// 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.
#ifndef RE2_SPARSE_ARRAY_H_
#define RE2_SPARSE_ARRAY_H_
// 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 is an array dense_ and an array sparse_ of identical size.
// At any point, the number of elements in the sparse array is size_.
//
// The array 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_ maps from indices in [0,m) to indices in [0,size_).
// For indices present in the array, dense_[sparse_[i]].index_ == i.
// For indices not present in the array, sparse_ can contain any value at all,
// perhaps outside the range [0, size_) but perhaps not.
//
// The lax requirement on sparse_ 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_[i] is in [0, size_) AND
// dense_[sparse_[i]].index_ == i.
// If both these properties hold, only then it is safe to refer to
// dense_[sparse_[i]].value_
// as the value associated with index i.
//
// To insert a new entry, set sparse_[i] to size_,
// initialize dense_[size_], and then increment size_.
//
// 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 resize(). They immediately become inaccessible, but
// they are only guaranteed to be destroyed when the SparseArray destructor is
// called.
//
// A moved-from SparseArray will be empty.
// Doing this simplifies the logic below.
#ifndef __has_feature
#define __has_feature(x) 0
#endif
#include <assert.h>
#include <stdint.h>
#if __has_feature(memory_sanitizer)
#include <sanitizer/msan_interface.h>
#endif
#include <algorithm>
#include <memory>
#include <utility>
#include "re2/pod_array.h"
namespace re2 {
template<typename Value>
class SparseArray {
public:
SparseArray();
explicit SparseArray(int max_size);
~SparseArray();
// IndexValue pairs: exposed in SparseArray::iterator.
class IndexValue;
typedef IndexValue* iterator;
typedef const IndexValue* const_iterator;
SparseArray(const SparseArray& src);
SparseArray(SparseArray&& src);
SparseArray& operator=(const SparseArray& src);
SparseArray& operator=(SparseArray&& src);
// Return the number of entries in the array.
int size() const {
return size_;
}
// Indicate whether the array is empty.
int empty() const {
return size_ == 0;
}
// Iterate over the array.
iterator begin() {
return dense_.data();
}
iterator end() {
return dense_.data() + size_;
}
const_iterator begin() const {
return dense_.data();
}
const_iterator end() const {
return dense_.data() + size_;
}
// Change the maximum size of the array.
// Invalidates all iterators.
void resize(int new_max_size);
// Return the maximum size of the array.
// Indices can be in the range [0, max_size).
int max_size() const {
if (dense_.data() != NULL)
return dense_.size();
else
return 0;
}
// Clear the array.
void clear() {
size_ = 0;
}
// Check whether index i is in the array.
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
// std::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.
iterator set(int i, const Value& v) {
return SetInternal(true, i, v);
}
// Set the value at new index i to v.
// Fast but unsafe: only use if has_index(i) is false.
iterator set_new(int i, const Value& v) {
return SetInternal(false, i, v);
}
// Set the value at index i to v.
// Fast but unsafe: only use if has_index(i) is true.
iterator set_existing(int i, const Value& v) {
return SetExistingInternal(i, v);
}
// Get the value at index i.
// Fast but unsafe: only use if has_index(i) is true.
Value& get_existing(int i) {
assert(has_index(i));
return dense_[sparse_[i]].value_;
}
const Value& get_existing(int i) const {
assert(has_index(i));
return dense_[sparse_[i]].value_;
}
private:
iterator SetInternal(bool allow_existing, int i, const Value& v) {
DebugCheckInvariants();
if (static_cast<uint32_t>(i) >= static_cast<uint32_t>(max_size())) {
assert(false && "illegal index");
// 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 (!allow_existing) {
assert(!has_index(i));
create_index(i);
} else {
if (!has_index(i))
create_index(i);
}
return SetExistingInternal(i, v);
}
iterator SetExistingInternal(int i, const Value& v) {
DebugCheckInvariants();
assert(has_index(i));
dense_[sparse_[i]].value_ = v;
DebugCheckInvariants();
return dense_.data() + sparse_[i];
}
// 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.
