2001-06-29 10:41:16 +08:00
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from __future__ import nested_scopes
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2001-06-24 04:45:43 +08:00
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tutorial_tests = """
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2001-06-24 04:27:04 +08:00
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Let's try a simple generator:
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>>> def f():
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... yield 1
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... yield 2
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2001-06-24 11:44:52 +08:00
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>>> for i in f():
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... print i
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1
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2
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2001-06-24 04:27:04 +08:00
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>>> g = f()
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>>> g.next()
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1
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>>> g.next()
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2
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2001-06-24 15:10:02 +08:00
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2001-06-25 09:30:12 +08:00
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"Falling off the end" stops the generator:
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2001-06-24 15:10:02 +08:00
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2001-06-24 04:27:04 +08:00
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>>> g.next()
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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File "<stdin>", line 2, in g
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StopIteration
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2001-06-24 15:10:02 +08:00
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"return" also stops the generator:
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2001-06-24 04:27:04 +08:00
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>>> def f():
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... yield 1
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... return
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... yield 2 # never reached
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...
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>>> g = f()
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>>> g.next()
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1
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>>> g.next()
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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File "<stdin>", line 3, in f
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StopIteration
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>>> g.next() # once stopped, can't be resumed
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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StopIteration
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"raise StopIteration" stops the generator too:
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>>> def f():
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... yield 1
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... return
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... yield 2 # never reached
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...
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>>> g = f()
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>>> g.next()
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1
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>>> g.next()
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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StopIteration
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>>> g.next()
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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StopIteration
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However, they are not exactly equivalent:
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>>> def g1():
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... try:
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... return
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... except:
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... yield 1
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...
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>>> list(g1())
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[]
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>>> def g2():
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... try:
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... raise StopIteration
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... except:
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... yield 42
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>>> print list(g2())
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[42]
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This may be surprising at first:
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>>> def g3():
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... try:
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... return
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... finally:
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... yield 1
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...
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>>> list(g3())
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[1]
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Let's create an alternate range() function implemented as a generator:
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>>> def yrange(n):
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... for i in range(n):
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... yield i
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...
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>>> list(yrange(5))
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[0, 1, 2, 3, 4]
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Generators always return to the most recent caller:
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>>> def creator():
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... r = yrange(5)
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... print "creator", r.next()
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... return r
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...
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>>> def caller():
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... r = creator()
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... for i in r:
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... print "caller", i
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...
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>>> caller()
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creator 0
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caller 1
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caller 2
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caller 3
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caller 4
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Generators can call other generators:
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>>> def zrange(n):
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... for i in yrange(n):
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... yield i
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...
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>>> list(zrange(5))
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[0, 1, 2, 3, 4]
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"""
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2001-06-24 04:45:43 +08:00
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# The examples from PEP 255.
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pep_tests = """
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Specification: Return
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Note that return isn't always equivalent to raising StopIteration: the
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difference lies in how enclosing try/except constructs are treated.
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For example,
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>>> def f1():
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... try:
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... return
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... except:
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... yield 1
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>>> print list(f1())
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[]
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because, as in any function, return simply exits, but
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>>> def f2():
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... try:
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... raise StopIteration
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... except:
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... yield 42
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>>> print list(f2())
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[42]
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because StopIteration is captured by a bare "except", as is any
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exception.
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Specification: Generators and Exception Propagation
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>>> def f():
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... return 1/0
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>>> def g():
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... yield f() # the zero division exception propagates
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... yield 42 # and we'll never get here
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>>> k = g()
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>>> k.next()
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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File "<stdin>", line 2, in g
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File "<stdin>", line 2, in f
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ZeroDivisionError: integer division or modulo by zero
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>>> k.next() # and the generator cannot be resumed
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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StopIteration
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>>>
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Specification: Try/Except/Finally
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>>> def f():
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... try:
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... yield 1
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... try:
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... yield 2
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... 1/0
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... yield 3 # never get here
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... except ZeroDivisionError:
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... yield 4
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... yield 5
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... raise
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... except:
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... yield 6
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... yield 7 # the "raise" above stops this
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... except:
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... yield 8
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... yield 9
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... try:
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... x = 12
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... finally:
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... yield 10
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... yield 11
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>>> print list(f())
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[1, 2, 4, 5, 8, 9, 10, 11]
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>>>
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Guido's binary tree example.
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>>> # A binary tree class.
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>>> class Tree:
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...
