first move.
   1176         def first():
   1177             if m < 1 or n < 1:
   1178                 return
   1179 
   1180             # Since we're looking for a cycle, it doesn't matter where we
   1181             # start.  Starting in a corner makes the 2nd move easy.
   1182             corner = self.coords2index(0, 0)
   1183             remove_from_successors(corner)
   1184             self.lastij = corner
   1185             yield corner
   1186             add_to_successors(corner)
   1187 
   1188         # Generate the second moves.
   1189         def second():
   1190             corner = self.coords2index(0, 0)
   1191             assert self.lastij == corner  # i.e., we started in the corner
   1192             if m < 3 or n < 3:
   1193                 return
   1194             assert len(succs[corner]) == 2
   1195             assert self.coords2index(1, 2) in succs[corner]
   1196             assert self.coords2index(2, 1) in succs[corner]
   1197             # Only two choices.  Whichever we pick, the other must be the
   1198             # square picked on move m*n, as it's the only way to get back
   1199             # to (0, 0).  Save its index in self.final so that moves before
   1200             # the last know it must be kept free.
   1201             for i, j in (1, 2), (2, 1):
   1202                 this  = self.coords2index(i, j)
   1203                 final = self.coords2index(3-i, 3-j)
   1204                 self.final = final
   1205 
   1206                 remove_from_successors(this)
   1207                 succs[final].append(corner)
   1208                 self.lastij = this
   1209                 yield this
   1210                 succs[final].remove(corner)
   1211                 add_to_successors(this)
   1212 
   1213         # Generate moves 3 thru m*n-1.
   1214         def advance(len=len):
   1215             # If some successor has only one exit, must take it.
   1216             # Else favor successors with fewer exits.
   1217             candidates = []
   1218             for i in succs[self.lastij]:
   1219                 e = len(succs[i])
   1220                 assert e > 0, "else remove_from_successors() pruning flawed"
   1221                 if e == 1:
   1222                     candidates = [(e, i)]
   1223                     break
   1224                 candidates.append((e, i))
   1225             else:
   1226                 candidates.sort()
   1227 
   1228             for e, i in candidates:
   1229                 if i != self.final:
   1230                     if remove_from_successors(i):
   1231                         self.lastij = i
   1232                         yield i
   1233                     add_to_successors(i)
   1234 
   1235         # Generate moves 3 thru m*n-1.  Alternative version using a
   1236         # stronger (but more expensive) heuristic to order successors.
   1237         # Since the # of backtracking levels is m*n, a poor move early on
   1238         # can take eons to undo.  Smallest square board for which this
   1239         # matters a lot is 52x52.
   1240         def advance_hard(vmid=(m-1)/2.0, hmid=(n-1)/2.0, len=len):
   1241             # If some successor has only one exit, must take it.
   1242             # Else favor successors with fewer exits.
   1243             # Break ties via max distance from board centerpoint (favor
   1244             # corners and edges whenever possible).
   1245             candidates = []
   1246             for i in succs[self.lastij]:
   1247                 e = len(succs[i])
   1248                 assert e > 0, "else remove_from_successors() pruning flawed"
   1249                 if e == 1:
   1250                     candidates = [(e, 0, i)]
   1251                     break
   1252                 i1, j1 = self.index2coords(i)
   1253                 d = (i1 - vmid)**2 + (j1 - hmid)**2
   1254                 candidates.append((e, -d, i))
   1255             else:
   1256                 candidates.sort()
   1257 
   1258             for e, d, i in candidates:
   1259                 if i != self.final:
   1260                     if remove_from_successors(i):
   1261                         self.lastij = i
   1262                         yield i
   1263                     add_to_successors(i)
   1264 
   1265         # Generate the last move.
