/usr/include/sdsl/rrr_vector.hpp is in libsdsl-dev 2.0.3-4.
This file is owned by root:root, with mode 0o644.
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Copyright (C) 2011-2013 Simon Gog
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/ .
*/
/*! \file rrr_vector.hpp
\brief rrr_vector.hpp contains the sdsl::rrr_vector class, and
classes which support rank and select for rrr_vector.
\author Simon Gog, Matthias Petri
*/
#ifndef INCLUDED_SDSL_RRR_VECTOR
#define INCLUDED_SDSL_RRR_VECTOR
#include "int_vector.hpp"
#include "util.hpp"
#include "rrr_helper.hpp" // for binomial helper class
#include "iterators.hpp"
#include <vector>
#include <algorithm> // for next_permutation
#include <iostream>
//! Namespace for the succinct data structure library
namespace sdsl
{
// forward declaration needed for friend declaration
template<uint8_t t_b=1, uint16_t t_bs=15, class t_rac=int_vector<>, uint16_t t_k=32>
class rank_support_rrr; // in rrr_vector
// forward declaration needed for friend declaration
template<uint8_t t_b=1, uint16_t t_bs=15, class t_rac=int_vector<>, uint16_t t_k=32>
class select_support_rrr; // in rrr_vector
//! A \f$H_0f$-compressed bitvector representation.
/*!
* \tparam t_bs Size of a basic block.
* \tparam t_rac Random access integer vector. Use to store the block types.
* It is possible to use WTs for t_rac.
* \tparam t_k A rank sample value is stored before every t_k-th basic block.
*
* References:
* - Rasmus Pagh
* Low redundancy in dictionaries with O(1) worst case lookup time
* Technical Report 1998.
* ftp://ftp.cs.au.dk/BRICS/Reports/RS/98/28/BRICS-RS-98-28.pdf, Section 2.
* - Rajeev Raman, V. Raman and S. Srinivasa Rao
* Succinct Indexable Dictionaries with Applications to representations
* of k-ary trees and multi-sets.
* SODA 2002.
* - Francisco Claude, Gonzalo Navarro:
* Practical Rank/Select Queries over Arbitrary Sequences.
* SPIRE 2008: 176-187
* - On the fly-decoding and encoding was discovered in;
* Gonzalo Navarro, Eliana Providel:
* Fast, Small, Simple Rank/Select on Bitmaps.
* SEA 2012
*
* In this version the block size can be adjust by the template parameter t_bs!
* \sa sdsl::rrr_vector for a specialized version for block_size=15
*/
template<uint16_t t_bs=63, class t_rac=int_vector<>, uint16_t t_k=32>
class rrr_vector
{
static_assert(t_bs >= 3 and t_bs <= 256 , "rrr_vector: block size t_bs must be 3 <= t_bs <= 256.");
static_assert(t_k > 1, "rrr_vector: t_k must be > 0.");
public:
typedef bit_vector::size_type size_type;
typedef bit_vector::value_type value_type;
typedef bit_vector::difference_type difference_type;
typedef t_rac rac_type;
typedef random_access_const_iterator<rrr_vector> iterator;
typedef bv_tag index_category;
typedef rank_support_rrr<1, t_bs, t_rac, t_k> rank_1_type;
typedef rank_support_rrr<0, t_bs, t_rac, t_k> rank_0_type;
typedef select_support_rrr<1, t_bs, t_rac, t_k> select_1_type;
typedef select_support_rrr<0, t_bs, t_rac, t_k> select_0_type;
friend class rank_support_rrr<0, t_bs, t_rac, t_k>;
friend class rank_support_rrr<1, t_bs, t_rac, t_k>;
friend class select_support_rrr<0, t_bs, t_rac, t_k>;
friend class select_support_rrr<1, t_bs, t_rac, t_k>;
typedef rrr_helper<t_bs> rrr_helper_type;
typedef typename rrr_helper_type::number_type number_type;
enum { block_size = t_bs };
private:
size_type m_size = 0; // Size of the original bit_vector.
