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#ifndef UTIL_SPARSE_ARRAY_H_
6#define UTIL_SPARSE_ARRAY_H_
7
8// DESCRIPTION
9//
10// SparseArray<T>(m) is a map from integers in [0, m) to T values.
11// It requires (sizeof(T)+sizeof(int))*m memory, but it provides
12// fast iteration through the elements in the array and fast clearing
13// of the array. The array has a concept of certain elements being
14// uninitialized (having no value).
15//
16// Insertion and deletion are constant time operations.
17//
18// Allocating the array is a constant time operation
19// when memory allocation is a constant time operation.
20//
21// Clearing the array is a constant time operation (unusual!).
22//
23// Iterating through the array is an O(n) operation, where n
24// is the number of items in the array (not O(m)).
25//
26// The array iterator visits entries in the order they were first
27// inserted into the array. It is safe to add items to the array while
28// using an iterator: the iterator will visit indices added to the array
29// during the iteration, but will not re-visit indices whose values
30// change after visiting. Thus SparseArray can be a convenient
31// implementation of a work queue.
32//
33// The SparseArray implementation is NOT thread-safe. It is up to the
34// caller to make sure only one thread is accessing the array. (Typically
35// these arrays are temporary values and used in situations where speed is
36// important.)
37//
38// The SparseArray interface does not present all the usual STL bells and
39// whistles.
40//
41// Implemented with reference to Briggs & Torczon, An Efficient
42// Representation for Sparse Sets, ACM Letters on Programming Languages
43// and Systems, Volume 2, Issue 1-4 (March-Dec. 1993), pp. 59-69.
44//
45// Briggs & Torczon popularized this technique, but it had been known
46// long before their paper. They point out that Aho, Hopcroft, and
47// Ullman's 1974 Design and Analysis of Computer Algorithms and Bentley's
48// 1986 Programming Pearls both hint at the technique in exercises to the
49// reader (in Aho & Hopcroft, exercise 2.12; in Bentley, column 1
50// exercise 8).
51//
52// Briggs & Torczon describe a sparse set implementation. I have
53// trivially generalized it to create a sparse array (actually the original
54// target of the AHU and Bentley exercises).
55
56// IMPLEMENTATION
57//
58// SparseArray is an array dense_ and an array sparse_ of identical size.
59// At any point, the number of elements in the sparse array is size_.
60//
61// The array dense_ contains the size_ elements in the sparse array (with
62// their indices),
63// in the order that the elements were first inserted. This array is dense:
64// the size_ pairs are dense_[0] through dense_[size_-1].
65//
66// The array sparse_ maps from indices in [0,m) to indices in [0,size_).
67// For indices present in the array, dense_[sparse_[i]].index_ == i.
68// For indices not present in the array, sparse_ can contain any value at all,
69// perhaps outside the range [0, size_) but perhaps not.
70//
71// The lax requirement on sparse_ values makes clearing the array very easy:
72// set size_ to 0. Lookups are slightly more complicated.
73// An index i has a value in the array if and only if:
74// sparse_[i] is in [0, size_) AND
75// dense_[sparse_[i]].index_ == i.
76// If both these properties hold, only then it is safe to refer to
77// dense_[sparse_[i]].value_
78// as the value associated with index i.
79//
80// To insert a new entry, set sparse_[i] to size_,
81// initialize dense_[size_], and then increment size_.
82//
83// To make the sparse array as efficient as possible for non-primitive types,
84// elements may or may not be destroyed when they are deleted from the sparse
85// array through a call to resize(). They immediately become inaccessible, but
86// they are only guaranteed to be destroyed when the SparseArray destructor is
87// called.
88//
89// A moved-from SparseArray will be empty.
90
91// Doing this simplifies the logic below.
92#ifndef __has_feature
93#define __has_feature(x) 0
94#endif
95
96#include <assert.h>
97#include <stdint.h>
98#if __has_feature(memory_sanitizer)
99#include <sanitizer/msan_interface.h>
100#endif
101#include <algorithm>
102#include <memory>
103#include <utility>
104
105#include "util/pod_array.h"
106
107namespace re2 {
108
109template<typename Value>
110class SparseArray {
111 public:
112 SparseArray();
113 explicit SparseArray(int max_size);
114 ~SparseArray();
115
116 // IndexValue pairs: exposed in SparseArray::iterator.
