# -*- coding: iso-8859-15 -*-
"""Immutable integer set type.
Integer set class.
Copyright (C) 2006, Heiko Wundram.
Released under the MIT license:
Copyright (c) 2006, Heiko Wundram.
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
* The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""
# Version information
# -------------------
__author__ = "Heiko Wundram <me@modelnine.org>"
__version__ = "0.2"
__revision__ = "7"
__date__ = "2006-01-23"
# Utility classes
# ---------------
class _Infinity(object):
"""Internal type used to represent infinity values."""
__slots__ = ["_neg"]
def __init__(self,neg):
self._neg = neg
def __lt__(self,value):
if not isinstance(value,(int,long,_Infinity)):
return NotImplemented
return ( self._neg and
not ( isinstance(value,_Infinity) and value._neg ) )
def __le__(self,value):
if not isinstance(value,(int,long,_Infinity)):
return NotImplemented
return self._neg
def __gt__(self,value):
if not isinstance(value,(int,long,_Infinity)):
return NotImplemented
return not ( self._neg or
( isinstance(value,_Infinity) and not value._neg ) )
def __ge__(self,value):
if not isinstance(value,(int,long,_Infinity)):
return NotImplemented
return not self._neg
def __eq__(self,value):
if not isinstance(value,(int,long,_Infinity)):
return NotImplemented
return isinstance(value,_Infinity) and self._neg == value._neg
def __ne__(self,value):
if not isinstance(value,(int,long,_Infinity)):
return NotImplemented
return not isinstance(value,_Infinity) or self._neg <> value._neg
def __repr__(self):
return "None"
# Constants
# ---------
_MININF = _Infinity(True)
_MAXINF = _Infinity(False)
# Integer set class
# -----------------
class IntSet(object):
"""Integer set class with efficient storage in a RLE format of ranges.
Supports minus and plus infinity in the range."""
__slots__ = ["_ranges","_min","_max","_hash"]
def __init__(self,*args,**kwargs):
"""Initialize an integer set. The constructor accepts an unlimited
number of arguments that may either be tuples in the form of
(start,stop) where either start or stop may be a number or None to
represent maximum/minimum in that direction. The range specified by
(start,stop) is always inclusive (differing from the builtin range
operator).
Keyword arguments that can be passed to an integer set are min and
max, which specify the minimum and maximum number in the set,
respectively. You can also pass None here to represent minus or plus
infinity, which is also the default.
"""
# Special case copy constructor.
if len(args) == 1 and isinstance(args[0],IntSet):
if kwargs:
raise ValueError("No keyword arguments for copy constructor.")
self._min = args[0]._min
self._max = args[0]._max
self._ranges = args[0]._ranges
self._hash = args[0]._hash
return
# Initialize set.
self._ranges = []
# Process keyword arguments.
self._min = kwargs.pop("min",_MININF)
self._max = kwargs.pop("max",_MAXINF)
if self._min is None:
self._min = _MININF
if self._max is None:
self._max = _MAXINF
# Check keyword arguments.
if kwargs:
raise ValueError("Invalid keyword argument.")
if not ( isinstance(self._min,(int,long)) or self._min is _MININF ):
raise TypeError("Invalid type of min argument.")
if not ( isinstance(self._max,(int,long)) or self._max is _MAXINF ):
raise TypeError("Invalid type of max argument.")
if ( self._min is not _MININF and self._max is not _MAXINF and
self._min > self._max ):
raise ValueError("Minimum is not smaller than maximum.")
if isinstance(self._max,(int,long)):
self._max += 1
# Process arguments.
for arg in args:
if isinstance(arg,(int,long)):
start, stop = arg, arg+1
elif isinstance(arg,tuple):
if len(arg) <> 2:
raise ValueError("Invalid tuple, must be (start,stop).")
# Process argument.
start, stop = arg
if start is None:
start = self._min
if stop is None:
stop = self._max
# Check arguments.
if not ( isinstance(start,(int,long)) or start is _MININF ):
raise TypeError("Invalid type of tuple start.")
if not ( isinstance(stop,(int,long)) or stop is _MAXINF ):
raise TypeError("Invalid type of tuple stop.")
if ( start is not _MININF and stop is not _MAXINF and
start > stop ):
continue
if isinstance(stop,(int,long)):
stop += 1
else:
raise TypeError("Invalid argument.")
