[Spambayes-checkins] spambayes/22compat heapq.py,NONE,1.1.2.1 sets.py,NONE,1.1.2.1

[Anthony Baxter]

Update of /cvsroot/spambayes/spambayes/22compat
In directory sc8-pr-cvs1:/tmp/cvs-serv9389/22compat

Added Files:
      Tag: reorg-branch
	heapq.py sets.py 
Log Message:
Checkpointing before I head home.

Still to do: 
 - distutils magic to make sure that the 22compat modules are 
   installed when needed.
 - Walking through testtools and utilities and fixing imports.
 - Documentation.

hammie works, everything else that people use in day-to-day operation
should work - please give it a go.



--- NEW FILE: heapq.py ---
# -*- coding: Latin-1 -*-

"""Heap queue algorithm (a.k.a. priority queue).

Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
all k, counting elements from 0.  For the sake of comparison,
non-existing elements are considered to be infinite.  The interesting
property of a heap is that a[0] is always its smallest element.

Usage:

heap = []            # creates an empty heap
heappush(heap, item) # pushes a new item on the heap
item = heappop(heap) # pops the smallest item from the heap
item = heap[0]       # smallest item on the heap without popping it
heapify(x)           # transforms list into a heap, in-place, in linear time
item = heapreplace(heap, item) # pops and returns smallest item, and adds
                               # new item; the heap size is unchanged

Our API differs from textbook heap algorithms as follows:

- We use 0-based indexing.  This makes the relationship between the
  index for a node and the indexes for its children slightly less
  obvious, but is more suitable since Python uses 0-based indexing.

- Our heappop() method returns the smallest item, not the largest.

These two make it possible to view the heap as a regular Python list
without surprises: heap[0] is the smallest item, and heap.sort()
maintains the heap invariant!
"""

# Original code by Kevin O'Connor, augmented by Tim Peters

__about__ = """Heap queues

[explanation by François Pinard]

Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
all k, counting elements from 0.  For the sake of comparison,
non-existing elements are considered to be infinite.  The interesting
property of a heap is that a[0] is always its smallest element.

The strange invariant above is meant to be an efficient memory
representation for a tournament.  The numbers below are `k', not a[k]:

                                   0

                  1                                 2

          3               4                5               6

      7       8       9       10      11      12      13      14

    15 16   17 18   19 20   21 22   23 24   25 26   27 28   29 30


In the tree above, each cell `k' is topping `2*k+1' and `2*k+2'.  In
an usual binary tournament we see in sports, each cell is the winner
over the two cells it tops, and we can trace the winner down the tree
to see all opponents s/he had.  However, in many computer applications
of such tournaments, we do not need to trace the history of a winner.
To be more memory efficient, when a winner is promoted, we try to
replace it by something else at a lower level, and the rule becomes
that a cell and the two cells it tops contain three different items,
but the top cell "wins" over the two topped cells.

If this heap invariant is protected at all time, index 0 is clearly
the overall winner.  The simplest algorithmic way to remove it and
find the "next" winner is to move some loser (let's say cell 30 in the
diagram above) into the 0 position, and then percolate this new 0 down
the tree, exchanging values, until the invariant is re-established.
This is clearly logarithmic on the total number of items in the tree.
By iterating over all items, you get an O(n ln n) sort.

A nice feature of this sort is that you can efficiently insert new
items while the sort is going on, provided that the inserted items are
not "better" than the last 0'th element you extracted.  This is
especially useful in simulation contexts, where the tree holds all
incoming events, and the "win" condition means the smallest scheduled
time.  When an event schedule other events for execution, they are
scheduled into the future, so they can easily go into the heap.  So, a
heap is a good structure for implementing schedulers (this is what I
used for my MIDI sequencer :-).

Various structures for implementing schedulers have been extensively
studied, and heaps are good for this, as they are reasonably speedy,
the speed is almost constant, and the worst case is not much different
than the average case.  However, there are other representations which
are more efficient overall, yet the worst cases might be terrible.