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... def __init__(self, label, left=None, right=None):
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... self.label = label
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... self.left = left
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... self.right = right
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...
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... def __repr__(self, level=0, indent=" "):
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... s = level*indent + `self.label`
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... if self.left:
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... s = s + "\\n" + self.left.__repr__(level+1, indent)
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... if self.right:
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... s = s + "\\n" + self.right.__repr__(level+1, indent)
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... return s
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...
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... def __iter__(self):
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... return inorder(self)
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>>> # Create a Tree from a list.
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>>> def tree(list):
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... n = len(list)
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... if n == 0:
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... return []
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... i = n / 2
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... return Tree(list[i], tree(list[:i]), tree(list[i+1:]))
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>>> # Show it off: create a tree.
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>>> t = tree("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
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>>> # A recursive generator that generates Tree leaves in in-order.
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>>> def inorder(t):
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... if t:
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... for x in inorder(t.left):
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... yield x
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... yield t.label
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... for x in inorder(t.right):
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... yield x
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>>> # Show it off: create a tree.
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... t = tree("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
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... # Print the nodes of the tree in in-order.
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... for x in t:
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... print x,
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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
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>>> # A non-recursive generator.
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>>> def inorder(node):
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... stack = []
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... while node:
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... while node.left:
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... stack.append(node)
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... node = node.left
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... yield node.label
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... while not node.right:
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... try:
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... node = stack.pop()
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... except IndexError:
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... return
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... yield node.label
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... node = node.right
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>>> # Exercise the non-recursive generator.
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>>> for x in t:
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... print x,
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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
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"""
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2001-06-24 18:14:27 +08:00
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# Examples from Iterator-List and Python-Dev and c.l.py.
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2001-06-24 04:45:43 +08:00
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email_tests = """
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The difference between yielding None and returning it.
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>>> def g():
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... for i in range(3):
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... yield None
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... yield None
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... return
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>>> list(g())
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[None, None, None, None]
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Ensure that explicitly raising StopIteration acts like any other exception
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in try/except, not like a return.
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>>> def g():
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... yield 1
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... try:
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... raise StopIteration
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... except:
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... yield 2
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... yield 3
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>>> list(g())
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[1, 2, 3]
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2001-06-24 11:44:52 +08:00
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A generator can't be resumed while it's already running.
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>>> def g():
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... i = me.next()
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... yield i
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>>> me = g()
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>>> me.next()
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Traceback (most recent call last):
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...
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File "<string>", line 2, in g
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ValueError: generator already executing
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2001-06-24 18:14:27 +08:00
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Next one was posted to c.l.py.
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>>> def gcomb(x, k):
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... "Generate all combinations of k elements from list x."
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...
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... if k > len(x):
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... return
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... if k == 0:
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... yield []
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... else:
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... first, rest = x[0], x[1:]
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... # A combination does or doesn't contain first.
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... # If it does, the remainder is a k-1 comb of rest.
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... for c in gcomb(rest, k-1):
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... c.insert(0, first)
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... yield c
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... # If it doesn't contain first, it's a k comb of rest.
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... for c in gcomb(rest, k):
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... yield c
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>>> seq = range(1, 5)
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>>> for k in range(len(seq) + 2):
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... print "%d-combs of %s:" % (k, seq)
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... for c in gcomb(seq, k):
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... print " ", c
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0-combs of [1, 2, 3, 4]:
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[]
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1-combs of [1, 2, 3, 4]:
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[1]
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[2]
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[3]
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[4]
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2-combs of [1, 2, 3, 4]:
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[1, 2]
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[1, 3]
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[1, 4]
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[2, 3]
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[2, 4]
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[3, 4]
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3-combs of [1, 2, 3, 4]:
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[1, 2, 3]
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[1, 2, 4]
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[1, 3, 4]
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[2, 3, 4]
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4-combs of [1, 2, 3, 4]:
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[1, 2, 3, 4]
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5-combs of [1, 2, 3, 4]:
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2001-06-26 03:46:25 +08:00
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2001-06-27 06:24:51 +08:00
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From the Iterators list, about the types of these things.
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2001-06-26 03:46:25 +08:00
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>>> def g():
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... yield 1
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...
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>>> type(g)
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<type 'function'>
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>>> i = g()
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>>> type(i)
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<type 'generator'>
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>>> dir(i)
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2001-06-27 06:24:51 +08:00
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['gi_frame', 'gi_running', 'next']
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2001-06-26 03:46:25 +08:00
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>>> print i.next.__doc__
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next() -- get the next value, or raise StopIteration
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>>> iter(i) is i
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1
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>>> import types
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>>> isinstance(i, types.GeneratorType)
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1
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2001-06-27 06:24:51 +08:00
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And more, added later.