117 class IndexValue;
118
119 typedef IndexValue* iterator;
120 typedef const IndexValue* const_iterator;
121
122 SparseArray(const SparseArray& src);
123 SparseArray(SparseArray&& src);
124
125 SparseArray& operator=(const SparseArray& src);
126 SparseArray& operator=(SparseArray&& src);
127
128 // Return the number of entries in the array.
129 int size() const {
130 return size_;
131 }
132
133 // Indicate whether the array is empty.
134 int empty() const {
135 return size_ == 0;
136 }
137
138 // Iterate over the array.
139 iterator begin() {
140 return dense_.data();
141 }
142 iterator end() {
143 return dense_.data() + size_;
144 }
145
146 const_iterator begin() const {
147 return dense_.data();
148 }
149 const_iterator end() const {
150 return dense_.data() + size_;
151 }
152
153 // Change the maximum size of the array.
154 // Invalidates all iterators.
155 void resize(int new_max_size);
156
157 // Return the maximum size of the array.
158 // Indices can be in the range [0, max_size).
159 int max_size() const {
160 if (dense_.data() != NULL)
161 return dense_.size();
162 else
163 return 0;
164 }
165
166 // Clear the array.
167 void clear() {
168 size_ = 0;
169 }
170
171 // Check whether index i is in the array.
172 bool has_index(int i) const;
173
174 // Comparison function for sorting.
175 // Can sort the sparse array so that future iterations
176 // will visit indices in increasing order using
177 // std::sort(arr.begin(), arr.end(), arr.less);
178 static bool less(const IndexValue& a, const IndexValue& b);
179
180 public:
181 // Set the value at index i to v.
182 iterator set(int i, const Value& v) {
183 return SetInternal(true, i, v);
184 }
185
186 // Set the value at new index i to v.
187 // Fast but unsafe: only use if has_index(i) is false.
188 iterator set_new(int i, const Value& v) {
189 return SetInternal(false, i, v);
190 }
191
192 // Set the value at index i to v.
193 // Fast but unsafe: only use if has_index(i) is true.
194 iterator set_existing(int i, const Value& v) {
195 return SetExistingInternal(i, v);
196 }
197
198 // Get the value at index i.
199 // Fast but unsafe: only use if has_index(i) is true.
200 Value& get_existing(int i) {
201 assert(has_index(i));
202 return dense_[sparse_[i]].value_;
203 }
204 const Value& get_existing(int i) const {
205 assert(has_index(i));
206 return dense_[sparse_[i]].value_;
207 }
208
209 private:
210 iterator SetInternal(bool allow_existing, int i, const Value& v) {
211 DebugCheckInvariants();
212 if (static_cast<uint32_t>(i) >= static_cast<uint32_t>(max_size())) {
213 assert(false && "illegal index");
214 // Semantically, end() would be better here, but we already know
215 // the user did something stupid, so begin() insulates them from
216 // dereferencing an invalid pointer.
217 return begin();
218 }
219 if (!allow_existing) {
220 assert(!has_index(i));
221 create_index(i);
222 } else {
223 if (!has_index(i))
224 create_index(i);
225 }
226 return SetExistingInternal(i, v);
227 }
228
229 iterator SetExistingInternal(int i, const Value& v) {
230 DebugCheckInvariants();
231 assert(has_index(i));
232 dense_[sparse_[i]].value_ = v;
233 DebugCheckInvariants();
234 return dense_.data() + sparse_[i];
235 }
236
237 // Add the index i to the array.
238 // Only use if has_index(i) is known to be false.
239 // Since it doesn't set the value associated with i,
240 // this function is private, only intended as a helper
241 // for other methods.
242 void create_index(int i);
243
244 // In debug mode, verify that some invariant properties of the class
245 // are being maintained. This is called at the end of the constructor
246 // and at the beginning and end of all public non-const member functions.
247 void DebugCheckInvariants() const;
248
249 // Initializes memory for elements [min, max).