   1266         def last():
   1267             assert self.final in succs[self.lastij]
   1268             yield self.final
   1269 
   1270         if m*n < 4:
   1271             self.squaregenerators = [first]
   1272         else:
   1273             self.squaregenerators = [first, second] + \
   1274                 [hard and advance_hard or advance] * (m*n - 3) + \
   1275                 [last]
   1276 
   1277     def coords2index(self, i, j):
   1278         assert 0 <= i < self.m
   1279         assert 0 <= j < self.n
   1280         return i * self.n + j
   1281 
   1282     def index2coords(self, index):
   1283         assert 0 <= index < self.m * self.n
   1284         return divmod(index, self.n)
   1285 
   1286     def _init_board(self):
   1287         succs = self.succs
   1288         del succs[:]
   1289         m, n = self.m, self.n
   1290         c2i = self.coords2index
   1291 
   1292         offsets = [( 1,  2), ( 2,  1), ( 2, -1), ( 1, -2),
   1293                    (-1, -2), (-2, -1), (-2,  1), (-1,  2)]
   1294         rangen = range(n)
   1295         for i in range(m):
   1296             for j in rangen:
   1297                 s = [c2i(i+io, j+jo) for io, jo in offsets
   1298                                      if 0 <= i+io < m and
   1299                                         0 <= j+jo < n]
   1300                 succs.append(s)
   1301 
   1302     # Generate solutions.
   1303     def solve(self):
   1304         self._init_board()
   1305         for x in conjoin(self.squaregenerators):
   1306             yield x
   1307 
   1308     def printsolution(self, x):
   1309         m, n = self.m, self.n
   1310         assert len(x) == m*n
   1311         w = len(str(m*n))
   1312         format = "%" + str(w) + "d"
   1313 
   1314         squares = [[None] * n for i in range(m)]
   1315         k = 1
   1316         for i in x:
   1317             i1, j1 = self.index2coords(i)
   1318             squares[i1][j1] = format % k
   1319             k += 1
   1320 
   1321         sep = "+" + ("-" * w + "+") * n
   1322         print sep
   1323         for i in range(m):
   1324             row = squares[i]
   1325             print "|" + "|".join(row) + "|"
   1326             print sep
   1327 
   1328 conjoin_tests = """
   1329 
   1330 Generate the 3-bit binary numbers in order.  This illustrates dumbest-
   1331 possible use of conjoin, just to generate the full cross-product.
   1332 
   1333 >>> for c in conjoin([lambda: iter((0, 1))] * 3):
   1334 ...     print c
   1335 [0, 0, 0]
   1336 [0, 0, 1]
   1337 [0, 1, 0]
   1338 [0, 1, 1]
   1339 [1, 0, 0]
   1340 [1, 0, 1]
   1341 [1, 1, 0]
   1342 [1, 1, 1]
   1343 
   1344 For efficiency in typical backtracking apps, conjoin() yields the same list
   1345 object each time.  So if you want to save away a full account of its
   1346 generated sequence, you need to copy its results.
   1347 
   1348 >>> def gencopy(iterator):
   1349 ...     for x in iterator:
   1350 ...         yield x[:]
   1351 
   1352 >>> for n in range(10):
   1353 ...     all = list(gencopy(conjoin([lambda: iter((0, 1))] * n)))
