1 // See www.openfst.org for extensive documentation on this weighted
2 // finite-state transducer library.
4 // Functions and classes to create a partition of states.
6 #ifndef FST_LIB_PARTITION_H_
7 #define FST_LIB_PARTITION_H_
13 #include <fst/queue.h>
20 class PartitionIterator;
22 // Defines a partitioning of elements, used to represent equivalence classes
23 // for FST operations like minimization. T must be a signed integer type.
25 // The elements are numbered from 0 to num_elements - 1.
26 // Initialize(num_elements) sets up the class for a given number of elements.
27 // We maintain a partition of these elements into classes. The classes are also
28 // numbered from zero; you can add a class with AddClass(), or add them in bulk
29 // with AllocateClasses(num_classes). Initially the elements are not assigned
30 // to any class; you set up the initial mapping from elements to classes by
31 // calling Add(element_id, class_id). You can also move an element to a
32 // different class by calling Move(element_id, class_id).
34 // We also support a rather specialized interface that allows you to efficiently
35 // split classes in the Hopcroft minimization algorithm. This maintains a
36 // binary partition of each class. Let's call these, rather arbitrarily, the
37 // 'yes' subset and the 'no' subset of each class, and assume that by default,
38 // each element of a class is in its 'no' subset. When one calls
39 // SplitOn(element_id), element_id is moved to the 'yes' subset of its class.
40 // (If it was already in the 'yes' set, it just stays there). The aim is to
41 // enable (later) splitting the class in two in time no greater than the time
42 // already spent calling SplitOn() for that class. We keep a list of the classes
43 // which have nonempty 'yes' sets, as visited_classes_. When one calls
44 // FinalizeSplit(Queue *l), for each class in visited_classes_ whose 'yes'
45 // and 'no' sets are both nonempty, it will create a new class consisting of
46 // the smaller of the two subsets (and this class will be added to the queue),
47 // and the old class will now be the larger of the two subsets. This call also
48 // resets all the yes/no partitions so that everything is in the 'no' subsets.
50 // One cannot use the Move() function if SplitOn() has been called without
51 // a subsequent call to FinalizeSplit()
57 explicit Partition(T num_elements) { Initialize(num_elements); }
59 // Creates an empty partition for num_elements. This means that the elements
60 // are not assigned to a class (i.e class_index = -1); you should set up the
61 // number of classes using AllocateClasses() or AddClass(), and allocate each
62 // element to a class by calling Add(element, class_id).
63 void Initialize(size_t num_elements) {
64 elements_.resize(num_elements);
65 classes_.reserve(num_elements);
70 // Adds a class; returns new number of classes.
72 auto num_classes = classes_.size();
73 classes_.resize(num_classes + 1);
77 // Adds 'num_classes' new (empty) classes.
78 void AllocateClasses(T num_classes) {
79 classes_.resize(classes_.size() + num_classes);
82 // Adds element_id to class_id. element_id should already have been allocated
83 // by calling Initialize(num_elements)---or the constructor taking
84 // num_elements---with num_elements > element_id. element_id must not
85 // currently be a member of any class; once elements have been added to a
86 // class, use the Move() method to move them from one class to another.
87 void Add(T element_id, T class_id) {
88 auto &this_element = elements_[element_id];
89 auto &this_class = classes_[class_id];
91 // Adds the element to the 'no' subset of the class.
92 auto no_head = this_class.no_head;
93 if (no_head >= 0) elements_[no_head].prev_element = element_id;
94 this_class.no_head = element_id;
95 this_element.class_id = class_id;
96 // Adds to the 'no' subset of the class.
98 this_element.next_element = no_head;
99 this_element.prev_element = -1;
102 // Moves element_id from 'no' subset of its current class to 'no' subset of
103 // class class_id. This may not work correctly if you have called SplitOn()
104 // [for any element] and haven't subsequently called FinalizeSplit().
105 void Move(T element_id, T class_id) {
106 auto elements = &(elements_[0]);
107 auto &element = elements[element_id];
108 auto &old_class = classes_[element.class_id];
110 CHECK(old_class.size >= 0 && old_class.yes_size == 0);
111 // Excises the element from the 'no' list of its old class, where it is
113 if (element.prev_element >= 0) {
114 elements[element.prev_element].next_element = element.next_element;
116 CHECK(old_class.no_head == element_id);
117 old_class.no_head = element.next_element;
119 if (element.next_element >= 0) {
120 elements[element.next_element].prev_element = element.prev_element;
122 // Adds to new class.
123 Add(element_id, class_id);
126 // Moves element_id to the 'yes' subset of its class if it was in the 'no'
127 // subset, and marks the class as having been visited.
128 void SplitOn(T element_id) {
129 auto elements = &(elements_[0]);
130 auto &element = elements[element_id];
131 if (element.yes == yes_counter_) {
132 return; // Already in the 'yes' set; nothing to do.
134 auto class_id = element.class_id;
135 auto &this_class = classes_[class_id];
136 // Excises the element from the 'no' list of its class.
137 if (element.prev_element >= 0) {
138 elements[element.prev_element].next_element = element.next_element;
140 CHECK(this_class.no_head == element_id);
141 this_class.no_head = element.next_element;
143 if (element.next_element >= 0) {
144 elements[element.next_element].prev_element = element.prev_element;
146 // Adds the element to the 'yes' list.
147 if (this_class.yes_head >= 0) {
148 elements[this_class.yes_head].prev_element = element_id;
150 visited_classes_.push_back(class_id);
152 element.yes = yes_counter_;
153 element.next_element = this_class.yes_head;
154 element.prev_element = -1;
155 this_class.yes_head = element_id;
156 this_class.yes_size++;
157 CHECK(this_class.yes_size <= this_class.size);
160 // This should be called after one has possibly called SplitOn for one or more
161 // elements, thus moving those elements to the 'yes' subset for their class.