Heaps are also very useful in big disk sorts.  You most probably all
know that a big sort implies producing "runs" (which are pre-sorted
sequences, which size is usually related to the amount of CPU memory),
followed by a merging passes for these runs, which merging is often
very cleverly organised[1].  It is very important that the initial
sort produces the longest runs possible.  Tournaments are a good way
to that.  If, using all the memory available to hold a tournament, you
replace and percolate items that happen to fit the current run, you'll
produce runs which are twice the size of the memory for random input,
and much better for input fuzzily ordered.

Moreover, if you output the 0'th item on disk and get an input which
may not fit in the current tournament (because the value "wins" over
the last output value), it cannot fit in the heap, so the size of the
heap decreases.  The freed memory could be cleverly reused immediately
for progressively building a second heap, which grows at exactly the
same rate the first heap is melting.  When the first heap completely
vanishes, you switch heaps and start a new run.  Clever and quite
effective!

In a word, heaps are useful memory structures to know.  I use them in
a few applications, and I think it is good to keep a `heap' module
around. :-)

--------------------
[1] The disk balancing algorithms which are current, nowadays, are
more annoying than clever, and this is a consequence of the seeking
capabilities of the disks.  On devices which cannot seek, like big
tape drives, the story was quite different, and one had to be very
clever to ensure (far in advance) that each tape movement will be the
most effective possible (that is, will best participate at
"progressing" the merge).  Some tapes were even able to read
backwards, and this was also used to avoid the rewinding time.
Believe me, real good tape sorts were quite spectacular to watch!
>From all times, sorting has always been a Great Art! :-)
"""

def heappush(heap, item):
    """Push item onto heap, maintaining the heap invariant."""
    heap.append(item)
    _siftdown(heap, 0, len(heap)-1)

def heappop(heap):
    """Pop the smallest item off the heap, maintaining the heap invariant."""
    lastelt = heap.pop()    # raises appropriate IndexError if heap is empty
    if heap:
        returnitem = heap[0]
        heap[0] = lastelt
        _siftup(heap, 0)
    else:
        returnitem = lastelt
    return returnitem

def heapreplace(heap, item):
    """Pop and return the current smallest value, and add the new item.

    This is more efficient than heappop() followed by heappush(), and can be
    more appropriate when using a fixed-size heap.  Note that the value
    returned may be larger than item!  That constrains reasonable uses of
    this routine.
    """
    returnitem = heap[0]    # raises appropriate IndexError if heap is empty
    heap[0] = item
    _siftup(heap, 0)
    return returnitem

def heapify(x):
    """Transform list into a heap, in-place, in O(len(heap)) time."""
    n = len(x)
    # Transform bottom-up.  The largest index there's any point to looking at
    # is the largest with a child index in-range, so must have 2*i + 1 < n,
    # or i < (n-1)/2.  If n is even = 2*j, this is (2*j-1)/2 = j-1/2 so
    # j-1 is the largest, which is n//2 - 1.  If n is odd = 2*j+1, this is
    # (2*j+1-1)/2 = j so j-1 is the largest, and that's again n//2-1.
    for i in xrange(n//2 - 1, -1, -1):
        _siftup(x, i)

# 'heap' is a heap at all indices >= startpos, except possibly for pos.  pos
# is the index of a leaf with a possibly out-of-order value.  Restore the
# heap invariant.
def _siftdown(heap, startpos, pos):
    newitem = heap[pos]
    # Follow the path to the root, moving parents down until finding a place
    # newitem fits.
    while pos > startpos:
        parentpos = (pos - 1) >> 1
        parent = heap[parentpos]
        if parent <= newitem:
            break
        heap[pos] = parent
        pos = parentpos
    heap[pos] = newitem