   1354 ...     print n, len(all), all[0] == [0] * n, all[-1] == [1] * n
   1355 0 1 True True
   1356 1 2 True True
   1357 2 4 True True
   1358 3 8 True True
   1359 4 16 True True
   1360 5 32 True True
   1361 6 64 True True
   1362 7 128 True True
   1363 8 256 True True
   1364 9 512 True True
   1365 
   1366 And run an 8-queens solver.
   1367 
   1368 >>> q = Queens(8)
   1369 >>> LIMIT = 2
   1370 >>> count = 0
   1371 >>> for row2col in q.solve():
   1372 ...     count += 1
   1373 ...     if count <= LIMIT:
   1374 ...         print "Solution", count
   1375 ...         q.printsolution(row2col)
   1376 Solution 1
   1377 +-+-+-+-+-+-+-+-+
   1378 |Q| | | | | | | |
   1379 +-+-+-+-+-+-+-+-+
   1380 | | | | |Q| | | |
   1381 +-+-+-+-+-+-+-+-+
   1382 | | | | | | | |Q|
   1383 +-+-+-+-+-+-+-+-+
   1384 | | | | | |Q| | |
   1385 +-+-+-+-+-+-+-+-+
   1386 | | |Q| | | | | |
   1387 +-+-+-+-+-+-+-+-+
   1388 | | | | | | |Q| |
   1389 +-+-+-+-+-+-+-+-+
   1390 | |Q| | | | | | |
   1391 +-+-+-+-+-+-+-+-+
   1392 | | | |Q| | | | |
   1393 +-+-+-+-+-+-+-+-+
   1394 Solution 2
   1395 +-+-+-+-+-+-+-+-+
   1396 |Q| | | | | | | |
   1397 +-+-+-+-+-+-+-+-+
   1398 | | | | | |Q| | |
   1399 +-+-+-+-+-+-+-+-+
   1400 | | | | | | | |Q|
   1401 +-+-+-+-+-+-+-+-+
   1402 | | |Q| | | | | |
   1403 +-+-+-+-+-+-+-+-+
   1404 | | | | | | |Q| |
   1405 +-+-+-+-+-+-+-+-+
   1406 | | | |Q| | | | |
   1407 +-+-+-+-+-+-+-+-+
   1408 | |Q| | | | | | |
   1409 +-+-+-+-+-+-+-+-+
   1410 | | | | |Q| | | |
   1411 +-+-+-+-+-+-+-+-+
   1412 
   1413 >>> print count, "solutions in all."
   1414 92 solutions in all.
   1415 
   1416 And run a Knight's Tour on a 10x10 board.  Note that there are about
   1417 20,000 solutions even on a 6x6 board, so don't dare run this to exhaustion.
   1418 
   1419 >>> k = Knights(10, 10)
   1420 >>> LIMIT = 2
   1421 >>> count = 0
   1422 >>> for x in k.solve():
   1423 ...     count += 1
   1424 ...     if count <= LIMIT:
   1425 ...         print "Solution", count
   1426 ...         k.printsolution(x)
   1427 ...     else:
   1428 ...         break
   1429 Solution 1
   1430 +---+---+---+---+---+---+---+---+---+---+
   1431 |  1| 58| 27| 34|  3| 40| 29| 10|  5|  8|
   1432 +---+---+---+---+---+---+---+---+---+---+
   1433 | 26| 35|  2| 57| 28| 33|  4|  7| 30| 11|
   1434 +---+---+---+---+---+---+---+---+---+---+
   1435 | 59|100| 73| 36| 41| 56| 39| 32|  9|  6|
   1436 +---+---+---+---+---+---+---+---+---+---+
   1437 | 74| 25| 60| 55| 72| 37| 42| 49| 12| 31|
   1438 +---+---+---+---+---+---+---+---+---+---+
   1439 | 61| 86| 99| 76| 63| 52| 47| 38| 43| 50|
   1440 +---+---+---+---+---+---+---+---+---+---+
   1441 | 24| 75| 62| 85| 54| 71| 64| 51| 48| 13|
   1442 +---+---+---+---+---+---+---+---+---+---+
   1443 | 87| 98| 91| 80| 77| 84| 53| 46| 65| 44|
   1444 +---+---+---+---+---+---+---+---+---+---+
   1445 | 90| 23| 88| 95| 70| 79| 68| 83| 14| 17|
   1446 +---+---+---+---+---+---+---+---+---+---+
   1447 | 97| 92| 21| 78| 81| 94| 19| 16| 45| 66|
   1448 +---+---+---+---+---+---+---+---+---+---+
   1449 | 22| 89| 96| 93| 20| 69| 82| 67| 18| 15|
   1450 +---+---+---+---+---+---+---+---+---+---+
   1451 Solution 2