if start > self._max:
continue
elif start < self._min:
start = self._min
if stop < self._min:
continue
elif stop > self._max:
stop = self._max
self._ranges.append((start,stop))
# Normalize set.
self._normalize()
# Utility functions for set operations
# ------------------------------------
def _iterranges(self,r1,r2,minval=_MININF,maxval=_MAXINF):
curval = minval
curstates = {"r1":False,"r2":False}
imax, jmax = 2*len(r1), 2*len(r2)
i, j = 0, 0
while i < imax or j < jmax:
if i < imax and ( ( j < jmax and
r1[i>>1][i&1] < r2[j>>1][j&1] ) or
j == jmax ):
cur_r, newname, newstate = r1[i>>1][i&1], "r1", not (i&1)
i += 1
else:
cur_r, newname, newstate = r2[j>>1][j&1], "r2", not (j&1)
j += 1
if curval < cur_r:
if cur_r > maxval:
break
yield curstates, (curval,cur_r)
curval = cur_r
curstates[newname] = newstate
if curval < maxval:
yield curstates, (curval,maxval)
def _normalize(self):
self._ranges.sort()
i = 1
while i < len(self._ranges):
if self._ranges[i][0] < self._ranges[i-1][1]:
self._ranges[i-1] = (self._ranges[i-1][0],
max(self._ranges[i-1][1],
self._ranges[i][1]))
del self._ranges[i]
else:
i += 1
self._ranges = tuple(self._ranges)
self._hash = hash(self._ranges)
def __coerce__(self,other):
if isinstance(other,IntSet):
return self, other
elif isinstance(other,(int,long,tuple)):
try:
return self, self.__class__(other)
except TypeError:
# Catch a type error, in that case the structure specified by
# other is something we can't coerce, return NotImplemented.
# ValueErrors are not caught, they signal that the data was
# invalid for the constructor. This is appropriate to signal
# as a ValueError to the caller.
return NotImplemented
elif isinstance(other,list):
try:
return self, self.__class__(*other)
except TypeError:
# See above.
return NotImplemented
return NotImplemented
# Set function definitions
# ------------------------
def _make_function(name,type,doc,pall,pany=None):
"""Makes a function to match two ranges. Accepts two types: either
'set', which defines a function which returns a set with all ranges
matching pall (pany is ignored), or 'bool', which returns True if pall
matches for all ranges and pany matches for any one range. doc is the
dostring to give this function. pany may be none to ignore the any
match.
The predicates get a dict with two keys, 'r1', 'r2', which denote
whether the current range is present in range1 (self) and/or range2
(other) or none of the two, respectively."""
if type == "set":
def f(self,other):
coerced = self.__coerce__(other)
if coerced is NotImplemented:
return NotImplemented
other = coerced[1]
newset = self.__class__.__new__(self.__class__)
newset._min = min(self._min,other._min)
newset._max = max(self._max,other._max)
newset._ranges = []
for states, (start,stop) in \
self._iterranges(self._ranges,other._ranges,
newset._min,newset._max):
if pall(states):
if newset._ranges and newset._ranges[-1][1] == start:
newset._ranges[-1] = (newset._ranges[-1][0],stop)
else:
newset._ranges.append((start,stop))
newset._ranges = tuple(newset._ranges)
newset._hash = hash(self._ranges)
return newset
elif type == "bool":
def f(self,other):
coerced = self.__coerce__(other)
if coerced is NotImplemented:
return NotImplemented
other = coerced[1]
_min = min(self._min,other._min)
_max = max(self._max,other._max)
found = not pany
for states, (start,stop) in \
self._iterranges(self._ranges,other._ranges,_min,_max):
if not pall(states):
return False
found = found or pany(states)
return found
else:
raise ValueError("Invalid type of function to create.")
f.func_name = name
f.func_doc = doc
return f
# Intersection.
__and__ = _make_function("__and__","set",
"Intersection of two sets as a new set.",
lambda s: s["r1"] and s["r2"])
__rand__ = _make_function("__rand__","set",
"Intersection of two sets as a new set.",
lambda s: s["r1"] and s["r2"])
intersection = _make_function("intersection","set",
"Intersection of two sets as a new set.",
lambda s: s["r1"] and s["r2"])
# Union.
__or__ = _make_function("__or__","set",
"Union of two sets as a new set.",
lambda s: s["r1"] or s["r2"])
__ror__ = _make_function("__ror__","set",
"Union of two sets as a new set.",
lambda s: s["r1"] or s["r2"])
union = _make_function("union","set",
"Union of two sets as a new set.",
lambda s: s["r1"] or s["r2"])
# Difference.
__sub__ = _make_function("__sub__","set",
"Difference of two sets as a new set.",
lambda s: s["r1"] and not s["r2"])
__rsub__ = _make_function("__rsub__","set",
"Difference of two sets as a new set.",
lambda s: s["r2"] and not s["r1"])
difference = _make_function("difference","set",
"Difference of two sets as a new set.",
lambda s: s["r1"] and not s["r2"])
# Symmetric difference.
__xor__ = _make_function("__xor__","set",
"Symmetric difference of two sets as a new set.",
lambda s: s["r1"] ^ s["r2"])
__rxor__ = _make_function("__rxor__","set",
"Symmetric difference of two sets as a new set.",
lambda s: s["r1"] ^ s["r2"])
symmetric_difference = _make_function("symmetric_difference","set",
"Symmetric difference of two sets as a new set.",
lambda s: s["r1"] ^ s["r2"])