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>>> i.gi_running
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0
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>>> type(i.gi_frame)
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<type 'frame'>
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>>> i.gi_running = 42
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Traceback (most recent call last):
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...
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TypeError: object has read-only attributes
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>>> def g():
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... yield me.gi_running
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>>> me = g()
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>>> me.gi_running
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0
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>>> me.next()
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1
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|
>>> me.gi_running
|
|
|
|
0
|
2001-06-24 04:45:43 +08:00
|
|
|
"""
|
|
|
|
|
2001-06-24 05:01:47 +08:00
|
|
|
# Fun tests (for sufficiently warped notions of "fun").
|
|
|
|
|
|
|
|
fun_tests = """
|
|
|
|
|
|
|
|
Build up to a recursive Sieve of Eratosthenes generator.
|
|
|
|
|
|
|
|
>>> def firstn(g, n):
|
|
|
|
... return [g.next() for i in range(n)]
|
|
|
|
|
|
|
|
>>> def intsfrom(i):
|
|
|
|
... while 1:
|
|
|
|
... yield i
|
|
|
|
... i += 1
|
|
|
|
|
|
|
|
>>> firstn(intsfrom(5), 7)
|
|
|
|
[5, 6, 7, 8, 9, 10, 11]
|
|
|
|
|
|
|
|
>>> def exclude_multiples(n, ints):
|
|
|
|
... for i in ints:
|
|
|
|
... if i % n:
|
|
|
|
... yield i
|
|
|
|
|
|
|
|
>>> firstn(exclude_multiples(3, intsfrom(1)), 6)
|
|
|
|
[1, 2, 4, 5, 7, 8]
|
|
|
|
|
|
|
|
>>> def sieve(ints):
|
|
|
|
... prime = ints.next()
|
|
|
|
... yield prime
|
|
|
|
... not_divisible_by_prime = exclude_multiples(prime, ints)
|
|
|
|
... for p in sieve(not_divisible_by_prime):
|
|
|
|
... yield p
|
|
|
|
|
|
|
|
>>> primes = sieve(intsfrom(2))
|
|
|
|
>>> firstn(primes, 20)
|
|
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
|
2001-06-24 11:44:52 +08:00
|
|
|
|
2001-06-27 15:17:57 +08:00
|
|
|
|
2001-06-24 11:44:52 +08:00
|
|
|
Another famous problem: generate all integers of the form
|
|
|
|
2**i * 3**j * 5**k
|
|
|
|
in increasing order, where i,j,k >= 0. Trickier than it may look at first!
|
|
|
|
Try writing it without generators, and correctly, and without generating
|
|
|
|
3 internal results for each result output.
|
|
|
|
|
|
|
|
>>> def times(n, g):
|
|
|
|
... for i in g:
|
|
|
|
... yield n * i
|
|
|
|
>>> firstn(times(10, intsfrom(1)), 10)
|
|
|
|
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
|
|
|
|
|
|
|
|
>>> def merge(g, h):
|
|
|
|
... ng = g.next()
|
|
|
|
... nh = h.next()
|
|
|
|
... while 1:
|
|
|
|
... if ng < nh:
|
|
|
|
... yield ng
|
|
|
|
... ng = g.next()
|
|
|
|
... elif ng > nh:
|
|
|
|
... yield nh
|
|
|
|
... nh = h.next()
|
|
|
|
... else:
|
|
|
|
... yield ng
|
|
|
|
... ng = g.next()
|
|
|
|
... nh = h.next()
|
|
|
|
|
2001-06-27 15:17:57 +08:00
|
|
|
The following works, but is doing a whale of a lot of redundant work --
|
|
|
|
it's not clear how to get the internal uses of m235 to share a single
|
|
|
|
generator. Note that me_times2 (etc) each need to see every element in the
|
|
|
|
result sequence. So this is an example where lazy lists are more natural
|
|
|
|
(you can look at the head of a lazy list any number of times).
