|
| 1 | +from .powerSet.powerSetCalc import calcPSetOf |
| 2 | + |
| 3 | + |
| 4 | +class Set: |
| 5 | + def __init__(self, *elements, universe=[]): |
| 6 | + """ |
| 7 | + Constructs a set object/converts lists to Sets |
| 8 | + :param elements: A list of elements in the set (repeating elements will be removed) |
| 9 | + :param universe: Universe of discourse (Set that should be used when calculating the complement) |
| 10 | + """ |
| 11 | + # Iteration variable for tracking iterations |
| 12 | + self.current = 0 |
| 13 | + |
| 14 | + # If the user mistakenly enters a single list to contain all elements then that list is converted into an |
| 15 | + # elements list |
| 16 | + if len(elements) == 1 and (type(elements[0]) == list or type(elements[0]) == tuple): |
| 17 | + elements = elements[0] |
| 18 | + |
| 19 | + if type(universe) != list and not isinstance(universe, Set): |
| 20 | + print("Error! Universal sets must be specified as a list or Set!") |
| 21 | + raise TypeError |
| 22 | + elif isinstance(universe, Set): |
| 23 | + universe = universe.__list__() |
| 24 | + |
| 25 | + self.elements = elements |
| 26 | + # elements = self.duplicateRemoval() |
| 27 | + elements = self.elements |
| 28 | + # universe of discourse |
| 29 | + self.universe = universe |
| 30 | + # Converts each iterable element in the set into a set object |
| 31 | + self.elements = tuple(self.toSet(elements)) |
| 32 | + self.isProduct = False |
| 33 | + |
| 34 | + def __len__(self): |
| 35 | + return len(self.elements) |
| 36 | + |
| 37 | + def __iter__(self): |
| 38 | + # This is strictly used for the beginning of iteration |
| 39 | + return self |
| 40 | + |
| 41 | + def __getitem__(self, index): |
| 42 | + # Used for brackets element accessing |
| 43 | + return self.elements[index] |
| 44 | + |
| 45 | + def __next__(self): |
| 46 | + # Accesses the next element during iteration |
| 47 | + if self.current < len(self): |
| 48 | + c = self.current |
| 49 | + self.current += 1 |
| 50 | + return self.elements[c] |
| 51 | + else: |
| 52 | + self.current = 0 |
| 53 | + raise StopIteration |
| 54 | + |
| 55 | + def __str__(self): |
| 56 | + return str(self.__list__()).replace("[", '{').replace(']','}') |
| 57 | + |
| 58 | + def __list__(self): |
| 59 | + """ |
| 60 | + Converts the current instance of the set object into a standard list (along with each of its set elements) |
| 61 | + :return: A list of the elements the set |
| 62 | + """ |
| 63 | + |
| 64 | + return_list = [0 for i in range(len(self.elements))] |
| 65 | + |
| 66 | + for i in range(len(self.elements)): |
| 67 | + # Checks if the current element is iterable |
| 68 | + isIter = Set.isIterable(self.elements[i]) |
| 69 | + |
| 70 | + if isIter and type(self.elements[i]) != tuple and not isinstance(self.elements[i], Set): |
| 71 | + # List/dictionaries and other iterable objects are converted to lists using the standard constructor |
| 72 | + return_list[i] = list(self.elements[i]) |
| 73 | + elif isIter and type(self.elements[i]) != tuple: |
| 74 | + # Converts set objects to lists |
| 75 | + return_list[i] = self.elements[i].__list__() |
| 76 | + else: |
| 77 | + # If an element is not mutable than it can be added to the return list as is |
| 78 | + return_list[i] = self.elements[i] |
| 79 | + return return_list |
| 80 | + |
| 81 | + def __set__(self): |
| 82 | + return set(self.__list__()) |
| 83 | + |
| 84 | + def __eq__(self, other): |
| 85 | + return self.equal(other) |
| 86 | + |
| 87 | + def __abs__(self): |
| 88 | + return len(self) |
| 89 | + |
| 90 | + def __add__(self, other): |
| 91 | + return self.union(other) |
| 92 | + |
| 93 | + def __sub__(self, other): |
| 94 | + return self.setMinus(other) |
| 95 | + |
| 96 | + def __and__(self, other): |
| 97 | + return self.intersection(other) |
| 98 | + |
| 99 | + def __mul__(self, other): |
| 100 | + return self.cartesianProduct(other) |
| 101 | + |
| 102 | + @staticmethod |
| 103 | + def tryConvert(obj): |
| 104 | + """ |
| 105 | + Tries to convert the input object into a set object. |