   1452 +---+---+---+---+---+---+---+---+---+---+
   1453 |  1| 58| 27| 34|  3| 40| 29| 10|  5|  8|
   1454 +---+---+---+---+---+---+---+---+---+---+
   1455 | 26| 35|  2| 57| 28| 33|  4|  7| 30| 11|
   1456 +---+---+---+---+---+---+---+---+---+---+
   1457 | 59|100| 73| 36| 41| 56| 39| 32|  9|  6|
   1458 +---+---+---+---+---+---+---+---+---+---+
   1459 | 74| 25| 60| 55| 72| 37| 42| 49| 12| 31|
   1460 +---+---+---+---+---+---+---+---+---+---+
   1461 | 61| 86| 99| 76| 63| 52| 47| 38| 43| 50|
   1462 +---+---+---+---+---+---+---+---+---+---+
   1463 | 24| 75| 62| 85| 54| 71| 64| 51| 48| 13|
   1464 +---+---+---+---+---+---+---+---+---+---+
   1465 | 87| 98| 89| 80| 77| 84| 53| 46| 65| 44|
   1466 +---+---+---+---+---+---+---+---+---+---+
   1467 | 90| 23| 92| 95| 70| 79| 68| 83| 14| 17|
   1468 +---+---+---+---+---+---+---+---+---+---+
   1469 | 97| 88| 21| 78| 81| 94| 19| 16| 45| 66|
   1470 +---+---+---+---+---+---+---+---+---+---+
   1471 | 22| 91| 96| 93| 20| 69| 82| 67| 18| 15|
   1472 +---+---+---+---+---+---+---+---+---+---+
   1473 """
   1474 
   1475 weakref_tests = """\
   1476 Generators are weakly referencable:
   1477 
   1478 >>> import weakref
   1479 >>> def gen():
   1480 ...     yield 'foo!'
   1481 ...
   1482 >>> wr = weakref.ref(gen)
   1483 >>> wr() is gen
   1484 True
   1485 >>> p = weakref.proxy(gen)
   1486 
   1487 Generator-iterators are weakly referencable as well:
   1488 
   1489 >>> gi = gen()
   1490 >>> wr = weakref.ref(gi)
   1491 >>> wr() is gi
   1492 True
   1493 >>> p = weakref.proxy(gi)
   1494 >>> list(p)
   1495 ['foo!']
   1496 
   1497 """
   1498 
   1499 coroutine_tests = """\
   1500 Sending a value into a started generator:
   1501 
   1502 >>> def f():
   1503 ...     print (yield 1)
   1504 ...     yield 2
   1505 >>> g = f()
   1506 >>> g.next()
   1507 1
   1508 >>> g.send(42)
   1509 42
   1510 2
   1511 
   1512 Sending a value into a new generator produces a TypeError:
   1513 
   1514 >>> f().send("foo")
   1515 Traceback (most recent call last):
   1516 ...
   1517 TypeError: can't send non-None value to a just-started generator
   1518 
   1519 
   1520 Yield by itself yields None:
   1521 
   1522 >>> def f(): yield
   1523 >>> list(f())
   1524 [None]
   1525 
   1526 
   1527 Yield is allowed only in the outermost iterable in generator expression:
   1528 
   1529 >>> def f(): list(i for i in [(yield 26)])
   1530 >>> type(f())
   1531 <type 'generator'>
   1532 
   1533 
   1534 A yield expression with augmented assignment.
   1535 
   1536 >>> def coroutine(seq):
   1537 ...     count = 0
   1538 ...     while count < 200:
   1539 ...         count += yield
   1540 ...         seq.append(count)
   1541 >>> seq = []
   1542 >>> c = coroutine(seq)
   1543 >>> c.next()
   1544 >>> print seq
   1545 []
   1546 >>> c.send(10)
   1547 >>> print seq
   1548 [10]
   1549 >>> c.send(10)
   1550 >>> print seq
   1551 [10, 20]
   1552 >>> c.send(10)
   1553 >>> print seq
   1554 [10, 20, 30]
   1555 
   1556 
   1557 Check some syntax errors for yield expressions:
   1558 
   1559 >>> f=lambda: (yield 1),(yield 2)
   1560 Traceback (most recent call last):
   1561   ...