|
2001-06-24 11:44:52 +08:00
|
|
|
|
|
|
|
>>> def m235():
|
|
|
|
... yield 1
|
|
|
|
... me_times2 = times(2, m235())
|
|
|
|
... me_times3 = times(3, m235())
|
|
|
|
... me_times5 = times(5, m235())
|
|
|
|
... for i in merge(merge(me_times2,
|
|
|
|
... me_times3),
|
|
|
|
... me_times5):
|
|
|
|
... yield i
|
|
|
|
|
2001-06-27 15:17:57 +08:00
|
|
|
Don't print "too many" of these -- the implementation above is extremely
|
|
|
|
inefficient: each call of m235() leads to 3 recursive calls, and in
|
|
|
|
turn each of those 3 more, and so on, and so on, until we've descended
|
|
|
|
enough levels to satisfy the print stmts. Very odd: when I printed 5
|
|
|
|
lines of results below, this managed to screw up Win98's malloc in "the
|
|
|
|
usual" way, i.e. the heap grew over 4Mb so Win98 started fragmenting
|
|
|
|
address space, and it *looked* like a very slow leak.
|
|
|
|
|
2001-06-24 11:44:52 +08:00
|
|
|
>>> result = m235()
|
2001-06-27 15:17:57 +08:00
|
|
|
>>> for i in range(3):
|
2001-06-24 11:44:52 +08:00
|
|
|
... print firstn(result, 15)
|
|
|
|
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
|
|
|
|
[25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
|
|
|
|
[81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
|
2001-06-24 13:47:06 +08:00
|
|
|
|
|
|
|
Heh. Here's one way to get a shared list, complete with an excruciating
|
|
|
|
namespace renaming trick. The *pretty* part is that the times() and merge()
|
|
|
|
functions can be reused as-is, because they only assume their stream
|
|
|
|
arguments are iterable -- a LazyList is the same as a generator to times().
|
|
|
|
|
|
|
|
>>> class LazyList:
|
|
|
|
... def __init__(self, g):
|
|
|
|
... self.sofar = []
|
|
|
|
... self.fetch = g.next
|
|
|
|
...
|
|
|
|
... def __getitem__(self, i):
|
|
|
|
... sofar, fetch = self.sofar, self.fetch
|
|
|
|
... while i >= len(sofar):
|
|
|
|
... sofar.append(fetch())
|
|
|
|
... return sofar[i]
|
2001-06-27 15:17:57 +08:00
|
|
|
...
|
|
|
|
... def clear(self):
|
|
|
|
... self.__dict__.clear()
|
2001-06-24 13:47:06 +08:00
|
|
|
|
|
|
|
>>> def m235():
|
|
|
|
... yield 1
|
2001-06-24 15:10:02 +08:00
|
|
|
... # Gack: m235 below actually refers to a LazyList.
|
2001-06-24 13:47:06 +08:00
|
|
|
... me_times2 = times(2, m235)
|
|
|
|
... me_times3 = times(3, m235)
|
|
|
|
... me_times5 = times(5, m235)
|
|
|
|
... for i in merge(merge(me_times2,
|
|
|
|
... me_times3),
|
|
|
|
... me_times5):
|
|
|
|
... yield i
|
|
|
|
|
2001-06-27 15:17:57 +08:00
|
|
|
Print as many of these as you like -- *this* implementation is memory-
|
|
|
|
efficient. XXX Except that it leaks unless you clear the dict!
|
|
|
|
|
2001-06-24 13:47:06 +08:00
|
|
|
>>> m235 = LazyList(m235())
|
|
|
|
>>> for i in range(5):
|
|
|
|
... print [m235[j] for j in range(15*i, 15*(i+1))]
|
|
|
|
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
|
|
|
|
[25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80]
|
|
|
|
[81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192]
|
|
|
|
[200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384]
|
|
|
|
[400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675]
|
2001-06-27 15:17:57 +08:00
|
|
|
|
|
|
|
>>> m235.clear() # XXX memory leak without this
|
|
|
|
|
|
|
|
|
|
|
|
Ye olde Fibonacci generator, LazyList style.
|
|
|
|
|
|
|
|
>>> def fibgen(a, b):
|
|
|
|
...
|
|
|
|
... def sum(g, h):
|
|
|
|
... while 1:
|
|
|
|
... yield g.next() + h.next()
|
|
|
|
...
|
|
|
|
... def tail(g):
|
|
|
|
... g.next() # throw first away
|
|
|
|
... for x in g:
|
|
|
|
... yield x
|
|
|
|
...
