// Copyright 2006 The RE2 Authors. All Rights Reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // DESCRIPTION // // SparseArray<T>(m) is a map from integers in [0, m) to T values. // It requires (sizeof(T)+sizeof(int))*m memory, but it provides // fast iteration through the elements in the array and fast clearing // of the array. The array has a concept of certain elements being // uninitialized (having no value). // // Insertion and deletion are constant time operations. // // Allocating the array is a constant time operation // when memory allocation is a constant time operation. // // Clearing the array is a constant time operation (unusual!). // // Iterating through the array is an O(n) operation, where n // is the number of items in the array (not O(m)). // // The array iterator visits entries in the order they were first // inserted into the array. It is safe to add items to the array while // using an iterator: the iterator will visit indices added to the array // during the iteration, but will not re-visit indices whose values // change after visiting. Thus SparseArray can be a convenient // implementation of a work queue. // // The SparseArray implementation is NOT thread-safe. It is up to the // caller to make sure only one thread is accessing the array. (Typically // these arrays are temporary values and used in situations where speed is // important.) // // The SparseArray interface does not present all the usual STL bells and // whistles. // // Implemented with reference to Briggs & Torczon, An Efficient // Representation for Sparse Sets, ACM Letters on Programming Languages // and Systems, Volume 2, Issue 1-4 (March-Dec. 1993), pp. 59-69. // // Briggs & Torczon popularized this technique, but it had been known // long before their paper. They point out that Aho, Hopcroft, and // Ullman's 1974 Design and Analysis of Computer Algorithms and Bentley's // 1986 Programming Pearls both hint at the technique in exercises to the // reader (in Aho & Hopcroft, exercise 2.12; in Bentley, column 1 // exercise 8). // // Briggs & Torczon describe a sparse set implementation. I have // trivially generalized it to create a sparse array (actually the original // target of the AHU and Bentley exercises). // IMPLEMENTATION // // SparseArray uses a vector dense_ and an array sparse_to_dense_, both of // size max_size_. At any point, the number of elements in the sparse array is // size_. // // The vector dense_ contains the size_ elements in the sparse array (with // their indices), // in the order that the elements were first inserted. This array is dense: // the size_ pairs are dense_[0] through dense_[size_-1]. // // The array sparse_to_dense_ maps from indices in [0,m) to indices in // [0,size_). // For indices present in the array, dense_[sparse_to_dense_[i]].index_ == i. // For indices not present in the array, sparse_to_dense_ can contain // any value at all, perhaps outside the range [0, size_) but perhaps not. // // The lax requirement on sparse_to_dense_ values makes clearing // the array very easy: set size_ to 0. Lookups are slightly more // complicated. An index i has a value in the array if and only if: // sparse_to_dense_[i] is in [0, size_) AND // dense_[sparse_to_dense_[i]].index_ == i. // If both these properties hold, only then it is safe to refer to // dense_[sparse_to_dense_[i]].value_ // as the value associated with index i. // // To insert a new entry, set sparse_to_dense_[i] to size_, // initialize dense_[size_], and then increment size_. // // Deletion of specific values from the array is implemented by // swapping dense_[size_-1] and the dense_ being deleted and then // updating the appropriate sparse_to_dense_ entries. // // To make the sparse array as efficient as possible for non-primitive types, // elements may or may not be destroyed when they are deleted from the sparse // array through a call to erase(), erase_existing() or resize(). They // immediately become inaccessible, but they are only guaranteed to be // destroyed when the SparseArray destructor is called. #ifndef RE2_UTIL_SPARSE_ARRAY_H__ #define RE2_UTIL_SPARSE_ARRAY_H__ #include "util/util.h" namespace re2 { template<typename Value> class SparseArray { public: SparseArray(); SparseArray(int max_size); ~SparseArray(); // IndexValue pairs: exposed in SparseArray::iterator. class IndexValue; typedef IndexValue value_type; typedef typename vector<IndexValue>::iterator iterator; typedef