   1562   File "<doctest test.test_generators.__test__.coroutine[21]>", line 1
   1563 SyntaxError: 'yield' outside function
   1564 
   1565 >>> def f(): return lambda x=(yield): 1
   1566 Traceback (most recent call last):
   1567   ...
   1568 SyntaxError: 'return' with argument inside generator (<doctest test.test_generators.__test__.coroutine[21]>, line 1)
   1569 
   1570 >>> def f(): x = yield = y
   1571 Traceback (most recent call last):
   1572   ...
   1573   File "<doctest test.test_generators.__test__.coroutine[23]>", line 1
   1574 SyntaxError: assignment to yield expression not possible
   1575 
   1576 >>> def f(): (yield bar) = y
   1577 Traceback (most recent call last):
   1578   ...
   1579   File "<doctest test.test_generators.__test__.coroutine[24]>", line 1
   1580 SyntaxError: can't assign to yield expression
   1581 
   1582 >>> def f(): (yield bar) += y
   1583 Traceback (most recent call last):
   1584   ...
   1585   File "<doctest test.test_generators.__test__.coroutine[25]>", line 1
   1586 SyntaxError: can't assign to yield expression
   1587 
   1588 
   1589 Now check some throw() conditions:
   1590 
   1591 >>> def f():
   1592 ...     while True:
   1593 ...         try:
   1594 ...             print (yield)
   1595 ...         except ValueError,v:
   1596 ...             print "caught ValueError (%s)" % (v),
   1597 >>> import sys
   1598 >>> g = f()
   1599 >>> g.next()
   1600 
   1601 >>> g.throw(ValueError) # type only
   1602 caught ValueError ()
   1603 
   1604 >>> g.throw(ValueError("xyz"))  # value only
   1605 caught ValueError (xyz)
   1606 
   1607 >>> g.throw(ValueError, ValueError(1))   # value+matching type
   1608 caught ValueError (1)
   1609 
   1610 >>> g.throw(ValueError, TypeError(1))  # mismatched type, rewrapped
   1611 caught ValueError (1)
   1612 
   1613 >>> g.throw(ValueError, ValueError(1), None)   # explicit None traceback
   1614 caught ValueError (1)
   1615 
   1616 >>> g.throw(ValueError(1), "foo")       # bad args
   1617 Traceback (most recent call last):
   1618   ...
   1619 TypeError: instance exception may not have a separate value
   1620 
   1621 >>> g.throw(ValueError, "foo", 23)      # bad args
   1622 Traceback (most recent call last):
   1623   ...
   1624 TypeError: throw() third argument must be a traceback object
   1625 
   1626 >>> def throw(g,exc):
   1627 ...     try:
   1628 ...         raise exc
   1629 ...     except:
   1630 ...         g.throw(*sys.exc_info())
   1631 >>> throw(g,ValueError) # do it with traceback included
   1632 caught ValueError ()
   1633 
   1634 >>> g.send(1)
   1635 1
   1636 
   1637 >>> throw(g,TypeError)  # terminate the generator
   1638 Traceback (most recent call last):
   1639   ...
   1640 TypeError
   1641 
   1642 >>> print g.gi_frame
   1643 None
   1644 
   1645 >>> g.send(2)
   1646 Traceback (most recent call last):
   1647   ...
   1648 StopIteration
   1649 
   1650 >>> g.throw(ValueError,6)       # throw on closed generator
   1651 Traceback (most recent call last):
   1652   ...
   1653 ValueError: 6
   1654 
   1655 >>> f().throw(ValueError,7)     # throw on just-opened generator
   1656 Traceback (most recent call last):
   1657   ...
   1658 ValueError: 7
   1659 
   1660 >>> f().throw("abc")     # throw on just-opened generator
   1661 Traceback (most recent call last):
   1662   ...