|
|
|
|
... yield a
|
|
|
|
... yield b
|
|
|
|
... for s in sum(iter(fib),
|
|
|
|
... tail(iter(fib))):
|
|
|
|
... yield s
|
|
|
|
|
|
|
|
>>> fib = LazyList(fibgen(1, 2))
|
|
|
|
>>> firstn(iter(fib), 17)
|
|
|
|
[1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
|
|
|
|
|
|
|
|
>>> fib.clear() # XXX memory leak without this
|
2001-06-24 05:01:47 +08:00
|
|
|
"""
|
|
|
|
|
2001-06-26 11:36:28 +08:00
|
|
|
# syntax_tests mostly provokes SyntaxErrors. Also fiddling with #if 0
|
|
|
|
# hackery.
|
2001-06-24 15:10:02 +08:00
|
|
|
|
|
|
|
syntax_tests = """
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... return 22
|
|
|
|
... yield 1
|
|
|
|
Traceback (most recent call last):
|
|
|
|
...
|
|
|
|
SyntaxError: 'return' with argument inside generator (<string>, line 2)
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... yield 1
|
|
|
|
... return 22
|
|
|
|
Traceback (most recent call last):
|
|
|
|
...
|
|
|
|
SyntaxError: 'return' with argument inside generator (<string>, line 3)
|
|
|
|
|
|
|
|
"return None" is not the same as "return" in a generator:
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... yield 1
|
|
|
|
... return None
|
|
|
|
Traceback (most recent call last):
|
|
|
|
...
|
|
|
|
SyntaxError: 'return' with argument inside generator (<string>, line 3)
|
|
|
|
|
|
|
|
This one is fine:
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... yield 1
|
|
|
|
... return
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... try:
|
|
|
|
... yield 1
|
|
|
|
... finally:
|
|
|
|
... pass
|
|
|
|
Traceback (most recent call last):
|
|
|
|
...
|
|
|
|
SyntaxError: 'yield' not allowed in a 'try' block with a 'finally' clause (<string>, line 3)
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... try:
|
|
|
|
... try:
|
|
|
|
... 1/0
|
|
|
|
... except ZeroDivisionError:
|
|
|
|
... yield 666 # bad because *outer* try has finally
|
|
|
|
... except:
|
|
|
|
... pass
|
|
|
|
... finally:
|
|
|
|
... pass
|
|
|
|
Traceback (most recent call last):
|
|
|
|
...
|
|
|
|
SyntaxError: 'yield' not allowed in a 'try' block with a 'finally' clause (<string>, line 6)
|
|
|
|
|
|
|
|
But this is fine:
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... try:
|
|
|
|
... try:
|
|
|
|
... yield 12
|
|
|
|
... 1/0
|
|
|
|
... except ZeroDivisionError:
|
|
|
|
... yield 666
|
|
|
|
... except:
|
|
|
|
... try:
|
|
|
|
... x = 12
|
|
|
|
... finally:
|
|
|
|
... yield 12
|
|
|
|
... except:
|
|
|
|
... return
|
|
|
|
>>> list(f())
|
|
|
|
[12, 666]
|
2001-06-26 11:36:28 +08:00
|
|
|
|
2001-06-28 09:52:22 +08:00
|
|
|
>>> def f():
|
|
|
|
... yield
|
|
|
|
Traceback (most recent call last):
|
|
|
|
SyntaxError: invalid syntax
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... if 0:
|
|
|
|
... yield
|
|
|
|
Traceback (most recent call last):
|
|
|
|
SyntaxError: invalid syntax
|
|
|
|
|
2001-06-26 11:36:28 +08:00
|
|
|
>>> def f():
|
|
|
|
... if 0:
|
|
|
|
... yield 1
|
|
|
|
>>> type(f())
|
|
|
|
<type 'generator'>
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... if "":
|
|
|
|
... yield None
|
|
|
|
>>> type(f())
|
|
|
|
<type 'generator'>
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... return
|
|
|
|
... try:
|
|
|
|
... if x==4:
|
|
|
|
... pass
|
|
|
|
... elif 0:
|
|
|
|
... try:
|
|
|
|
... 1/0
|
|
|
|
... except SyntaxError:
|
|
|
|
... pass
|
|
|
|
... else:
|
|
|
|
... if 0:
|
|
|
|
... while 12:
|
|
|
|
... x += 1
|
|
|
|
... yield 2 # don't blink
|
|
|
|
... f(a, b, c, d, e)
|
|
|
|
... else:
|
|
|
|
... pass
|
|
|
|
... except:
|
|
|
|
... x = 1
|
|
|
|
... return
|
|
|
|
>>> type(f())
|
|
|
|
<type 'generator'>
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... if 0:
|
|
|
|
... def g():
|
|
|
|
... yield 1
|
|
|
|
...