rac_type m_bt; // Vector for the block types (bt). bt equals the
// number of set bits in the block.
bit_vector m_btnr; // Compressed block type numbers.
int_vector<> m_btnrp; // Sample pointers into m_btnr.
int_vector<> m_rank; // Sample rank values.
bit_vector m_invert; // Specifies if a superblock (i.e. t_k blocks)
// have to be considered as inverted i.e. 1 and
// 0 are swapped
void copy(const rrr_vector& rrr) {
m_size = rrr.m_size;
m_bt = rrr.m_bt;
m_btnr = rrr.m_btnr;
m_btnrp = rrr.m_btnrp;
m_rank = rrr.m_rank;
m_invert = rrr.m_invert;
}
public:
const rac_type& bt = m_bt;
const bit_vector& btnr = m_btnr;
//! Default constructor
rrr_vector() {};
//! Copy constructor
rrr_vector(const rrr_vector& rrr) {
copy(rrr);
}
//! Move constructor
rrr_vector(rrr_vector&& rrr) : m_size(std::move(rrr.m_size)),
m_bt(std::move(rrr.m_bt)),
m_btnr(std::move(rrr.m_btnr)), m_btnrp(std::move(rrr.m_btnrp)),
m_rank(std::move(rrr.m_rank)), m_invert(std::move(rrr.m_invert)) {}
//! Constructor
/*!
* \param bv Uncompressed bitvector.
* \param k Store rank samples and pointers each k-th blocks.
*/
rrr_vector(const bit_vector& bv) {
m_size = bv.size();
int_vector<> bt_array;
bt_array.width(bits::hi(t_bs)+1);
bt_array.resize((m_size+t_bs)/((size_type)t_bs)); // blocks for the bt_array + a dummy block at the end,
// if m_size%t_bs == 0
// (1) calculate the block types and store them in m_bt
size_type pos = 0, i = 0, x;
size_type btnr_pos = 0;
size_type sum_rank = 0;
while (pos + t_bs <= m_size) { // handle all blocks full blocks
bt_array[ i++ ] = x = rrr_helper_type::get_bt(bv, pos, t_bs);
sum_rank += x;
btnr_pos += rrr_helper_type::space_for_bt(x);
pos += t_bs;
}
if (pos < m_size) { // handle last not full block
bt_array[ i++ ] = x = rrr_helper_type::get_bt(bv, pos, m_size - pos);
sum_rank += x;
btnr_pos += rrr_helper_type::space_for_bt(x);
}
m_btnr = bit_vector(std::max(btnr_pos, (size_type)64), 0); // max necessary for case: t_bs == 1
m_btnrp = int_vector<>((bt_array.size()+t_k-1)/t_k, 0, bits::hi(btnr_pos)+1);
m_rank = int_vector<>((bt_array.size()+t_k-1)/t_k + ((m_size % (t_k*t_bs))>0), 0, bits::hi(sum_rank)+1);
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// only add a finishing block, if the last block of the superblock is not a dummy block
m_invert = bit_vector((bt_array.size()+t_k-1)/t_k, 0);
// (2) calculate block type numbers and pointers into btnr and rank samples
pos = 0; i = 0;
btnr_pos= 0, sum_rank = 0;
bool invert = false;
while (pos + t_bs <= m_size) { // handle all full blocks
if ((i % t_k) == (size_type)0) {
m_btnrp[ i/t_k ] = btnr_pos;
m_rank[ i/t_k ] = sum_rank;
// calculate invert bit for that superblock
if (i+t_k <= bt_array.size()) {
size_type gt_half_t_bs = 0; // counter for blocks greater than half of the blocksize
for (size_type j=i; j < i+t_k; ++j) {
if (bt_array[j] > t_bs/2)
++gt_half_t_bs;
}
if (gt_half_t_bs > (t_k/2)) {