   1663 TypeError: exceptions must be classes, or instances, not str
   1664 
   1665 Now let's try closing a generator:
   1666 
   1667 >>> def f():
   1668 ...     try: yield
   1669 ...     except GeneratorExit:
   1670 ...         print "exiting"
   1671 
   1672 >>> g = f()
   1673 >>> g.next()
   1674 >>> g.close()
   1675 exiting
   1676 >>> g.close()  # should be no-op now
   1677 
   1678 >>> f().close()  # close on just-opened generator should be fine
   1679 
   1680 >>> def f(): yield      # an even simpler generator
   1681 >>> f().close()         # close before opening
   1682 >>> g = f()
   1683 >>> g.next()
   1684 >>> g.close()           # close normally
   1685 
   1686 And finalization:
   1687 
   1688 >>> def f():
   1689 ...     try: yield
   1690 ...     finally:
   1691 ...         print "exiting"
   1692 
   1693 >>> g = f()
   1694 >>> g.next()
   1695 >>> del g
   1696 exiting
   1697 
   1698 >>> class context(object):
   1699 ...    def __enter__(self): pass
   1700 ...    def __exit__(self, *args): print 'exiting'
   1701 >>> def f():
   1702 ...     with context():
   1703 ...          yield
   1704 >>> g = f()
   1705 >>> g.next()
   1706 >>> del g
   1707 exiting
   1708 
   1709 
   1710 GeneratorExit is not caught by except Exception:
   1711 
   1712 >>> def f():
   1713 ...     try: yield
   1714 ...     except Exception: print 'except'
   1715 ...     finally: print 'finally'
   1716 
   1717 >>> g = f()
   1718 >>> g.next()
   1719 >>> del g
   1720 finally
   1721 
   1722 
   1723 Now let's try some ill-behaved generators:
   1724 
   1725 >>> def f():
   1726 ...     try: yield
   1727 ...     except GeneratorExit:
   1728 ...         yield "foo!"
   1729 >>> g = f()
   1730 >>> g.next()
   1731 >>> g.close()
   1732 Traceback (most recent call last):
   1733   ...
   1734 RuntimeError: generator ignored GeneratorExit
   1735 >>> g.close()
   1736 
   1737 
   1738 Our ill-behaved code should be invoked during GC:
   1739 
   1740 >>> import sys, StringIO
   1741 >>> old, sys.stderr = sys.stderr, StringIO.StringIO()
   1742 >>> g = f()
   1743 >>> g.next()
   1744 >>> del g
   1745 >>> sys.stderr.getvalue().startswith(
   1746 ...     "Exception RuntimeError: 'generator ignored GeneratorExit' in "
   1747 ... )
   1748 True
   1749 >>> sys.stderr = old
   1750 
   1751 
   1752 And errors thrown during closing should propagate:
   1753 
   1754 >>> def f():
   1755 ...     try: yield
   1756 ...     except GeneratorExit:
   1757 ...         raise TypeError("fie!")
   1758 >>> g = f()
   1759 >>> g.next()
   1760 >>> g.close()
   1761 Traceback (most recent call last):
   1762   ...
   1763 TypeError: fie!
   1764 
   1765 
   1766 Ensure that various yield expression constructs make their
   1767 enclosing function a generator:
   1768 
   1769 >>> def f(): x += yield
   1770 >>> type(f())
   1771 <type 'generator'>
   1772 
   1773 >>> def f(): x = yield
   1774 >>> type(f())
   1775 <type 'generator'>
   1776 
   1777 >>> def f(): lambda x=(yield): 1
   1778 >>> type(f())
   1779 <type 'generator'>
   1780 
   1781 >>> def f(): x=(i for i in (yield) if i)
   1782 >>> type(f())
   1783 <type 'generator'>
   1784 
   1785 >>> def f(d): d[(yield "a")] = d[(yield "b")] = 27
   1786 >>> data = [1,2]
   1787 >>> g = f(data)
   1788 >>> type(g)
   1789 <type 'generator'>
   1790 >>> g.send(None)
   1791 'a'
   1792 >>> data
   1793 [1, 2]
   1794 >>> g.send(0)
   1795 'b'
   1796 >>> data
   1797 [27, 2]
   1798 >>> try: g.send(1)
   1799 ... except StopIteration: pass
   1800 >>> data
   1801 [27, 27]
   1802 
   1803 """
   1804 
   1805 refleaks_tests = """
   1806 Prior to adding cycle-GC support to itertools.tee, this code would leak
   1807 references. We add it to the standard suite so the routine refleak-tests
   1808 would trigger if it starts being uncleanable again.
