Вот относительно простая реализация, которая должна обеспечить разумный быстрый поиск (с использованием хэш-таблицы), а также быструю итерацию по ненулевым элементам в строке / столбце.
// Copyright 2014 Leo Osvald
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#ifndef UTIL_IMMUTABLE_SPARSE_MATRIX_HPP_
#define UTIL_IMMUTABLE_SPARSE_MATRIX_HPP_
#include <algorithm>
#include <limits>
#include <map>
#include <type_traits>
#include <unordered_map>
#include <utility>
#include <vector>
// A simple time-efficient implementation of an immutable sparse matrix
// Provides efficient iteration of non-zero elements by rows/cols,
// e.g. to iterate over a range [row_from, row_to) x [col_from, col_to):
// for (int row = row_from; row < row_to; ++row) {
// for (auto col_range = sm.nonzero_col_range(row, col_from, col_to);
// col_range.first != col_range.second; ++col_range.first) {
// int col = *col_range.first;
// // use sm(row, col)
// ...
// }
template<typename T = double, class Coord = int>
class SparseMatrix {
struct PointHasher;
typedef std::map< Coord, std::vector<Coord> > NonZeroList;
typedef std::pair<Coord, Coord> Point;
public:
typedef T ValueType;
typedef Coord CoordType;
typedef typename NonZeroList::mapped_type::const_iterator CoordIter;
typedef std::pair<CoordIter, CoordIter> CoordIterRange;
SparseMatrix() = default;
// Reads a matrix stored in MatrixMarket-like format, i.e.:
// <num_rows> <num_cols> <num_entries>
// <row_1> <col_1> <val_1>
// ...
// Note: the header (lines starting with '%' are ignored).
template<class InputStream, size_t max_line_length = 1024>
void Init(InputStream& is) {
rows_.clear(), cols_.clear();
values_.clear();
// skip the header (lines beginning with '%', if any)
decltype(is.tellg()) offset = 0;
for (char buf[max_line_length + 1];
is.getline(buf, sizeof(buf)) && buf[0] == '%'; )
offset = is.tellg();
is.seekg(offset);
size_t n;
is >> row_count_ >> col_count_ >> n;
values_.reserve(n);
while (n--) {
Coord row, col;
typename std::remove_cv<T>::type val;
is >> row >> col >> val;
values_[Point(--row, --col)] = val;
rows_[col].push_back(row);
cols_[row].push_back(col);
}
SortAndShrink(rows_);
SortAndShrink(cols_);
}
const T& operator()(const Coord& row, const Coord& col) const {
static const T kZero = T();
auto it = values_.find(Point(row, col));
if (it != values_.end())
return it->second;
return kZero;
}
CoordIterRange
nonzero_col_range(Coord row, Coord col_from, Coord col_to) const {
CoordIterRange r;
GetRange(cols_, row, col_from, col_to, &r);
return r;
}
CoordIterRange
nonzero_row_range(Coord col, Coord row_from, Coord row_to) const {
CoordIterRange r;
GetRange(rows_, col, row_from, row_to, &r);
return r;
}
Coord row_count() const { return row_count_; }
Coord col_count() const { return col_count_; }
size_t nonzero_count() const { return values_.size(); }
size_t element_count() const { return size_t(row_count_) * col_count_; }
private:
typedef std::unordered_map<Point,
typename std::remove_cv<T>::type,
PointHasher> ValueMap;
struct PointHasher {
size_t operator()(const Point& p) const {
return p.first << (std::numeric_limits<Coord>::digits >> 1) ^ p.second;
}
};
static void SortAndShrink(NonZeroList& list) {
for (auto& it : list) {
auto& indices = it.second;
indices.shrink_to_fit();
std::sort(indices.begin(), indices.end());
}
// insert a sentinel vector to handle the case of all zeroes
if (list.empty())
list.emplace(Coord(), std::vector<Coord>(Coord()));
}
static void GetRange(const NonZeroList& list, Coord i, Coord from, Coord to,
CoordIterRange* r) {
auto lr = list.equal_range(i);
if (lr.first == lr.second) {
r->first = r->second = list.begin()->second.end();
return;
}
auto begin = lr.first->second.begin(), end = lr.first->second.end();
r->first = lower_bound(begin, end, from);
r->second = lower_bound(r->first, end, to);
}
ValueMap values_;
NonZeroList rows_, cols_;
Coord row_count_, col_count_;
};
#endif /* UTIL_IMMUTABLE_SPARSE_MATRIX_HPP_ */
Для простоты это immutable, но вы можете сделать его изменчивым; Обязательно измените std::vector на std::set, если вы хотите разумные эффективные "вставки" (с заменой нуля на ненулевой).