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.
void DebugCheckInvariants() const;
// Initializes memory for elements [min, max).
void MaybeInitializeMemory(int min, int max) {
#if __has_feature(memory_sanitizer)
__msan_unpoison(sparse_.data() + min, (max - min) * sizeof sparse_[0]);
#elif defined(RE2_ON_VALGRIND)
for (int i = min; i < max; i++) {
sparse_[i] = 0xababababU;
}
#endif
}
int size_ = 0;
PODArray<int> sparse_;
PODArray<IndexValue> dense_;
};
template<typename Value>
SparseArray<Value>::SparseArray() = default;
template<typename Value>
SparseArray<Value>::SparseArray(const SparseArray& src)
: size_(src.size_),
sparse_(src.max_size()),
dense_(src.max_size()) {
std::copy_n(src.sparse_.data(), src.max_size(), sparse_.data());
std::copy_n(src.dense_.data(), src.max_size(), dense_.data());
}
template<typename Value>
SparseArray<Value>::SparseArray(SparseArray&& src)
: size_(src.size_),
sparse_(std::move(src.sparse_)),
dense_(std::move(src.dense_)) {
src.size_ = 0;
}
template<typename Value>
SparseArray<Value>& SparseArray<Value>::operator=(const SparseArray& src) {
// Construct these first for exception safety.
PODArray<int> a(src.max_size());
PODArray<IndexValue> b(src.max_size());
size_ = src.size_;
sparse_ = std::move(a);
dense_ = std::move(b);
std::copy_n(src.sparse_.data(), src.max_size(), sparse_.data());
std::copy_n(src.dense_.data(), src.max_size(), dense_.data());
return *this;
}
template<typename Value>
SparseArray<Value>& SparseArray<Value>::operator=(SparseArray&& src) {
size_ = src.size_;
sparse_ = std::move(src.sparse_);
dense_ = std::move(src.dense_);
src.size_ = 0;
return *this;
}
// IndexValue pairs: exposed in SparseArray::iterator.
template<typename Value>
class SparseArray<Value>::IndexValue {
public:
int index() const { return index_; }
Value& value() { return value_; }
const Value& value() const { return value_; }
private:
friend class SparseArray;
int index_;
Value value_;
};
// 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()) {
const int old_max_size = max_size();
// Construct these first for exception safety.
PODArray<int> a(new_max_size);
PODArray<IndexValue> b(new_max_size);
std::copy_n(sparse_.data(), old_max_size, a.data());
std::copy_n(dense_.data(), old_max_size, b.data());
sparse_ = std::move(a);
dense_ = std::move(b);
MaybeInitializeMemory(old_max_size, new_max_size);
}
if (size_ > new_max_size)
size_ = new_max_size;
DebugCheckInvariants();
}
// Check whether index i is in the array.
template<typename Value>
bool SparseArray<Value>::has_index(int i) const {
assert(i >= 0);
assert(i < max_size());
if (static_cast<uint32_t>(i) >= static_cast<uint32_t>(max_size())) {
return false;
}
// Unsigned comparison avoids checking sparse_[i] < 0.
return (uint32_t)sparse_[i] < (uint32_t)size_ &&
dense_[sparse_[i]].index_ == i;
}
template<typename Value>
void SparseArray<Value>::create_index(int i) {
assert(!has_index(i));
assert(size_ < max_size());
sparse_[i] = size_;
dense_[size_].index_ = i;
size_++;
}
template<typename Value> SparseArray<Value>::SparseArray(int max_size) :
sparse_(max_size), dense_(max_size) {
MaybeInitializeMemory(size_, max_size);
DebugCheckInvariants();
}
template<typename Value> SparseArray<Value>::~SparseArray() {
DebugCheckInvariants();
}
template<typename Value> void SparseArray<Value>::DebugCheckInvariants() const {
assert(0 <= size_);
assert(size_ <= max_size());
}
// 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_SPARSE_ARRAY_H_