| 106 | + :param obj: Object to be converted into a set |
| 107 | + :return: Unchanged obj if it is already a set object; otherwise, the object is attempted to be converted into a |
| 108 | + set if possible, if this can't be done, a value error is thrown |
| 109 | + """ |
| 110 | + if not isinstance(obj, Set): |
| 111 | + if Set.isIterable(obj) and type(obj) != tuple: |
| 112 | + obj = Set(obj) |
| 113 | + else: |
| 114 | + print("Please input a set object") |
| 115 | + raise TypeError |
| 116 | + return obj |
| 117 | + |
| 118 | + def union(self, setb): |
| 119 | + """ |
| 120 | + Takes the union of two sets |
| 121 | + :param setb: Set object to be unionized with self |
| 122 | + :return: The set of all elements in either the calling set or setb |
| 123 | + """ |
| 124 | + setb = Set.tryConvert(setb) |
| 125 | + |
| 126 | + result = [] |
| 127 | + |
| 128 | + for x in self: |
| 129 | + if x not in result: |
| 130 | + result.append(x) |
| 131 | + for x in setb: |
| 132 | + if x not in result: |
| 133 | + result.append(x) |
| 134 | + |
| 135 | + return Set(result) |
| 136 | + |
| 137 | + def setMinus(self, setb): |
| 138 | + """ |
| 139 | + Calculates the disjoint of self - setb |
| 140 | + :param setb: The return set should be disjoint with |
| 141 | + :return: A set containing all elements of the calling that are not in setb |
| 142 | + """ |
| 143 | + setb = Set.tryConvert(setb) |
| 144 | + result = [] |
| 145 | + |
| 146 | + for x in self: |
| 147 | + if x not in setb: |
| 148 | + result.append(x) |
| 149 | + return Set(result) |
| 150 | + |
| 151 | + def complement(self): |
| 152 | + """ |
| 153 | + Calculates the complement of the calling set with its declared universe |
| 154 | + :return: All elements in the calling set, but not in the universal set |
| 155 | + """ |
| 156 | + return self.setMinus(Set(self.universe)) |
| 157 | + |
| 158 | + |
| 159 | + @staticmethod |
| 160 | + def isIterable(obj): |
| 161 | + """ |
| 162 | + Checks if the object passed is ierable |
| 163 | + :param obj: Any object |
| 164 | + :return: True if the object is iterable and false if not |
| 165 | + """ |
| 166 | + try: |
| 167 | + getattr(obj, '__iter__') |
| 168 | + except AttributeError: |
| 169 | + return False |
| 170 | + return True |
| 171 | + |
| 172 | + def intersection(self, setb): |
| 173 | + """ |
| 174 | + Calculates the intersection of two sets |
| 175 | + :param setb: set to be intersected with the calling set |
| 176 | + :return: All elements in the calling set and in setb |
| 177 | + """ |
| 178 | + setb = Set.tryConvert(setb) |
| 179 | + result = [] |
| 180 | + |
| 181 | + for x in self: |
| 182 | + if x in setb: |
| 183 | + result.append(x) |
| 184 | + |
| 185 | + return Set(result) |
| 186 | + |
| 187 | + def toSet(self, elements): |
| 188 | + ''' |
| 189 | + A helper function used to convert a list of elements to a set; however the constructor should be called for this |
| 190 | + purpose not this method |
| 191 | + :param elements: A list of elements |
| 192 | + :return: A list of elements where all mutable elements have been converted to set objects |
| 193 | + ''' |
| 194 | + |
| 195 | + return_list = [0 for i in range(len(elements))] |
| 196 | + |
| 197 | + for i in range(len(elements)): |
| 198 | + |
| 199 | + # Checks to see if the current element is iterable |
| 200 | + isIter = Set.isIterable(elements[i]) |
| 201 | + |
| 202 | + if isIter and type(elements[i]) != tuple and not isinstance(elements[i], Set): |
| 203 | + # Converts the current element to a set object |
| 204 | + return_list[i] = Set(elements[i], universe=self.universe) |
| 205 | + else: |
| 206 | + # If the current object is a base type, then it does not need to be converted and is kept as is |
| 207 | + return_list[i] = elements[i] |
| 208 | + return return_list |
| 209 | + |
| 210 | + def duplicateRemoval(self): |
| 211 | + ''' |
| 212 | + Removes duplicate elements from the given set object (this is not intended to be called from outside the class |
| 213 | + :return: A list of non-repeating elements |