# The child indices of heap index pos are already heaps, and we want to make
# a heap at index pos too.  We do this by bubbling the smaller child of
# pos up (and so on with that child's children, etc) until hitting a leaf,
# then using _siftdown to move the oddball originally at index pos into place.
#
# We *could* break out of the loop as soon as we find a pos where newitem <=
# both its children, but turns out that's not a good idea, and despite that
# many books write the algorithm that way.  During a heap pop, the last array
# element is sifted in, and that tends to be large, so that comparing it
# against values starting from the root usually doesn't pay (= usually doesn't
# get us out of the loop early).  See Knuth, Volume 3, where this is
# explained and quantified in an exercise.
#
# Cutting the # of comparisons is important, since these routines have no
# way to extract "the priority" from an array element, so that intelligence
# is likely to be hiding in custom __cmp__ methods, or in array elements
# storing (priority, record) tuples.  Comparisons are thus potentially
# expensive.
#
# On random arrays of length 1000, making this change cut the number of
# comparisons made by heapify() a little, and those made by exhaustive
# heappop() a lot, in accord with theory.  Here are typical results from 3
# runs (3 just to demonstrate how small the variance is):
#
# Compares needed by heapify     Compares needed by 1000 heapppops
# --------------------------     ---------------------------------
# 1837 cut to 1663               14996 cut to 8680
# 1855 cut to 1659               14966 cut to 8678
# 1847 cut to 1660               15024 cut to 8703
#
# Building the heap by using heappush() 1000 times instead required
# 2198, 2148, and 2219 compares:  heapify() is more efficient, when
# you can use it.
#
# The total compares needed by list.sort() on the same lists were 8627,
# 8627, and 8632 (this should be compared to the sum of heapify() and
# heappop() compares):  list.sort() is (unsurprisingly!) more efficient
# for sorting.

def _siftup(heap, pos):
    endpos = len(heap)
    startpos = pos
    newitem = heap[pos]
    # Bubble up the smaller child until hitting a leaf.
    childpos = 2*pos + 1    # leftmost child position
    while childpos < endpos:
        # Set childpos to index of smaller child.
        rightpos = childpos + 1
        if rightpos < endpos and heap[rightpos] <= heap[childpos]:
            childpos = rightpos
        # Move the smaller child up.
        heap[pos] = heap[childpos]
        pos = childpos
        childpos = 2*pos + 1
    # The leaf at pos is empty now.  Put newitem there, and and bubble it up
    # to its final resting place (by sifting its parents down).
    heap[pos] = newitem
    _siftdown(heap, startpos, pos)

if __name__ == "__main__":
    # Simple sanity test
    heap = []
    data = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]
    for item in data:
        heappush(heap, item)
    sort = []
    while heap:
        sort.append(heappop(heap))
    print sort

--- NEW FILE: sets.py ---
"""Classes to represent arbitrary sets (including sets of sets).

This module implements sets using dictionaries whose values are
ignored.  The usual operations (union, intersection, deletion, etc.)
are provided as both methods and operators.

Important: sets are not sequences!  While they support 'x in s',
'len(s)', and 'for x in s', none of those operations are unique for
sequences; for example, mappings support all three as well.  The
characteristic operation for sequences is subscripting with small
integers: s[i], for i in range(len(s)).  Sets don't support
subscripting at all.  Also, sequences allow multiple occurrences and
their elements have a definite order; sets on the other hand don't
record multiple occurrences and don't remember the order of element
insertion (which is why they don't support s[i]).

The following classes are provided:

BaseSet -- All the operations common to both mutable and immutable
    sets. This is an abstract class, not meant to be directly
    instantiated.

Set -- Mutable sets, subclass of BaseSet; not hashable.

ImmutableSet -- Immutable sets, subclass of BaseSet; hashable.
    An iterable argument is mandatory to create an ImmutableSet.

_TemporarilyImmutableSet -- Not a subclass of BaseSet: just a wrapper
    around a Set, hashable, giving the same hash value as the
    immutable set equivalent would have.  Do not use this class
    directly.

Only hashable objects can be added to a Set. In particular, you cannot
really add a Set as an element to another Set; if you try, what is
actually added is an ImmutableSet built from it (it compares equal to
the one you tried adding).

