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| 1 // Copyright 2006 The RE2 Authors. All Rights Reserved. |
| 2 // Use of this source code is governed by a BSD-style |
| 3 // license that can be found in the LICENSE file. |
| 4 |
| 5 // DESCRIPTION |
| 6 // |
| 7 // SparseArray<T>(m) is a map from integers in [0, m) to T values. |
| 8 // It requires (sizeof(T)+sizeof(int))*m memory, but it provides |
| 9 // fast iteration through the elements in the array and fast clearing |
| 10 // of the array. The array has a concept of certain elements being |
| 11 // uninitialized (having no value). |
| 12 // |
| 13 // Insertion and deletion are constant time operations. |
| 14 // |
| 15 // Allocating the array is a constant time operation |
| 16 // when memory allocation is a constant time operation. |
| 17 // |
| 18 // Clearing the array is a constant time operation (unusual!). |
| 19 // |
| 20 // Iterating through the array is an O(n) operation, where n |
| 21 // is the number of items in the array (not O(m)). |
| 22 // |
| 23 // The array iterator visits entries in the order they were first |
| 24 // inserted into the array. It is safe to add items to the array while |
| 25 // using an iterator: the iterator will visit indices added to the array |
| 26 // during the iteration, but will not re-visit indices whose values |
| 27 // change after visiting. Thus SparseArray can be a convenient |
| 28 // implementation of a work queue. |
| 29 // |
| 30 // The SparseArray implementation is NOT thread-safe. It is up to the |
| 31 // caller to make sure only one thread is accessing the array. (Typically |
| 32 // these arrays are temporary values and used in situations where speed is |
| 33 // important.) |
| 34 // |
| 35 // The SparseArray interface does not present all the usual STL bells and |
| 36 // whistles. |
| 37 // |
| 38 // Implemented with reference to Briggs & Torczon, An Efficient |
| 39 // Representation for Sparse Sets, ACM Letters on Programming Languages |
| 40 // and Systems, Volume 2, Issue 1-4 (March-Dec. 1993), pp. 59-69. |
| 41 // |
| 42 // Briggs & Torczon popularized this technique, but it had been known |
| 43 // long before their paper. They point out that Aho, Hopcroft, and |
| 44 // Ullman's 1974 Design and Analysis of Computer Algorithms and Bentley's |
| 45 // 1986 Programming Pearls both hint at the technique in exercises to the |
| 46 // reader (in Aho & Hopcroft, exercise 2.12; in Bentley, column 1 |
| 47 // exercise 8). |
| 48 // |
| 49 // Briggs & Torczon describe a sparse set implementation. I have |
| 50 // trivially generalized it to create a sparse array (actually the original |
| 51 // target of the AHU and Bentley exercises). |
| 52 |
| 53 // IMPLEMENTATION |
| 54 // |
| 55 // SparseArray uses a vector dense_ and an array sparse_to_dense_, both of |
| 56 // size max_size_. At any point, the number of elements in the sparse array is |
| 57 // size_. |
| 58 // |
| 59 // The vector dense_ contains the size_ elements in the sparse array (with |
| 60 // their indices), |
| 61 // in the order that the elements were first inserted. This array is dense: |
| 62 // the size_ pairs are dense_[0] through dense_[size_-1]. |
| 63 // |
| 64 // The array sparse_to_dense_ maps from indices in [0,m) to indices in |
| 65 // [0,size_). |
| 66 // For indices present in the array, dense_[sparse_to_dense_[i]].index_ == i. |