m_invert[ i/t_k ] = 1;
for (size_type j=i; j < i+t_k; ++j) {
bt_array[j] = t_bs - bt_array[j];
}
invert = true;
} else {
invert = false;
}
} else {
invert = false;
}
}
uint16_t space_for_bt = rrr_helper_type::space_for_bt(x=bt_array[i++]);
sum_rank += (invert ? (t_bs - x) : x);
if (space_for_bt) {
number_type bin = rrr_helper_type::decode_btnr(bv, pos, t_bs);
number_type nr = rrr_helper_type::bin_to_nr(bin);
rrr_helper_type::set_bt(m_btnr, btnr_pos, nr, space_for_bt);
}
btnr_pos += space_for_bt;
pos += t_bs;
}
if (pos < m_size) { // handle last not full block
if ((i % t_k) == (size_type)0) {
m_btnrp[ i/t_k ] = btnr_pos;
m_rank[ i/t_k ] = sum_rank;
m_invert[ i/t_k ] = 0; // default: set last block to not inverted
invert = false;
}
uint16_t space_for_bt = rrr_helper_type::space_for_bt(x=bt_array[i++]);
// no extra dummy block added to bt_array, therefore this condition should hold
assert(i == bt_array.size());
sum_rank += invert ? (t_bs - x) : x;
if (space_for_bt) {
number_type bin = rrr_helper_type::decode_btnr(bv, pos, m_size-pos);
number_type nr = rrr_helper_type::bin_to_nr(bin);
rrr_helper_type::set_bt(m_btnr, btnr_pos, nr, space_for_bt);
}
btnr_pos += space_for_bt;
assert(m_rank.size()-1 == ((i+t_k-1)/t_k));
} else { // handle last empty full block
assert(m_rank.size()-1 == ((i+t_k-1)/t_k));
}
// for technical reasons we add a last element to m_rank
m_rank[ m_rank.size()-1 ] = sum_rank; // sum_rank contains the total number of set bits in bv
m_bt = bt_array;
}
//! Swap method
void swap(rrr_vector& rrr) {
if (this != &rrr) {
std::swap(m_size, rrr.m_size);
m_bt.swap(rrr.m_bt);
m_btnr.swap(rrr.m_btnr);
m_btnrp.swap(rrr.m_btnrp);
m_rank.swap(rrr.m_rank);
m_invert.swap(rrr.m_invert);
}
}
//! Accessing the i-th element of the original bit_vector
/*! \param i An index i with \f$ 0 \leq i < size() \f$.
\return The i-th bit of the original bit_vector
*/
value_type operator[](size_type i)const {
size_type bt_idx = i/t_bs;
uint16_t bt = m_bt[bt_idx];
size_type sample_pos = bt_idx/t_k;
if (m_invert[sample_pos])
bt = t_bs - bt;
#ifndef RRR_NO_OPT
if (bt == 0 or bt == t_bs) { // very effective optimization
return bt>0;
}
#endif
uint16_t off = i % t_bs; //i - bt_idx*t_bs;
size_type btnrp = m_btnrp[ sample_pos ];
for (size_type j = sample_pos*t_k; j < bt_idx; ++j) {
btnrp += rrr_helper_type::space_for_bt(m_bt[j]);
}
uint16_t btnrlen = rrr_helper_type::space_for_bt(bt);
number_type btnr = rrr_helper_type::decode_btnr(m_btnr, btnrp, btnrlen);
return rrr_helper_type::decode_bit(bt, btnr, off);
}
//! Get the integer value of the binary string of length len starting at position idx.
/*! \param idx Starting index of the binary representation of the integer.
* \param len Length of the binary representation of the integer. Default value is 64.
* \returns The integer value of the binary string of length len starting at position idx.