| 214 | + ''' |
| 215 | + clean = [] |
| 216 | + for element in self.elements: |
| 217 | + if element not in clean: |
| 218 | + clean.append(element) |
| 219 | + return clean |
| 220 | + |
| 221 | + @staticmethod |
| 222 | + def inCheck(element, set): |
| 223 | + """ |
| 224 | + Checks if an element is in set (this was used for purposes of preventing infinite recursion using the |
| 225 | + __contains__ operator |
| 226 | + :param element: Any object to be inspected for membership of set |
| 227 | + :param set: The Set that element should be checked for membership against |
| 228 | + :return: |
| 229 | + """ |
| 230 | + for x in set: |
| 231 | + if x == element: |
| 232 | + return True |
| 233 | + return False |
| 234 | + |
| 235 | + def powerSet(self): |
| 236 | + ''' |
| 237 | + Calculates the powerset of a set |
| 238 | + :return: A set containing all subsets of the calling set |
| 239 | + ''' |
| 240 | + |
| 241 | + _self = self.__list__() |
| 242 | + # This relies on the compiled python extension imported |
| 243 | + powerSet = calcPSetOf(_self) |
| 244 | + return Set(powerSet) |
| 245 | + |
| 246 | + def subsetof(self, setb): |
| 247 | + """ |
| 248 | + Checks if the current set is a subset of the input set |
| 249 | + :param setb: comparison set |
| 250 | + :return: Is this set a subset of setb |
| 251 | + """ |
| 252 | + setb = Set.tryConvert(setb) |
| 253 | + for y in self.elements: |
| 254 | + found = False |
| 255 | + for x in setb.elements: |
| 256 | + found = x == y |
| 257 | + if found: |
| 258 | + break |
| 259 | + if not found: |
| 260 | + return False |
| 261 | + return True |
| 262 | + |
| 263 | + def equal(self, setb): |
| 264 | + """ |
| 265 | + Checks if the calling set is equal to setb (that it is a subset of setb and setb is a subset of it) |
| 266 | + :param setb: It's checked if the calling set is a subset of this set |
| 267 | + :return: True if the calling set is a subset of this set and false if not |
| 268 | + """ |
| 269 | + |
| 270 | + if isinstance(setb, Set): |
| 271 | + if self.subsetof(setb) and setb.subsetof(self): |
| 272 | + return True |
| 273 | + return False |
| 274 | + |
| 275 | + def setDisplayMode(self): |
| 276 | + """ |
| 277 | + Displays each element of the current set by hitting enter each time. This is a good way to display a very long |
| 278 | + set especially when copying |
| 279 | + :return: Nothing |
| 280 | + """ |
| 281 | + |
| 282 | + for x in self: |
| 283 | + print(x, end="\n") |
| 284 | + input() |
| 285 | + |
| 286 | + def cartesianProduct(self, *setb): |
| 287 | + """ |
| 288 | + Calculates the cartesian product of the calling set and the variable number of sets input. |
| 289 | + Input 2 sets for a normal product = |
| 290 | + Input 3 sets for a triple product |
| 291 | + etc. |
| 292 | + :param setb: Multiple sets separated by commas |
| 293 | + :return: A set of ordered pairs. When doing a normal product (A*B), each element is of the form (a,b), |
| 294 | + where a is in the calling set (A) and b is in B |
| 295 | + """ |
| 296 | + return Set(self.aCartesianProduct(setb)) |
| 297 | + |
| 298 | + def aCartesianProduct(self, *setb): |
| 299 | + """ |
| 300 | + The helper function to calculate various cartesian products |
| 301 | + :param setb: A list of sets to be used in the cartesian product |
| 302 | + :return: A list of ordered pairs representing the cartesian product of self with all the sets in setb |
| 303 | + """ |
| 304 | + |
| 305 | + result = [] |
| 306 | + if type(setb[0]) == list or type(setb[0]) == tuple and len(setb) == 1: |
| 307 | + setb = setb[0] |
| 308 | + |
| 309 | + if len(setb) == 1: |
| 310 | + for x in self: |
| 311 | + for y in setb[0]: |
| 312 | + result.append((x,y)) |
| 313 | + else: |
| 314 | + otherComb = setb[0].cartesianProduct(setb[1:]) |
| 315 | + for i in range(len(self)): |
| 316 | + for y in otherComb: |
| 317 | + _y = list(y) |
| 318 | + _y.insert(0, self[i]) |
| 319 | + result.append(tuple(_y)) |
| 320 | + return result |
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