| 67 // For indices not present in the array, sparse_to_dense_ can contain |
| 68 // any value at all, perhaps outside the range [0, size_) but perhaps not. |
| 69 // |
| 70 // The lax requirement on sparse_to_dense_ values makes clearing |
| 71 // the array very easy: set size_ to 0. Lookups are slightly more |
| 72 // complicated. An index i has a value in the array if and only if: |
| 73 // sparse_to_dense_[i] is in [0, size_) AND |
| 74 // dense_[sparse_to_dense_[i]].index_ == i. |
| 75 // If both these properties hold, only then it is safe to refer to |
| 76 // dense_[sparse_to_dense_[i]].value_ |
| 77 // as the value associated with index i. |
| 78 // |
| 79 // To insert a new entry, set sparse_to_dense_[i] to size_, |
| 80 // initialize dense_[size_], and then increment size_. |
| 81 // |
| 82 // Deletion of specific values from the array is implemented by |
| 83 // swapping dense_[size_-1] and the dense_ being deleted and then |
| 84 // updating the appropriate sparse_to_dense_ entries. |
| 85 // |
| 86 // To make the sparse array as efficient as possible for non-primitive types, |
| 87 // elements may or may not be destroyed when they are deleted from the sparse |
| 88 // array through a call to erase(), erase_existing() or resize(). They |
| 89 // immediately become inaccessible, but they are only guaranteed to be |
| 90 // destroyed when the SparseArray destructor is called. |
| 91 |
| 92 #ifndef RE2_UTIL_SPARSE_ARRAY_H__ |
| 93 #define RE2_UTIL_SPARSE_ARRAY_H__ |
| 94 |
| 95 #include "util/util.h" |
| 96 |
| 97 namespace re2 { |
| 98 |
| 99 template<typename Value> |
| 100 class SparseArray { |
| 101 public: |
| 102 SparseArray(); |
| 103 SparseArray(int max_size); |
| 104 ~SparseArray(); |
| 105 |
| 106 // IndexValue pairs: exposed in SparseArray::iterator. |
| 107 class IndexValue; |
| 108 |
| 109 typedef IndexValue value_type; |
| 110 typedef typename vector<IndexValue>::iterator iterator; |
| 111 typedef typename vector<IndexValue>::const_iterator const_iterator; |
| 112 |
| 113 inline const IndexValue& iv(int i) const; |
| 114 |
| 115 // Return the number of entries in the array. |
| 116 int size() const { |
| 117 return size_; |
| 118 } |
| 119 |
| 120 // Iterate over the array. |
| 121 iterator begin() { |
| 122 return dense_.begin(); |
| 123 } |
| 124 iterator end() { |
| 125 return dense_.begin() + size_; |
| 126 } |
| 127 |
| 128 const_iterator begin() const { |
| 129 return dense_.begin(); |
| 130 } |
| 131 const_iterator end() const { |
| 132 return dense_.begin() + size_; |
| 133 } |
| 134 |
| 135 // Change the maximum size of the array. |
| 136 // Invalidates all iterators. |
| 137 void resize(int max_size); |
| 138 |
| 139 // Return the maximum size of the array. |
| 140 // Indices can be in the range [0, max_size). |
| 141 int max_size() const { |
| 142 return max_size_; |
| 143 } |
| 144 |
| 145 // Clear the array. |
| 146 void clear() { |
| 147 size_ = 0; |
| 148 } |
| 149 |
| 150 // Check whether index i is in the array. |
| 151 inline bool has_index(int i) const; |
| 152 |
| 153 // Comparison function for sorting. |
| 154 // Can sort the sparse array so that future iterations |
| 155 // will visit indices in increasing order using |
| 156 // sort(arr.begin(), arr.end(), arr.less); |
| 157 static bool less(const IndexValue& a, const IndexValue& b); |
| 158 |
| 159 public: |