162 // For each class that has a nontrivial split (i.e., it's not the case that
163 // all members are in the 'yes' or 'no' subset), this function creates a new
164 // class containing the smaller of the two subsets of elements, leaving the
165 // larger group of elements in the old class. The identifier of the new class
166 // will be added to the queue provided as the pointer L. This method then
167 // moves all elements to the 'no' subset of their class.
168 template <class Queue>
169 void FinalizeSplit(Queue *queue) {
170 for (const auto &visited_class : visited_classes_) {
171 const auto new_class = SplitRefine(visited_class);
172 if (new_class != -1 && queue) queue->Enqueue(new_class);
174 visited_classes_.clear();
175 // Incrementation sets all the 'yes' members of the elements to false.
179 const T ClassId(T element_id) const { return elements_[element_id].class_id; }
181 const size_t ClassSize(T class_id) const { return classes_[class_id].size; }
183 const T NumClasses() const { return classes_.size(); }
186 friend class PartitionIterator<T>;
188 // Information about a given element.
190 T class_id; // Class ID of this element.
191 T yes; // This is to be interpreted as a bool, true if it's in the
192 // 'yes' set of this class. The interpretation as bool is
193 // (yes == yes_counter_ ? true : false).
194 T next_element; // Next element in the 'no' list or 'yes' list of this
195 // class, whichever of the two we belong to (think of
196 // this as the 'next' in a doubly-linked list, although
197 // it is an index into the elements array). Negative
198 // values corresponds to null.
199 T prev_element; // Previous element in the 'no' or 'yes' doubly linked
200 // list. Negative values corresponds to null.
203 // Information about a given class.
205 Class() : size(0), yes_size(0), no_head(-1), yes_head(-1) {}
206 T size; // Total number of elements in this class ('no' plus 'yes'
208 T yes_size; // Total number of elements of 'yes' subset of this class.
209 T no_head; // Index of head element of doubly-linked list in 'no' subset.
210 // Everything is in the 'no' subset until you call SplitOn().
211 // -1 means no element.
212 T yes_head; // Index of head element of doubly-linked list in 'yes' subset.
213 // -1 means no element.
216 // This method, called from FinalizeSplit(), checks whether a class has to
217 // be split (a class will be split only if its 'yes' and 'no' subsets are
218 // both nonempty, but one can assume that since this function was called, the
219 // 'yes' subset is nonempty). It splits by taking the smaller subset and
220 // making it a new class, and leaving the larger subset of elements in the
221 // 'no' subset of the old class. It returns the new class if created, or -1
222 // if none was created.
223 T SplitRefine(T class_id) {
224 auto yes_size = classes_[class_id].yes_size;
225 auto size = classes_[class_id].size;
226 auto no_size = size - yes_size;
228 // All members are in the 'yes' subset, so we don't have to create a new
229 // class, just move them all to the 'no' subset.
230 CHECK(classes_[class_id].no_head < 0); // NOLINT
231 classes_[class_id].no_head = classes_[class_id].yes_head;
232 classes_[class_id].yes_head = -1;
233 classes_[class_id].yes_size = 0;
236 auto new_class_id = classes_.size();
237 classes_.resize(classes_.size() + 1);
238 auto &old_class = classes_[class_id];
239 auto &new_class = classes_[new_class_id];
240 // The new_class will have the values from the constructor.
241 if (no_size < yes_size) {
242 // Moves the 'no' subset to new class ('no' subset).
243 new_class.no_head = old_class.no_head;
244 new_class.size = no_size;
245 // And makes the 'yes' subset of the old class ('no' subset).
246 old_class.no_head = old_class.yes_head;
247 old_class.yes_head = -1;
248 old_class.size = yes_size;
249 old_class.yes_size = 0;
251 // Moves the 'yes' subset to the new class (to the 'no' subset)
252 new_class.size = yes_size;
253 new_class.no_head = old_class.yes_head;
254 // Retains only the 'no' subset in the old class.
255 old_class.size = no_size;
256 old_class.yes_size = 0;
257 old_class.yes_head = -1;
259 auto elements = &(elements_[0]);
260 // Updates the 'class_id' of all the elements we moved.
261 for (auto e = new_class.no_head; e >= 0; e = elements[e].next_element) {
262 elements[e].class_id = new_class_id;
268 // elements_[i] contains all info about the i'th element.
269 std::vector<Element> elements_;
270 // classes_[i] contains all info about the i'th class.
271 std::vector<Class> classes_;
272 // Set of visited classes to be used in split refine.
273 std::vector<T> visited_classes_;
274 // yes_counter_ is used in interpreting the 'yes' members of class Element.
275 // If element.yes == yes_counter_, we interpret that element as being in the
276 // 'yes' subset of its class. This allows us to, in effect, set all those
277 // bools to false at a stroke by incrementing yes_counter_.
281 // Iterates over members of the 'no' subset of a class in a partition. (When
282 // this is used, everything is in the 'no' subset).
283 template <typename T>
284 class PartitionIterator {
286 using Element = typename Partition<T>::Element;
288 PartitionIterator(const Partition<T> &partition, T class_id)
289 : partition_(partition),
290 element_id_(partition_.classes_[class_id].no_head),
291 class_id_(class_id) {}
293 bool Done() { return element_id_ < 0; }
295 const T Value() { return element_id_; }
297 void Next() { element_id_ = partition_.elements_[element_id_].next_element; }
299 void Reset() { element_id_ = partition_.classes_[class_id_].no_head; }
302 const Partition<T> &partition_;
307 } // namespace internal
310 #endif // FST_LIB_PARTITION_H_