   1809 
   1810 >>> import itertools
   1811 >>> def leak():
   1812 ...     class gen:
   1813 ...         def __iter__(self):
   1814 ...             return self
   1815 ...         def next(self):
   1816 ...             return self.item
   1817 ...     g = gen()
   1818 ...     head, tail = itertools.tee(g)
   1819 ...     g.item = head
   1820 ...     return head
   1821 >>> it = leak()
   1822 
   1823 Make sure to also test the involvement of the tee-internal teedataobject,
   1824 which stores returned items.
   1825 
   1826 >>> item = it.next()
   1827 
   1828 
   1829 
   1830 This test leaked at one point due to generator finalization/destruction.
   1831 It was copied from Lib/test/leakers/test_generator_cycle.py before the file
   1832 was removed.
   1833 
   1834 >>> def leak():
   1835 ...    def gen():
   1836 ...        while True:
   1837 ...            yield g
   1838 ...    g = gen()
   1839 
   1840 >>> leak()
   1841 
   1842 
   1843 
   1844 This test isn't really generator related, but rather exception-in-cleanup
   1845 related. The coroutine tests (above) just happen to cause an exception in
   1846 the generator's __del__ (tp_del) method. We can also test for this
   1847 explicitly, without generators. We do have to redirect stderr to avoid
   1848 printing warnings and to doublecheck that we actually tested what we wanted
   1849 to test.
   1850 
   1851 >>> import sys, StringIO
   1852 >>> old = sys.stderr
   1853 >>> try:
   1854 ...     sys.stderr = StringIO.StringIO()
   1855 ...     class Leaker:
   1856 ...         def __del__(self):
   1857 ...             raise RuntimeError
   1858 ...
   1859 ...     l = Leaker()
   1860 ...     del l
   1861 ...     err = sys.stderr.getvalue().strip()
   1862 ...     err.startswith(
   1863 ...         "Exception RuntimeError: RuntimeError() in <"
   1864 ...     )
   1865 ...     err.endswith("> ignored")
   1866 ...     len(err.splitlines())
   1867 ... finally:
   1868 ...     sys.stderr = old
   1869 True
   1870 True
   1871 1
   1872 
   1873 
   1874 
   1875 These refleak tests should perhaps be in a testfile of their own,
   1876 test_generators just happened to be the test that drew these out.
   1877 
   1878 """
   1879 
   1880 __test__ = {"tut":      tutorial_tests,
   1881             "pep":      pep_tests,
   1882             "email":    email_tests,
   1883             "fun":      fun_tests,
   1884             "syntax":   syntax_tests,
   1885             "conjoin":  conjoin_tests,
   1886             "weakref":  weakref_tests,
   1887             "coroutine":  coroutine_tests,
   1888             "refleaks": refleaks_tests,
   1889             }
   1890 
   1891 # Magic test name that regrtest.py invokes *after* importing this module.
   1892 # This worms around a bootstrap problem.
   1893 # Note that doctest and regrtest both look in sys.argv for a "-v" argument,
   1894 # so this works as expected in both ways of running regrtest.
   1895 def test_main(verbose=None):
   1896     from test import test_support, test_generators
   1897     test_support.run_doctest(test_generators, verbose)
   1898 
   1899 # This part isn't needed for regrtest, but for running the test directly.
   1900 if __name__ == "__main__":
   1901     test_main(1)
   1902