| 160 // Set the value at index i to v. |
| 161 inline iterator set(int i, Value v); |
| 162 |
| 163 pair<iterator, bool> insert(const value_type& new_value); |
| 164 |
| 165 // Returns the value at index i |
| 166 // or defaultv if index i is not initialized in the array. |
| 167 inline Value get(int i, Value defaultv) const; |
| 168 |
| 169 iterator find(int i); |
| 170 |
| 171 const_iterator find(int i) const; |
| 172 |
| 173 // Change the value at index i to v. |
| 174 // Fast but unsafe: only use if has_index(i) is true. |
| 175 inline iterator set_existing(int i, Value v); |
| 176 |
| 177 // Set the value at the new index i to v. |
| 178 // Fast but unsafe: only use if has_index(i) is false. |
| 179 inline iterator set_new(int i, Value v); |
| 180 |
| 181 // Get the value at index i from the array.. |
| 182 // Fast but unsafe: only use if has_index(i) is true. |
| 183 inline Value get_existing(int i) const; |
| 184 |
| 185 // Erasing items from the array during iteration is in general |
| 186 // NOT safe. There is one special case, which is that the current |
| 187 // index-value pair can be erased as long as the iterator is then |
| 188 // checked for being at the end before being incremented. |
| 189 // For example: |
| 190 // |
| 191 // for (i = m.begin(); i != m.end(); ++i) { |
| 192 // if (ShouldErase(i->index(), i->value())) { |
| 193 // m.erase(i->index()); |
| 194 // --i; |
| 195 // } |
| 196 // } |
| 197 // |
| 198 // Except in the specific case just described, elements must |
| 199 // not be erased from the array (including clearing the array) |
| 200 // while iterators are walking over the array. Otherwise, |
| 201 // the iterators could walk past the end of the array. |
| 202 |
| 203 // Erases the element at index i from the array. |
| 204 inline void erase(int i); |
| 205 |
| 206 // Erases the element at index i from the array. |
| 207 // Fast but unsafe: only use if has_index(i) is true. |
| 208 inline void erase_existing(int i); |
| 209 |
| 210 private: |
| 211 // Add the index i to the array. |
| 212 // Only use if has_index(i) is known to be false. |
| 213 // Since it doesn't set the value associated with i, |
| 214 // this function is private, only intended as a helper |
| 215 // for other methods. |
| 216 inline void create_index(int i); |
| 217 |
| 218 // In debug mode, verify that some invariant properties of the class |
| 219 // are being maintained. This is called at the end of the constructor |
| 220 // and at the beginning and end of all public non-const member functions. |
| 221 inline void DebugCheckInvariants() const; |
| 222 |
| 223 int size_; |
| 224 int max_size_; |
| 225 int* sparse_to_dense_; |
| 226 vector<IndexValue> dense_; |
| 227 |
| 228 DISALLOW_EVIL_CONSTRUCTORS(SparseArray); |
| 229 }; |
| 230 |
| 231 template<typename Value> |
| 232 SparseArray<Value>::SparseArray() |
| 233 : size_(0), max_size_(0), sparse_to_dense_(NULL), dense_() {} |
| 234 |
| 235 // IndexValue pairs: exposed in SparseArray::iterator. |
| 236 template<typename Value> |
| 237 class SparseArray<Value>::IndexValue { |
| 238 friend class SparseArray; |
| 239 public: |
| 240 typedef int first_type; |
| 241 typedef Value second_type; |
| 242 |
| 243 IndexValue() {} |
| 244 IndexValue(int index, const Value& value) : second(value), index_(index) {} |
| 245 |
| 246 int index() const { return index_; } |
| 247 Value value() const { return second; } |