|
|
|
|
>>> type(f())
|
|
|
|
<type 'None'>
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... if 0:
|
|
|
|
... class C:
|
|
|
|
... def __init__(self):
|
|
|
|
... yield 1
|
|
|
|
... def f(self):
|
|
|
|
... yield 2
|
|
|
|
>>> type(f())
|
|
|
|
<type 'None'>
|
2001-06-28 09:52:22 +08:00
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... if 0:
|
|
|
|
... return
|
|
|
|
... if 0:
|
|
|
|
... yield 2
|
|
|
|
>>> type(f())
|
|
|
|
<type 'generator'>
|
|
|
|
|
|
|
|
|
|
|
|
>>> def f():
|
|
|
|
... if 0:
|
|
|
|
... lambda x: x # shouldn't trigger here
|
|
|
|
... return # or here
|
|
|
|
... def f(i):
|
|
|
|
... return 2*i # or here
|
|
|
|
... if 0:
|
|
|
|
... return 3 # but *this* sucks (line 8)
|
|
|
|
... if 0:
|
|
|
|
... yield 2 # because it's a generator
|
|
|
|
Traceback (most recent call last):
|
|
|
|
SyntaxError: 'return' with argument inside generator (<string>, line 8)
|
2001-06-26 11:36:28 +08:00
|
|
|
"""
|
|
|
|
|
2001-06-29 10:41:16 +08:00
|
|
|
# conjoin is a simple backtracking generator, named in honor of Icon's
|
|
|
|
# "conjunction" control structure. Pass a list of no-argument functions
|
|
|
|
# that return iterable objects. Easiest to explain by example: assume the
|
|
|
|
# function list [x, y, z] is passed. Then conjoin acts like:
|
|
|
|
#
|
|
|
|
# def g():
|
|
|
|
# values = [None] * 3
|
|
|
|
# for values[0] in x():
|
|
|
|
# for values[1] in y():
|
|
|
|
# for values[2] in z():
|
|
|
|
# yield values
|
|
|
|
#
|
|
|
|
# So some 3-lists of values *may* be generated, each time we successfully
|
|
|
|
# get into the innermost loop. If an iterator fails (is exhausted) before
|
|
|
|
# then, it "backtracks" to get the next value from the nearest enclosing
|
|
|
|
# iterator (the one "to the left"), and starts all over again at the next
|
|
|
|
# slot (pumps a fresh iterator). Of course this is most useful when the
|
|
|
|
# iterators have side-effects, so that which values *can* be generated at
|
|
|
|
# each slot depend on the values iterated at previous slots.
|
|
|
|
|
|
|
|
def conjoin(gs):
|
|
|
|
|
|
|
|
values = [None] * len(gs)
|
|
|
|
|
|
|
|
def gen(i, values=values):
|
|
|
|
if i >= len(gs):
|
|
|
|
yield values
|
|
|
|
else:
|
|
|
|
for values[i] in gs[i]():
|
|
|
|
for x in gen(i+1):
|
|
|
|
yield x
|
|
|
|
|
|
|
|
for x in gen(0):
|
|
|
|
yield x
|
|
|
|
|
2001-06-30 15:29:44 +08:00
|
|
|
# That works fine, but recursing a level and checking i against len(gs) for
|
|
|
|
# each item produced is inefficient. By doing manual loop unrolling across
|
|
|
|
# generator boundaries, it's possible to eliminate most of that overhead.
|
|
|
|
# This isn't worth the bother *in general* for generators, but conjoin() is
|
|
|
|
# a core building block for some CPU-intensive generator applications.
|
|
|
|
|
|
|
|
def conjoin(gs):
|
|
|
|
|
|
|
|
n = len(gs)
|
|
|
|
values = [None] * n
|
|
|
|
|
|
|
|
# Do one loop nest at time recursively, until the # of loop nests
|
|
|
|
# remaining is divisible by 3.
|
|
|
|
|
|
|
|
def gen(i, values=values):
|
|
|
|
if i >= n:
|
|
|
|
yield values
|
|
|
|
|
|
|
|
elif (n-i) % 3:
|
|
|
|
ip1 = i+1
|
|
|
|
for values[i] in gs[i]():
|
|
|
|
for x in gen(ip1):
|
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|
|
yield x
|
|
|
|
|
|
|
|
else:
|
|
|
|
for x in _gen3(i):