When you ask if `x in y' where x is a Set and y is a Set or
ImmutableSet, x is wrapped into a _TemporarilyImmutableSet z, and
what's tested is actually `z in y'.

"""

# Code history:
#
# - Greg V. Wilson wrote the first version, using a different approach
#   to the mutable/immutable problem, and inheriting from dict.
#
# - Alex Martelli modified Greg's version to implement the current
#   Set/ImmutableSet approach, and make the data an attribute.
#
# - Guido van Rossum rewrote much of the code, made some API changes,
#   and cleaned up the docstrings.
#
# - Raymond Hettinger added a number of speedups and other
#   improvements.


__all__ = ['BaseSet', 'Set', 'ImmutableSet']


try:
    True, False
except NameError:
    # Maintain compatibility with Python 2.2
    True, False = 1, 0


class BaseSet(object):
    """Common base class for mutable and immutable sets."""

    __slots__ = ['_data']

    # Constructor

    def __init__(self):
        """This is an abstract class."""
        # Don't call this from a concrete subclass!
        if self.__class__ is BaseSet:
            raise TypeError, ("BaseSet is an abstract class.  "
                              "Use Set or ImmutableSet.")

    # Standard protocols: __len__, __repr__, __str__, __iter__

    def __len__(self):
        """Return the number of elements of a set."""
        return len(self._data)

    def __repr__(self):
        """Return string representation of a set.

        This looks like 'Set([<list of elements>])'.
        """
        return self._repr()

    # __str__ is the same as __repr__
    __str__ = __repr__

    def _repr(self, sorted=False):
        elements = self._data.keys()
        if sorted:
            elements.sort()
        return '%s(%r)' % (self.__class__.__name__, elements)

    def __iter__(self):
        """Return an iterator over the elements or a set.

        This is the keys iterator for the underlying dict.
        """
        return self._data.iterkeys()

    # Equality comparisons using the underlying dicts

    def __eq__(self, other):
        self._binary_sanity_check(other)
        return self._data == other._data

    def __ne__(self, other):
        self._binary_sanity_check(other)
        return self._data != other._data

    # Copying operations

    def copy(self):
        """Return a shallow copy of a set."""
        result = self.__class__()
        result._data.update(self._data)
        return result

    __copy__ = copy # For the copy module

    def __deepcopy__(self, memo):
        """Return a deep copy of a set; used by copy module."""
        # This pre-creates the result and inserts it in the memo
        # early, in case the deep copy recurses into another reference
        # to this same set.  A set can't be an element of itself, but
        # it can certainly contain an object that has a reference to
        # itself.
        from copy import deepcopy
        result = self.__class__()
        memo[id(self)] = result
        data = result._data
        value = True
        for elt in self:
            data[deepcopy(elt, memo)] = value
        return result

    # Standard set operations: union, intersection, both differences.
    # Each has an operator version (e.g. __or__, invoked with |) and a
    # method version (e.g. union).
    # Subtle:  Each pair requires distinct code so that the outcome is
    # correct when the type of other isn't suitable.  For example, if
    # we did "union = __or__" instead, then Set().union(3) would return
    # NotImplemented instead of raising TypeError (albeit that *why* it
    # raises TypeError as-is is also a bit subtle).

    def __or__(self, other):
        """Return the union of two sets as a new set.

        (I.e. all elements that are in either set.)
        """
        if not isinstance(other, BaseSet):
            return NotImplemented
        result = self.__class__()
        result._data = self._data.copy()
        result._data.update(other._data)
        return result

    def union(self, other):
        """Return the union of two sets as a new set.

        (I.e. all elements that are in either set.)
        """
        return self | other

    def __and__(self, other):
        """Return the intersection of two sets as a new set.

        (I.e. all elements that are in both sets.)
        """
        if not isinstance(other, BaseSet):
            return NotImplemented
        if len(self) <= len(other):
            little, big = self, other
        else:
            little, big = other, self
        common = filter(big._data.has_key, little._data.iterkeys())
        return self.__class__(common)

    def intersection(self, other):
        """Return the intersection of two sets as a new set.