| 248 |
| 249 // Provide the data in the 'second' member so that the utilities |
| 250 // in map-util work. |
| 251 Value second; |
| 252 |
| 253 private: |
| 254 int index_; |
| 255 }; |
| 256 |
| 257 template<typename Value> |
| 258 const typename SparseArray<Value>::IndexValue& |
| 259 SparseArray<Value>::iv(int i) const { |
| 260 DCHECK_GE(i, 0); |
| 261 DCHECK_LT(i, size_); |
| 262 return dense_[i]; |
| 263 } |
| 264 |
| 265 // Change the maximum size of the array. |
| 266 // Invalidates all iterators. |
| 267 template<typename Value> |
| 268 void SparseArray<Value>::resize(int new_max_size) { |
| 269 DebugCheckInvariants(); |
| 270 if (new_max_size > max_size_) { |
| 271 int* a = new int[new_max_size]; |
| 272 if (sparse_to_dense_) { |
| 273 memmove(a, sparse_to_dense_, max_size_*sizeof a[0]); |
| 274 // Don't need to zero the memory but appease Valgrind. |
| 275 if (RunningOnValgrind()) { |
| 276 for (int i = max_size_; i < new_max_size; i++) |
| 277 a[i] = 0xababababU; |
| 278 } |
| 279 delete[] sparse_to_dense_; |
| 280 } |
| 281 sparse_to_dense_ = a; |
| 282 |
| 283 dense_.resize(new_max_size); |
| 284 } |
| 285 max_size_ = new_max_size; |
| 286 if (size_ > max_size_) |
| 287 size_ = max_size_; |
| 288 DebugCheckInvariants(); |
| 289 } |
| 290 |
| 291 // Check whether index i is in the array. |
| 292 template<typename Value> |
| 293 bool SparseArray<Value>::has_index(int i) const { |
| 294 DCHECK_GE(i, 0); |
| 295 DCHECK_LT(i, max_size_); |
| 296 if (static_cast<uint>(i) >= max_size_) { |
| 297 return false; |
| 298 } |
| 299 // Unsigned comparison avoids checking sparse_to_dense_[i] < 0. |
| 300 return (uint)sparse_to_dense_[i] < (uint)size_ && |
| 301 dense_[sparse_to_dense_[i]].index_ == i; |
| 302 } |
| 303 |
| 304 // Set the value at index i to v. |
| 305 template<typename Value> |
| 306 typename SparseArray<Value>::iterator SparseArray<Value>::set(int i, Value v) { |
| 307 DebugCheckInvariants(); |
| 308 if (static_cast<uint>(i) >= max_size_) { |
| 309 // Semantically, end() would be better here, but we already know |
| 310 // the user did something stupid, so begin() insulates them from |
| 311 // dereferencing an invalid pointer. |
| 312 return begin(); |
| 313 } |
| 314 if (!has_index(i)) |
| 315 create_index(i); |
| 316 return set_existing(i, v); |
| 317 } |
| 318 |
| 319 template<typename Value> |
| 320 pair<typename SparseArray<Value>::iterator, bool> SparseArray<Value>::insert( |
| 321 const value_type& new_value) { |
| 322 DebugCheckInvariants(); |
| 323 pair<typename SparseArray<Value>::iterator, bool> p; |
| 324 if (has_index(new_value.index_)) { |
| 325 p = make_pair(dense_.begin() + sparse_to_dense_[new_value.index_], false); |
| 326 } else { |
| 327 p = make_pair(set_new(new_value.index_, new_value.second), true); |
| 328 } |
| 329 DebugCheckInvariants(); |
| 330 return p; |
| 331 } |
| 332 |
| 333 template<typename Value> |
| 334 Value SparseArray<Value>::get(int i, Value defaultv) const { |
| 335 if (!has_index(i)) |
| 336 return defaultv; |
| 337 return get_existing(i); |
| 338 } |
| 339 |
| 340 template<typename Value> |
| 341 typename SparseArray<Value>::iterator SparseArray<Value>::find(int i) { |
| 342 if (has_index(i)) |
| 343 return dense_.begin() + sparse_to_dense_[i]; |
| 344 return end(); |
| 345 } |
| 346 |
| 347 template<typename Value> |
| 348 typename SparseArray<Value>::const_iterator |