typename vector<IndexValue>::const_iterator const_iterator; inline const IndexValue& iv(int i) const; // Return the number of entries in the array. int size() const { return size_; } // Iterate over the array. iterator begin() { return dense_.begin(); } iterator end() { return dense_.begin() + size_; } const_iterator begin() const { return dense_.begin(); } const_iterator end() const { return dense_.begin() + size_; } // Change the maximum size of the array. // Invalidates all iterators. void resize(int max_size); // Return the maximum size of the array. // Indices can be in the range [0, max_size). int max_size() const { return max_size_; } // Clear the array. void clear() { size_ = 0; } // Check whether index i is in the array. inline bool has_index(int i) const; // Comparison function for sorting. // Can sort the sparse array so that future iterations // will visit indices in increasing order using // sort(arr.begin(), arr.end(), arr.less); static bool less(const IndexValue& a, const IndexValue& b); public: // Set the value at index i to v. inline iterator set(int i, Value v); pair<iterator, bool> insert(const value_type& new_value); // Returns the value at index i // or defaultv if index i is not initialized in the array. inline Value get(int i, Value defaultv) const; iterator find(int i); const_iterator find(int i) const; // Change the value at index i to v. // Fast but unsafe: only use if has_index(i) is true. inline iterator set_existing(int i, Value v); // Set the value at the new index i to v. // Fast but unsafe: only use if has_index(i) is false. inline iterator set_new(int i, Value v); // Get the value at index i from the array.. // Fast but unsafe: only use if has_index(i) is true. inline Value get_existing(int i) const; // Erasing items from the array during iteration is in general // NOT safe. There is one special case, which is that the current // index-value pair can be erased as long as the iterator is then // checked for being at the end before being incremented. // For example: // // for (i = m.begin(); i != m.end(); ++i) { // if (ShouldErase(i->index(), i->value())) { // m.erase(i->index()); // --i; // } // } // // Except in the specific case just described, elements must // not be erased from the array (including clearing the array) // while iterators are walking over the array. Otherwise, // the iterators could walk past the end of the array. // Erases the element at index i from the array. inline void erase(int i); // Erases the element at index i from the array. // Fast but unsafe: only use if has_index(i) is true. inline void erase_existing(int i); private: // Add the index i to the array. // Only use if has_index(i) is known to be false. // Since it doesn't set the value associated with i, // this function is private, only intended as a helper // for other methods. inline void create_index(int i); // In debug mode, verify that some invariant properties of the class // are being maintained. This is called at the end of the constructor // and at the beginning and end of all public non-const member functions. inline void DebugCheckInvariants() const; int size_; int max_size_; int* sparse_to_dense_; vector<IndexValue> dense_; bool valgrind_; DISALLOW_EVIL_CONSTRUCTORS(SparseArray); }; template<typename Value> SparseArray<Value>::SparseArray() : size_(0), max_size_(0), sparse_to_dense_(NULL), dense_(), valgrind_(RunningOnValgrind()) {} // IndexValue pairs: exposed in SparseArray::iterator. template<typename Value> class SparseArray<Value>::IndexValue { friend class SparseArray; public: typedef int first_type; typedef Value second_type; IndexValue() {} IndexValue(int index, const Value& value) : second(value), index_(index) {} int index() const { return index_; } Value value() const { return second; } // Provide the data in the 'second' member so that the utilities // in map-util work. Value second; private: int index_; }; template<typename Value> const typename SparseArray<Value>::IndexValue& SparseArray<Value>::iv(int i) const { DCHECK_GE(i, 0); DCHECK_LT(i, size_); return dense_[i]; } // Change the maximum size of the array. // Invalidates all iterators. template<typename Value> void SparseArray<Value>::resize(int new_max_size) { DebugCheckInvariants(); if (new_max_size > max_size_) { int* a = new int[new_max_size]; if (sparse_to_dense_) { memmove(a, sparse_to_dense_, max_size_*sizeof a[0]); // Don't need to zero the memory but appease