        (I.e. all elements that are in both sets.)
        """
        return self & other

    def __xor__(self, other):
        """Return the symmetric difference of two sets as a new set.

        (I.e. all elements that are in exactly one of the sets.)
        """
        if not isinstance(other, BaseSet):
            return NotImplemented
        result = self.__class__()
        data = result._data
        value = True
        selfdata = self._data
        otherdata = other._data
        for elt in selfdata:
            if elt not in otherdata:
                data[elt] = value
        for elt in otherdata:
            if elt not in selfdata:
                data[elt] = value
        return result

    def symmetric_difference(self, other):
        """Return the symmetric difference of two sets as a new set.

        (I.e. all elements that are in exactly one of the sets.)
        """
        return self ^ other

    def  __sub__(self, other):
        """Return the difference of two sets as a new Set.

        (I.e. all elements that are in this set and not in the other.)
        """
        if not isinstance(other, BaseSet):
            return NotImplemented
        result = self.__class__()
        data = result._data
        otherdata = other._data
        value = True
        for elt in self:
            if elt not in otherdata:
                data[elt] = value
        return result

    def difference(self, other):
        """Return the difference of two sets as a new Set.

        (I.e. all elements that are in this set and not in the other.)
        """
        return self - other

    # Membership test

    def __contains__(self, element):
        """Report whether an element is a member of a set.

        (Called in response to the expression `element in self'.)
        """
        try:
            return element in self._data
        except TypeError:
            transform = getattr(element, "_as_temporarily_immutable", None)
            if transform is None:
                raise # re-raise the TypeError exception we caught
            return transform() in self._data

    # Subset and superset test

    def issubset(self, other):
        """Report whether another set contains this set."""
        self._binary_sanity_check(other)
        if len(self) > len(other):  # Fast check for obvious cases
            return False
        otherdata = other._data
        for elt in self:
            if elt not in otherdata:
                return False
        return True

    def issuperset(self, other):
        """Report whether this set contains another set."""
        self._binary_sanity_check(other)
        if len(self) < len(other):  # Fast check for obvious cases
            return False
        selfdata = self._data
        for elt in other:
            if elt not in selfdata:
                return False
        return True

    # Inequality comparisons using the is-subset relation.
    __le__ = issubset
    __ge__ = issuperset

    def __lt__(self, other):
        self._binary_sanity_check(other)
        return len(self) < len(other) and self.issubset(other)

    def __gt__(self, other):
        self._binary_sanity_check(other)
        return len(self) > len(other) and self.issuperset(other)

    # Assorted helpers

    def _binary_sanity_check(self, other):
        # Check that the other argument to a binary operation is also
        # a set, raising a TypeError otherwise.
        if not isinstance(other, BaseSet):
            raise TypeError, "Binary operation only permitted between sets"

    def _compute_hash(self):
        # Calculate hash code for a set by xor'ing the hash codes of
        # the elements.  This ensures that the hash code does not depend
        # on the order in which elements are added to the set.  This is
        # not called __hash__ because a BaseSet should not be hashable;
        # only an ImmutableSet is hashable.
        result = 0
        for elt in self:
            result ^= hash(elt)
        return result

    def _update(self, iterable):
        # The main loop for update() and the subclass __init__() methods.
        data = self._data

        # Use the fast update() method when a dictionary is available.
        if isinstance(iterable, BaseSet):
            data.update(iterable._data)
            return
        if isinstance(iterable, dict):
            data.update(iterable)
            return

        value = True
        it = iter(iterable)
        while True:
            try:
                for element in it:
                    data[element] = value
                return
            except TypeError:
                transform = getattr(element, "_as_immutable", None)
                if transform is None:
                    raise # re-raise the TypeError exception we caught
                data[transform()] = value


class ImmutableSet(BaseSet):
    """Immutable set class."""