|
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|
|
yield x
|
|
|
|
|
|
|
|
# Do three loop nests at a time, recursing only if at least three more
|
|
|
|
# remain. Don't call directly: this is an internal optimization for
|
|
|
|
# gen's use.
|
|
|
|
|
|
|
|
def _gen3(i, values=values):
|
|
|
|
assert i < n and (n-i) % 3 == 0
|
|
|
|
ip1, ip2, ip3 = i+1, i+2, i+3
|
|
|
|
g, g1, g2 = gs[i : ip3]
|
|
|
|
|
|
|
|
if ip3 >= n:
|
|
|
|
# These are the last three, so we can yield values directly.
|
|
|
|
for values[i] in g():
|
|
|
|
for values[ip1] in g1():
|
|
|
|
for values[ip2] in g2():
|
|
|
|
yield values
|
|
|
|
|
|
|
|
else:
|
|
|
|
# At least 6 loop nests remain; peel off 3 and recurse for the
|
|
|
|
# rest.
|
|
|
|
for values[i] in g():
|
|
|
|
for values[ip1] in g1():
|
|
|
|
for values[ip2] in g2():
|
|
|
|
for x in _gen3(ip3):
|
|
|
|
yield x
|
|
|
|
|
|
|
|
for x in gen(0):
|
|
|
|
yield x
|
|
|
|
|
2001-06-29 10:41:16 +08:00
|
|
|
# A conjoin-based N-Queens solver.
|
|
|
|
|
|
|
|
class Queens:
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|
|
def __init__(self, n):
|
|
|
|
self.n = n
|
|
|
|
rangen = range(n)
|
|
|
|
|
|
|
|
# Assign a unique int to each column and diagonal.
|
|
|
|
# columns: n of those, range(n).
|
|
|
|
# NW-SE diagonals: 2n-1 of these, i-j unique and invariant along
|
|
|
|
# each, smallest i-j is 0-(n-1) = 1-n, so add n-1 to shift to 0-
|
|
|
|
# based.
|
|
|
|
# NE-SW diagonals: 2n-1 of these, i+j unique and invariant along
|
|
|
|
# each, smallest i+j is 0, largest is 2n-2.
|
|
|
|
|
|
|
|
# For each square, compute a bit vector of the columns and
|
|
|
|
# diagonals it covers, and for each row compute a function that
|
|
|
|
# generates the possiblities for the columns in that row.
|
|
|
|
self.rowgenerators = []
|
|
|
|
for i in rangen:
|
|
|
|
rowuses = [(1L << j) | # column ordinal
|
|
|
|
(1L << (n + i-j + n-1)) | # NW-SE ordinal
|
|
|
|
(1L << (n + 2*n-1 + i+j)) # NE-SW ordinal
|
|
|
|
for j in rangen]
|
|
|
|
|
|
|
|
def rowgen(rowuses=rowuses):
|
|
|
|
for j in rangen:
|
|
|
|
uses = rowuses[j]
|
2001-06-30 15:29:44 +08:00
|
|
|
if uses & self.used == 0:
|
|
|
|
self.used |= uses
|
|
|
|
yield j
|
|
|
|
self.used &= ~uses
|
2001-06-29 10:41:16 +08:00
|
|
|
|
|
|
|
self.rowgenerators.append(rowgen)
|
|
|
|
|
|
|
|
# Generate solutions.
|
|
|
|
def solve(self):
|
|
|
|
self.used = 0
|
|
|
|
for row2col in conjoin(self.rowgenerators):
|
|
|
|
yield row2col
|
|
|
|
|
|
|
|
def printsolution(self, row2col):
|
|
|
|
n = self.n
|
|
|
|
assert n == len(row2col)
|
|
|
|
sep = "+" + "-+" * n
|
|
|
|
print sep
|
|
|
|
for i in range(n):
|
|
|
|
squares = [" " for j in range(n)]
|
|
|
|
squares[row2col[i]] = "Q"
|
|
|
|
print "|" + "|".join(squares) + "|"
|
|
|
|
print sep
|
|
|
|
|
|
|
|
conjoin_tests = """
|
|
|
|
|
|
|
|
Generate the 3-bit binary numbers in order. This illustrates dumbest-
|
|
|
|
possible use of conjoin, just to generate the full cross-product.
