// 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_(RunningOnValgrindOrMemorySanitizer()) {}
// 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_ = RunningOnValgrindOrMemorySanitizer();
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__