    __slots__ = ['_hashcode']

    # BaseSet + hashing

    def __init__(self, iterable=None):
        """Construct an immutable set from an optional iterable."""
        self._hashcode = None
        self._data = {}
        if iterable is not None:
            self._update(iterable)

    def __hash__(self):
        if self._hashcode is None:
            self._hashcode = self._compute_hash()
        return self._hashcode


class Set(BaseSet):
    """ Mutable set class."""

    __slots__ = []

    # BaseSet + operations requiring mutability; no hashing

    def __init__(self, iterable=None):
        """Construct a set from an optional iterable."""
        self._data = {}
        if iterable is not None:
            self._update(iterable)

    def __hash__(self):
        """A Set cannot be hashed."""
        # We inherit object.__hash__, so we must deny this explicitly
        raise TypeError, "Can't hash a Set, only an ImmutableSet."

    # In-place union, intersection, differences.
    # Subtle:  The xyz_update() functions deliberately return None,
    # as do all mutating operations on built-in container types.
    # The __xyz__ spellings have to return self, though.

    def __ior__(self, other):
        """Update a set with the union of itself and another."""
        self._binary_sanity_check(other)
        self._data.update(other._data)
        return self

    def union_update(self, other):
        """Update a set with the union of itself and another."""
        self |= other

    def __iand__(self, other):
        """Update a set with the intersection of itself and another."""
        self._binary_sanity_check(other)
        self._data = (self & other)._data
        return self

    def intersection_update(self, other):
        """Update a set with the intersection of itself and another."""
        self &= other

    def __ixor__(self, other):
        """Update a set with the symmetric difference of itself and another."""
        self._binary_sanity_check(other)
        data = self._data
        value = True
        for elt in other:
            if elt in data:
                del data[elt]
            else:
                data[elt] = value
        return self

    def symmetric_difference_update(self, other):
        """Update a set with the symmetric difference of itself and another."""
        self ^= other

    def __isub__(self, other):
        """Remove all elements of another set from this set."""
        self._binary_sanity_check(other)
        data = self._data
        for elt in other:
            if elt in data:
                del data[elt]
        return self

    def difference_update(self, other):
        """Remove all elements of another set from this set."""
        self -= other

    # Python dict-like mass mutations: update, clear

    def update(self, iterable):
        """Add all values from an iterable (such as a list or file)."""
        self._update(iterable)

    def clear(self):
        """Remove all elements from this set."""
        self._data.clear()

    # Single-element mutations: add, remove, discard

    def add(self, element):
        """Add an element to a set.

        This has no effect if the element is already present.
        """
        try:
            self._data[element] = True
        except TypeError:
            transform = getattr(element, "_as_immutable", None)
            if transform is None:
                raise # re-raise the TypeError exception we caught
            self._data[transform()] = True

    def remove(self, element):
        """Remove an element from a set; it must be a member.

        If the element is not a member, raise a KeyError.
        """
        try:
            del self._data[element]
        except TypeError:
            transform = getattr(element, "_as_temporarily_immutable", None)
            if transform is None:
                raise # re-raise the TypeError exception we caught
            del self._data[transform()]

    def discard(self, element):
        """Remove an element from a set if it is a member.

        If the element is not a member, do nothing.
        """
        try:
            self.remove(element)
        except KeyError:
            pass

    def pop(self):
        """Remove and return an arbitrary set element."""
        return self._data.popitem()[0]

    def _as_immutable(self):
        # Return a copy of self as an immutable set
        return ImmutableSet(self)

    def _as_temporarily_immutable(self):
        # Return self wrapped in a temporarily immutable set
        return _TemporarilyImmutableSet(self)


class _TemporarilyImmutableSet(BaseSet):
    # Wrap a mutable set as if it was temporarily immutable.
    # This only supplies hashing and equality comparisons.

    def __init__(self, set):
        self._set = set
        self._data = set._data  # Needed by ImmutableSet.__eq__()

    def __hash__(self):
        return self._set._compute_hash()