|
|
|
|
|
2001-06-30 15:29:44 +08:00
|
|
|
>>> for c in conjoin([lambda: (0, 1)] * 3):
|
2001-06-29 10:41:16 +08:00
|
|
|
... print c
|
|
|
|
[0, 0, 0]
|
|
|
|
[0, 0, 1]
|
|
|
|
[0, 1, 0]
|
|
|
|
[0, 1, 1]
|
|
|
|
[1, 0, 0]
|
|
|
|
[1, 0, 1]
|
|
|
|
[1, 1, 0]
|
|
|
|
[1, 1, 1]
|
|
|
|
|
2001-06-30 15:29:44 +08:00
|
|
|
For efficiency in typical backtracking apps, conjoin() yields the same list
|
|
|
|
object each time. So if you want to save away a full account of its
|
|
|
|
generated sequence, you need to copy its results.
|
|
|
|
|
|
|
|
>>> def gencopy(iterator):
|
|
|
|
... for x in iterator:
|
|
|
|
... yield x[:]
|
|
|
|
|
|
|
|
>>> for n in range(10):
|
|
|
|
... all = list(gencopy(conjoin([lambda: (0, 1)] * n)))
|
|
|
|
... print n, len(all), all[0] == [0] * n, all[-1] == [1] * n
|
|
|
|
0 1 1 1
|
|
|
|
1 2 1 1
|
|
|
|
2 4 1 1
|
|
|
|
3 8 1 1
|
|
|
|
4 16 1 1
|
|
|
|
5 32 1 1
|
|
|
|
6 64 1 1
|
|
|
|
7 128 1 1
|
|
|
|
8 256 1 1
|
|
|
|
9 512 1 1
|
|
|
|
|
2001-06-29 10:41:16 +08:00
|
|
|
And run an 8-queens solver.
|
|
|
|
|
|
|
|
>>> q = Queens(8)
|
|
|
|
>>> LIMIT = 2
|
|
|
|
>>> count = 0
|
|
|
|
>>> for row2col in q.solve():
|
|
|
|
... count += 1
|
|
|
|
... if count <= LIMIT:
|
|
|
|
... print "Solution", count
|
|
|
|
... q.printsolution(row2col)
|
|
|
|
Solution 1
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
|Q| | | | | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | |Q| | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | | | | |Q|
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | | |Q| | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | |Q| | | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | | | |Q| |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| |Q| | | | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | |Q| | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
Solution 2
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
|Q| | | | | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | | |Q| | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | | | | |Q|
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | |Q| | | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | | | |Q| |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | |Q| | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| |Q| | | | | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
| | | | |Q| | | |
|
|
|
|
+-+-+-+-+-+-+-+-+
|
|
|
|
|
|
|
|
>>> print count, "solutions in all."
|
|
|
|
92 solutions in all.
|
|
|
|
"""
|
|
|
|
|
2001-06-27 15:17:57 +08:00
|
|
|
__test__ = {"tut": tutorial_tests,
|
|
|
|
"pep": pep_tests,
|
|
|
|
"email": email_tests,
|
|
|
|
"fun": fun_tests,
|
2001-06-29 10:41:16 +08:00
|
|
|
"syntax": syntax_tests,
|
|
|
|
"conjoin": conjoin_tests}
|
2001-06-24 04:27:04 +08:00
|
|
|
|
|
|
|
# Magic test name that regrtest.py invokes *after* importing this module.
|
|
|
|
# This worms around a bootstrap problem.
|
|
|
|
# Note that doctest and regrtest both look in sys.argv for a "-v" argument,
|
|
|
|
# so this works as expected in both ways of running regrtest.
|
|
|
|
def test_main():
|
|
|
|
import doctest, test_generators
|
2001-06-25 09:30:12 +08:00
|
|
|
if 0:
|
|
|
|
# Temporary block to help track down leaks. So far, the blame
|
2001-06-27 15:17:57 +08:00
|
|
|
# fell mostly on doctest. Later: the only leaks remaining are
|
|
|
|
# in fun_tests, and only if you comment out the two LazyList.clear()
|
|
|
|
# calls.
|
|
|
|
for i in range(10000):
|
2001-06-25 09:30:12 +08:00
|
|
|
doctest.master = None
|
|
|
|
doctest.testmod(test_generators)
|
|
|
|
else:
|
|
|
|
doctest.testmod(test_generators)
|
2001-06-24 04:27:04 +08:00
|
|
|
|
|
|
|
# This part isn't needed for regrtest, but for running the test directly.
|
|
|
|
if __name__ == "__main__":
|
|
|
|
test_main()
|