Valgrind. if (valgrind_) { for (int i = max_size_; i < new_max_size; i++) a[i] = 0xababababU; } delete[] sparse_to_dense_; } sparse_to_dense_ = a; dense_.resize(new_max_size); } max_size_ = new_max_size; if (size_ > max_size_) size_ = max_size_; DebugCheckInvariants(); } // Check whether index i is in the array. template<typename Value> bool SparseArray<Value>::has_index(int i) const { DCHECK_GE(i, 0); DCHECK_LT(i, max_size_); if (static_cast<uint>(i) >= max_size_) { return false; } // Unsigned comparison avoids checking sparse_to_dense_[i] < 0. return (uint)sparse_to_dense_[i] < (uint)size_ && dense_[sparse_to_dense_[i]].index_ == i; } // Set the value at index i to v. template<typename Value> typename SparseArray<Value>::iterator SparseArray<Value>::set(int i, Value v) { DebugCheckInvariants(); if (static_cast<uint>(i) >= max_size_) { // Semantically, end() would be better here, but we already know // the user did something stupid, so begin() insulates them from // dereferencing an invalid pointer. return begin(); } if (!has_index(i)) create_index(i); return set_existing(i, v); } template<typename Value> pair<typename SparseArray<Value>::iterator, bool> SparseArray<Value>::insert( const value_type& new_value) { DebugCheckInvariants(); pair<typename SparseArray<Value>::iterator, bool> p; if (has_index(new_value.index_)) { p = make_pair(dense_.begin() + sparse_to_dense_[new_value.index_], false); } else { p = make_pair(set_new(new_value.index_, new_value.second), true); } DebugCheckInvariants(); return p; } template<typename Value> Value SparseArray<Value>::get(int i, Value defaultv) const { if (!has_index(i)) return defaultv; return get_existing(i); } template<typename Value> typename SparseArray<Value>::iterator SparseArray<Value>::find(int i) { if (has_index(i)) return dense_.begin() + sparse_to_dense_[i]; return end(); } template<typename Value> typename SparseArray<Value>::const_iterator SparseArray<Value>::find(int i) const { if (has_index(i)) { return dense_.begin() + sparse_to_dense_[i]; } return end(); } template<typename Value> typename SparseArray<Value>::iterator SparseArray<Value>::set_existing(int i, Value v) { DebugCheckInvariants(); DCHECK(has_index(i)); dense_[sparse_to_dense_[i]].second = v; DebugCheckInvariants(); return dense_.begin() + sparse_to_dense_[i]; } template<typename Value> typename SparseArray<Value>::iterator SparseArray<Value>::set_new(int i, Value v) { DebugCheckInvariants(); if (static_cast<uint>(i) >= max_size_) { // Semantically, end() would be better here, but we already know // the user did something stupid, so begin() insulates them from // dereferencing an invalid pointer. return begin(); } DCHECK(!has_index(i)); create_index(i); return set_existing(i, v); } template<typename Value> Value SparseArray<Value>::get_existing(int i) const { DCHECK(has_index(i)); return dense_[sparse_to_dense_[i]].second; } template<typename Value> void SparseArray<Value>::erase(int i) { DebugCheckInvariants(); if (has_index(i)) erase_existing(i); DebugCheckInvariants(); } template<typename Value> void SparseArray<Value>::erase_existing(int i) { DebugCheckInvariants(); DCHECK(has_index(i)); int di = sparse_to_dense_[i]; if (di < size_ - 1) { dense_[di] = dense_[size_ - 1]; sparse_to_dense_[dense_[di].index_] = di; } size_--; DebugCheckInvariants(); } template<typename Value> void SparseArray<Value>::create_index(int i) { DCHECK(!has_index(i)); DCHECK_LT(size_, max_size_); sparse_to_dense_[i] = size_; dense_[size_].index_ = i; size_++; } template<typename Value> SparseArray<Value>::SparseArray(int max_size) { max_size_ = max_size; sparse_to_dense_ = new int[max_size]; valgrind_ = RunningOnValgrind(); dense_.resize(max_size); // Don't need to zero the new memory, but appease Valgrind. if (valgrind_) { for (int i = 0; i < max_size; i++) { sparse_to_dense_[i] = 0xababababU; dense_[i].index_ = 0xababababU; } } size_ = 0; DebugCheckInvariants(); } template<typename Value> SparseArray<Value>::~SparseArray() { DebugCheckInvariants(); delete[] sparse_to_dense_; } template<typename Value> void SparseArray<Value>::DebugCheckInvariants() const { DCHECK_LE(0, size_); DCHECK_LE(size_, max_size_); DCHECK(size_ == 0 || sparse_to_dense_ != NULL); } // Comparison function for sorting. template<typename Value> bool SparseArray<Value>::less(const IndexValue& a, const IndexValue& b) { return a.index_ < b.index_; } } // namespace re2 #endif // RE2_UTIL_SPARSE_ARRAY_H__