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+#
+# A Set class that works all the way back to Python 1.5. From:
+#
+# Python Cookbook: Yet another Set class for Python
+# http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/106469
+# Goncalo Rodriques
+#
+# This is a pure Pythonic implementation of a set class. The syntax
+# and methods implemented are, for the most part, borrowed from
+# PEP 218 by Greg Wilson.
+#
+# Note that this class violates the formal definition of a set() by adding
+# a __getitem__() method so we can iterate over a set's elements under
+# Python 1.5 and 2.1, which don't support __iter__() and iterator types.
+#
+
+import string
+
+class Set:
+ """The set class. It can contain mutable objects."""
+
+ def __init__(self, seq = None):
+ """The constructor. It can take any object giving an iterator as an optional
+ argument to populate the new set."""
+ self.elems = []
+ if seq:
+ for elem in seq:
+ if elem not in self.elems:
+ self.elems.append(elem)
+
+ def __str__(self):
+ return "{%s}" % string.join(map(str, self.elems), ", ")
+
+
+ def copy(self):
+ """Shallow copy of a set object."""
+ return Set(self.elems)
+
+ def __contains__(self, elem):
+ return elem in self.elems
+
+ def __len__(self):
+ return len(self.elems)
+
+ def __getitem__(self, index):
+ # Added so that Python 1.5 can iterate over the elements.
+ # The cookbook recipe's author didn't like this because there
+ # really isn't any order in a set object, but this is necessary
+ # to make the class work well enough for our purposes.
+ return self.elems[index]
+
+ def items(self):
+ """Returns a list of the elements in the set."""
+ return self.elems
+
+ def add(self, elem):
+ """Add one element to the set."""
+ if elem not in self.elems:
+ self.elems.append(elem)
+
+ def remove(self, elem):
+ """Remove an element from the set. Return an error if elem is not in the set."""
+ try:
+ self.elems.remove(elem)
+ except ValueError:
+ raise LookupError, "Object %s is not a member of the set." % str(elem)
+
+ def discard(self, elem):
+ """Remove an element from the set. Do nothing if elem is not in the set."""
+ try:
+ self.elems.remove(elem)
+ except ValueError:
+ pass
+
+ def sort(self, func=cmp):
+ self.elems.sort(func)
+
+ #Define an iterator for a set.
+ def __iter__(self):
+ return iter(self.elems)
+
+ #The basic binary operations with sets.
+ def __or__(self, other):
+ """Union of two sets."""
+ ret = self.copy()
+ for elem in other.elems:
+ if elem not in ret:
+ ret.elems.append(elem)
+ return ret
+
+ def __sub__(self, other):
+ """Difference of two sets."""
+ ret = self.copy()
+ for elem in other.elems:
+ ret.discard(elem)
+ return ret
+
+ def __and__(self, other):
+ """Intersection of two sets."""
+ ret = Set()
+ for elem in self.elems:
+ if elem in other.elems:
+ ret.elems.append(elem)
+ return ret
+
+ def __add__(self, other):
+ """Symmetric difference of two sets."""
+ ret = Set()
+ temp = other.copy()
+ for elem in self.elems:
+ if elem in temp.elems:
+ temp.elems.remove(elem)
+ else:
+ ret.elems.append(elem)
+ #Add remaining elements.
+ for elem in temp.elems:
+ ret.elems.append(elem)
+ return ret
+
+ def __mul__(self, other):
+ """Cartesian product of two sets."""
+ ret = Set()
+ for elemself in self.elems:
+ x = map(lambda other, s=elemself: (s, other), other.elems)
+ ret.elems.extend(x)
+ return ret
+
+ #Some of the binary comparisons.
+ def __lt__(self, other):
+ """Returns 1 if the lhs set is contained but not equal to the rhs set."""
+ if len(self.elems) < len(other.elems):
+ temp = other.copy()
+ for elem in self.elems:
+ if elem in temp.elems:
+ temp.remove(elem)
+ else:
+ return 0
+ return len(temp.elems) == 0
+ else:
+ return 0
+
+ def __le__(self, other):
+ """Returns 1 if the lhs set is contained in the rhs set."""
+ if len(self.elems) <= len(other.elems):
+ ret = 1
+ for elem in self.elems:
+ if elem not in other.elems:
+ ret = 0
+ break
+ return ret
+ else:
+ return 0
+
+ def __eq__(self, other):
+ """Returns 1 if the sets are equal."""
+ if len(self.elems) != len(other.elems):
+ return 0
+ else:
+ return len(self - other) == 0