| 349 SparseArray<Value>::find(int i) const { |
| 350 if (has_index(i)) { |
| 351 return dense_.begin() + sparse_to_dense_[i]; |
| 352 } |
| 353 return end(); |
| 354 } |
| 355 |
| 356 template<typename Value> |
| 357 typename SparseArray<Value>::iterator |
| 358 SparseArray<Value>::set_existing(int i, Value v) { |
| 359 DebugCheckInvariants(); |
| 360 DCHECK(has_index(i)); |
| 361 dense_[sparse_to_dense_[i]].second = v; |
| 362 DebugCheckInvariants(); |
| 363 return dense_.begin() + sparse_to_dense_[i]; |
| 364 } |
| 365 |
| 366 template<typename Value> |
| 367 typename SparseArray<Value>::iterator |
| 368 SparseArray<Value>::set_new(int i, Value v) { |
| 369 DebugCheckInvariants(); |
| 370 if (static_cast<uint>(i) >= max_size_) { |
| 371 // Semantically, end() would be better here, but we already know |
| 372 // the user did something stupid, so begin() insulates them from |
| 373 // dereferencing an invalid pointer. |
| 374 return begin(); |
| 375 } |
| 376 DCHECK(!has_index(i)); |
| 377 create_index(i); |
| 378 return set_existing(i, v); |
| 379 } |
| 380 |
| 381 template<typename Value> |
| 382 Value SparseArray<Value>::get_existing(int i) const { |
| 383 DCHECK(has_index(i)); |
| 384 return dense_[sparse_to_dense_[i]].second; |
| 385 } |
| 386 |
| 387 template<typename Value> |
| 388 void SparseArray<Value>::erase(int i) { |
| 389 DebugCheckInvariants(); |
| 390 if (has_index(i)) |
| 391 erase_existing(i); |
| 392 DebugCheckInvariants(); |
| 393 } |
| 394 |
| 395 template<typename Value> |
| 396 void SparseArray<Value>::erase_existing(int i) { |
| 397 DebugCheckInvariants(); |
| 398 DCHECK(has_index(i)); |
| 399 int di = sparse_to_dense_[i]; |
| 400 if (di < size_ - 1) { |
| 401 dense_[di] = dense_[size_ - 1]; |
| 402 sparse_to_dense_[dense_[di].index_] = di; |
| 403 } |
| 404 size_--; |
| 405 DebugCheckInvariants(); |
| 406 } |
| 407 |
| 408 template<typename Value> |
| 409 void SparseArray<Value>::create_index(int i) { |
| 410 DCHECK(!has_index(i)); |
| 411 DCHECK_LT(size_, max_size_); |
| 412 sparse_to_dense_[i] = size_; |
| 413 dense_[size_].index_ = i; |
| 414 size_++; |
| 415 } |
| 416 |
| 417 template<typename Value> SparseArray<Value>::SparseArray(int max_size) { |
| 418 max_size_ = max_size; |
| 419 sparse_to_dense_ = new int[max_size]; |
| 420 dense_.resize(max_size); |
| 421 // Don't need to zero the new memory, but appease Valgrind. |
| 422 if (RunningOnValgrind()) { |
| 423 for (int i = 0; i < max_size; i++) { |
| 424 sparse_to_dense_[i] = 0xababababU; |
| 425 dense_[i].index_ = 0xababababU; |
| 426 } |
| 427 } |
| 428 size_ = 0; |
| 429 DebugCheckInvariants(); |
| 430 } |
| 431 |
| 432 template<typename Value> SparseArray<Value>::~SparseArray() { |
| 433 DebugCheckInvariants(); |
| 434 delete[] sparse_to_dense_; |
| 435 } |
| 436 |
| 437 template<typename Value> void SparseArray<Value>::DebugCheckInvariants() const { |
| 438 DCHECK_LE(0, size_); |
| 439 DCHECK_LE(size_, max_size_); |
| 440 DCHECK(size_ == 0 || sparse_to_dense_ != NULL); |
| 441 } |
| 442 |
| 443 // Comparison function for sorting. |
| 444 template<typename Value> bool SparseArray<Value>::less(const IndexValue& a, |
| 445 const IndexValue& b) { |
| 446 return a.index_ < b.index_; |
| 447 } |
| 448 |
| 449 } // namespace re2 |
| 450 |
| 451 #endif // RE2_UTIL_SPARSE_ARRAY_H__ |
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