# Containership testing.
__contains__ = _make_function("__contains__","bool",
"Returns true if self is superset of other.",
lambda s: s["r1"] or not s["r2"])
issubset = _make_function("issubset","bool",
"Returns true if self is subset of other.",
lambda s: s["r2"] or not s["r1"])
istruesubset = _make_function("istruesubset","bool",
"Returns true if self is true subset of other.",
lambda s: s["r2"] or not s["r1"],
lambda s: s["r2"] and not s["r1"])
issuperset = _make_function("issuperset","bool",
"Returns true if self is superset of other.",
lambda s: s["r1"] or not s["r2"])
istruesuperset = _make_function("istruesuperset","bool",
"Returns true if self is true superset of other.",
lambda s: s["r1"] or not s["r2"],
lambda s: s["r1"] and not s["r2"])
overlaps = _make_function("overlaps","bool",
"Returns true if self overlaps with other.",
lambda s: True,
lambda s: s["r1"] and s["r2"])
# Comparison.
__eq__ = _make_function("__eq__","bool",
"Returns true if self is equal to other.",
lambda s: not ( s["r1"] ^ s["r2"] ))
__ne__ = _make_function("__ne__","bool",
"Returns true if self is different to other.",
lambda s: True,
lambda s: s["r1"] ^ s["r2"])
# Clean up namespace.
del _make_function
# Define other functions.
def inverse(self):
"""Inverse of set as a new set."""
newset = self.__class__.__new__(self.__class__)
newset._min = self._min
newset._max = self._max
newset._ranges = []
laststop = self._min
for r in self._ranges:
if laststop < r[0]:
newset._ranges.append((laststop,r[0]))
laststop = r[1]
if laststop < self._max:
newset._ranges.append((laststop,self._max))
return newset
__invert__ = inverse
# Hashing
# -------
def __hash__(self):
"""Returns a hash value representing this integer set. As the set is
always stored normalized, the hash value is guaranteed to match for
matching ranges."""
return self._hash
# Iterating
# ---------
def __len__(self):
"""Get length of this integer set. In case the length is larger than
2**31 (including infinitely sized integer sets), it raises an
OverflowError. This is due to len() restricting the size to
0 <= len < 2**31."""
if not self._ranges:
return 0
if self._ranges[0][0] is _MININF or self._ranges[-1][1] is _MAXINF:
raise OverflowError("Infinitely sized integer set.")
rlen = 0
for r in self._ranges:
rlen += r[1]-r[0]
if rlen >= 2**31:
raise OverflowError("Integer set bigger than 2**31.")
return rlen
def len(self):
"""Returns the length of this integer set as an integer. In case the
length is infinite, returns -1. This function exists because of a
limitation of the builtin len() function which expects values in
the range 0 <= len < 2**31. Use this function in case your integer
set might be larger."""
if not self._ranges:
return 0
if self._ranges[0][0] is _MININF or self._ranges[-1][1] is _MAXINF:
return -1
rlen = 0
for r in self._ranges:
rlen += r[1]-r[0]
return rlen
def __nonzero__(self):
"""Returns true if this integer set contains at least one item."""
return bool(self._ranges)
def __iter__(self):
"""Iterate over all values in this integer set. Iteration always starts
by iterating from lowest to highest over the ranges that are bounded.
After processing these, all ranges that are unbounded (maximum 2) are
yielded intermixed."""
ubranges = []
for r in self._ranges:
if r[0] is _MININF:
if r[1] is _MAXINF:
ubranges.extend(([0,1],[-1,-1]))
else:
ubranges.append([r[1]-1,-1])
elif r[1] is _MAXINF:
ubranges.append([r[0],1])
else:
# Little hackish, but bombs out on 32-bit platforms if using
# xrange.
val = r[0]
while val < r[1]:
yield val
val += 1
if ubranges:
while True:
for ubrange in ubranges:
yield ubrange[0]
ubrange[0] += ubrange[1]
# Printing
# --------
def __repr__(self):
"""Return a representation of this integer set. The representation is
executable to get an equal integer set."""
rv = []
for start, stop in self._ranges:
if ( isinstance(start,(int,long)) and isinstance(stop,(int,long))
and stop-start == 1 ):
rv.append("%r" % start)
elif isinstance(stop,(int,long)):
rv.append("(%r,%r)" % (start,stop-1))
else:
rv.append("(%r,%r)" % (start,stop))
if self._min is not _MININF:
rv.append("min=%r" % self._min)
if self._max is not _MAXINF:
rv.append("max=%r" % self._max)
return "%s(%s)" % (self.__class__.__name__,",".join(rv))
if __name__ == "__main__":
# Little test script demonstrating functionality.
x = IntSet((10,20),30)
y = IntSet((10,20))
z = IntSet((10,20),30,(15,19),min=0,max=40)
print x
print x&110
print x|110
print x^(15,25)
print x-12
print 12 in x
print x.issubset(x)
print y.issubset(x)
print x.istruesubset(x)
print y.istruesubset(x)
for val in x:
print val
print x.inverse()
print x == z
print x == y
print x <> y
print hash(x)
print hash(z)
print len(x)
print x.len()