*
* \pre idx+len-1 in [0..size()-1]
* \pre len in [1..64]
*/
uint64_t get_int(size_type idx, uint8_t len=64)const {
uint64_t res = 0;
size_type bb_idx = idx/t_bs; // begin block index
size_type bb_off = idx%t_bs; // begin block offset
uint16_t bt = m_bt[bb_idx];
size_type sample_pos = bb_idx/t_k;
size_type eb_idx = (idx+len-1)/t_bs; // end block index
if (bb_idx == eb_idx) { // extract only in one block
if (m_invert[sample_pos])
bt = t_bs - bt;
if (bt == 0) { // all bits are zero
res = 0;
} else if (bt == t_bs and t_bs <= 64) { // all bits are zero
res = bits::lo_set[len];
} else {
size_type btnrp = m_btnrp[ sample_pos ];
for (size_type j = sample_pos*t_k; j < bb_idx; ++j) {
btnrp += rrr_helper_type::space_for_bt(m_bt[j]);
}
uint16_t btnrlen = rrr_helper_type::space_for_bt(bt);
number_type btnr = rrr_helper_type::decode_btnr(m_btnr, btnrp, btnrlen);
res = rrr_helper_type::decode_int(bt, btnr, bb_off, len);
}
} else { // solve multiple block case by recursion
uint16_t b_len = t_bs-bb_off; // remaining bits in first block
uint16_t b_len_sum = 0;
do {
res |= get_int(idx, b_len) << b_len_sum;
idx += b_len;
b_len_sum += b_len;
len -= b_len;
b_len = t_bs;
b_len = std::min((uint16_t)len, b_len);
} while (len > 0);
}
return res;
}
//! Assignment operator
rrr_vector& operator=(const rrr_vector& rrr) {
if (this != &rrr) {
copy(rrr);
}
return *this;
}
//! Move assignment operator
rrr_vector& operator=(rrr_vector&& rrr) {
swap(rrr);
return *this;
}
//! Returns the size of the original bit vector.
size_type size()const {
return m_size;
}
//! Answers select queries
//! Serializes the data structure into the given ostream
size_type serialize(std::ostream& out, structure_tree_node* v=nullptr, std::string name="")const {
structure_tree_node* child = structure_tree::add_child(v, name, util::class_name(*this));
size_type written_bytes = 0;
written_bytes += write_member(m_size, out, child, "size");
written_bytes += m_bt.serialize(out, child, "bt");
written_bytes += m_btnr.serialize(out, child, "btnr");
written_bytes += m_btnrp.serialize(out, child, "btnrp");
written_bytes += m_rank.serialize(out, child, "rank_samples");
written_bytes += m_invert.serialize(out, child, "invert");
structure_tree::add_size(child, written_bytes);
return written_bytes;
}
//! Loads the data structure from the given istream.
void load(std::istream& in) {
read_member(m_size, in);
m_bt.load(in);
m_btnr.load(in);
m_btnrp.load(in);
m_rank.load(in);
m_invert.load(in);
}
iterator begin() const {
return iterator(this, 0);
}
iterator end() const {
return iterator(this, size());
}
};
template<uint8_t t_bit_pattern>
struct rank_support_rrr_trait {
typedef bit_vector::size_type size_type;
static size_type adjust_rank(size_type r, SDSL_UNUSED size_type n) {
return r;
}
};
template<>
struct rank_support_rrr_trait<0> {
typedef bit_vector::size_type size_type;
static size_type adjust_rank(size_type r, size_type n) {
return n - r;
}
};
//! rank_support for the rrr_vector class
/*!
* \tparam t_b The bit pattern of size one. (so `0` or `1`)
* \tparam t_bs The block size of the corresponding rrr_vector
* \tparam t_rac Type used to store the block type in the corresponding rrr_vector.
* TODO: Test if the binary search can be speed up by
* saving the (n/2)-th rank value in T[0], the (n/4)-th in T[1],
* the (3n/4)-th in T[2],... for small number of rank values
* is this called hinted binary search???