250 void MaybeInitializeMemory(int min, int max) {
251#if __has_feature(memory_sanitizer)
252 __msan_unpoison(sparse_.data() + min, (max - min) * sizeof sparse_[0]);
253#elif defined(RE2_ON_VALGRIND)
254 for (int i = min; i < max; i++) {
255 sparse_[i] = 0xababababU;
256 }
257#endif
258 }
259
260 int size_ = 0;
261 PODArray<int> sparse_;
262 PODArray<IndexValue> dense_;
263};
264
265template<typename Value>
266SparseArray<Value>::SparseArray() = default;
267
268template<typename Value>
269SparseArray<Value>::SparseArray(const SparseArray& src)
270 : size_(src.size_),
271 sparse_(src.max_size()),
272 dense_(src.max_size()) {
273 std::copy_n(src.sparse_.data(), src.max_size(), sparse_.data());
274 std::copy_n(src.dense_.data(), src.max_size(), dense_.data());
275}
276
277template<typename Value>
278SparseArray<Value>::SparseArray(SparseArray&& src)
279 : size_(src.size_),
280 sparse_(std::move(src.sparse_)),
281 dense_(std::move(src.dense_)) {
282 src.size_ = 0;
283}
284
285template<typename Value>
286SparseArray<Value>& SparseArray<Value>::operator=(const SparseArray& src) {
287 // Construct these first for exception safety.
288 PODArray<int> a(src.max_size());
289 PODArray<IndexValue> b(src.max_size());
290
291 size_ = src.size_;
292 sparse_ = std::move(a);
293 dense_ = std::move(b);
294 std::copy_n(src.sparse_.data(), src.max_size(), sparse_.data());
295 std::copy_n(src.dense_.data(), src.max_size(), dense_.data());
296 return *this;
297}
298
299template<typename Value>
300SparseArray<Value>& SparseArray<Value>::operator=(SparseArray&& src) {
301 size_ = src.size_;
302 sparse_ = std::move(src.sparse_);
303 dense_ = std::move(src.dense_);
304 src.size_ = 0;
305 return *this;
306}
307
308// IndexValue pairs: exposed in SparseArray::iterator.
309template<typename Value>
310class SparseArray<Value>::IndexValue {
311 public:
312 int index() const { return index_; }
313 Value& value() { return value_; }
314 const Value& value() const { return value_; }
315
316 private:
317 friend class SparseArray;
318 int index_;
319 Value value_;
320};
321
322// Change the maximum size of the array.
323// Invalidates all iterators.
324template<typename Value>
325void SparseArray<Value>::resize(int new_max_size) {
326 DebugCheckInvariants();
327 if (new_max_size > max_size()) {
328 const int old_max_size = max_size();
329
330 // Construct these first for exception safety.
331 PODArray<int> a(new_max_size);
332 PODArray<IndexValue> b(new_max_size);
333
334 std::copy_n(sparse_.data(), old_max_size, a.data());
335 std::copy_n(dense_.data(), old_max_size, b.data());
336
337 sparse_ = std::move(a);
338 dense_ = std::move(b);
339
340 MaybeInitializeMemory(old_max_size, new_max_size);
341 }
342 if (size_ > new_max_size)
343 size_ = new_max_size;
344 DebugCheckInvariants();
345}
346
347// Check whether index i is in the array.
348template<typename Value>
349bool SparseArray<Value>::has_index(int i) const {
350 assert(i >= 0);
351 assert(i < max_size());
352 if (static_cast<uint32_t>(i) >= static_cast<uint32_t>(max_size())) {
353 return false;
354 }
355 // Unsigned comparison avoids checking sparse_[i] < 0.
356 return (uint32_t)sparse_[i] < (uint32_t)size_ &&
357 dense_[sparse_[i]].index_ == i;
358}
359
360template<typename Value>
361void SparseArray<Value>::create_index(int i) {
362 assert(!has_index(i));
363 assert(size_ < max_size());
364 sparse_[i] = size_;
365 dense_[size_].index_ = i;
366 size_++;
367}
368
369template<typename Value> SparseArray<Value>::SparseArray(int max_size) :
370 sparse_(max_size), dense_(max_size) {
371 MaybeInitializeMemory(size_, max_size);
372 DebugCheckInvariants();
373}
374
375template<typename Value> SparseArray<Value>::~SparseArray() {
376 DebugCheckInvariants();
377}
378
379template<typename Value> void SparseArray<Value>::DebugCheckInvariants() const {
380 assert(0 <= size_);
381 assert(size_ <= max_size());
382}
383
384// Comparison function for sorting.
385template<typename Value> bool SparseArray<Value>::less(const IndexValue& a,
386 const IndexValue& b) {
387 return a.index_ < b.index_;
388}
389
390} // namespace re2
391
392#endif // UTIL_SPARSE_ARRAY_H_
393