* or is this called
*/
template<uint8_t t_b, uint16_t t_bs, class t_rac, uint16_t t_k>
class rank_support_rrr
{
static_assert(t_b == 1u or t_b == 0u , "rank_support_rrr: bit pattern must be `0` or `1`");
public:
typedef rrr_vector<t_bs, t_rac, t_k> bit_vector_type;
typedef typename bit_vector_type::size_type size_type;
typedef typename bit_vector_type::rrr_helper_type rrr_helper_type;
typedef typename rrr_helper_type::number_type number_type;
enum { bit_pat = t_b };
private:
const bit_vector_type* m_v; //!< Pointer to the rank supported rrr_vector
public:
//! Standard constructor
/*! \param v Pointer to the rrr_vector, which should be supported
*/
explicit rank_support_rrr(const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Answers rank queries
/*! \param i Argument for the length of the prefix v[0..i-1], with \f$0\leq i \leq size()\f$.
\returns Number of 1-bits in the prefix [0..i-1] of the original bit_vector.
\par Time complexity
\f$ \Order{ sample\_rate of the rrr\_vector} \f$
*/
const size_type rank(size_type i)const {
assert(m_v != nullptr);
assert(i <= m_v->size());
size_type bt_idx = i/t_bs;
size_type sample_pos = bt_idx/t_k;
size_type btnrp = m_v->m_btnrp[ sample_pos ];
size_type rank = m_v->m_rank[ sample_pos ];
if (sample_pos+1 < m_v->m_rank.size()) {
size_type diff_rank = m_v->m_rank[ sample_pos+1 ] - rank;
#ifndef RRR_NO_OPT
if (diff_rank == (size_type)0) {
return rank_support_rrr_trait<t_b>::adjust_rank(rank, i);
} else if (diff_rank == (size_type)t_bs*t_k) {
return rank_support_rrr_trait<t_b>::adjust_rank(
rank + i - sample_pos*t_k*t_bs, i);
}
#endif
}
const bool inv = m_v->m_invert[ sample_pos ];
for (size_type j = sample_pos*t_k; j < bt_idx; ++j) {
uint16_t r = m_v->m_bt[j];
rank += (inv ? t_bs - r: r);
btnrp += rrr_helper_type::space_for_bt(r);
}
uint16_t off = i % t_bs;
if (!off) { // needed for special case: if i=size() is a multiple of t_bs
// the access to m_bt would cause a invalid memory access
return rank_support_rrr_trait<t_b>::adjust_rank(rank, i);
}
uint16_t bt = inv ? t_bs - m_v->m_bt[ bt_idx ] : m_v->m_bt[ bt_idx ];
uint16_t btnrlen = rrr_helper_type::space_for_bt(bt);
number_type btnr = rrr_helper_type::decode_btnr(m_v->m_btnr, btnrp, btnrlen);
uint16_t popcnt = rrr_helper_type::decode_popcount(bt, btnr, off);
return rank_support_rrr_trait<t_b>::adjust_rank(rank + popcnt, i);
}
//! Short hand for rank(i)
const size_type operator()(size_type i)const {
return rank(i);
}
//! Returns the size of the original vector
const size_type size()const {
return m_v->size();
}
//! Set the supported vector.
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
rank_support_rrr& operator=(const rank_support_rrr& rs) {
if (this != &rs) {
set_vector(rs.m_v);
}
return *this;
}
void swap(rank_support_rrr&) { }
//! Load the data structure from a stream and set the supported vector.
void load(std::istream&, const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Serializes the data structure into a stream.
size_type serialize(std::ostream&, structure_tree_node* v=nullptr, std::string name="")const {
structure_tree_node* child = structure_tree::add_child(v, name, util::class_name(*this));
structure_tree::add_size(child, 0);
return 0;
}
};
//! Select support for the rrr_vector class.
/*
* \tparam t_b The bit pattern of size one. (so `0` or `1`)
* \tparam t_bs The block size of the corresponding rrr_vector
* \tparam t_rac Type used to store the block type in the corresponding rrr_vector.
*
* Possible TODO: Add heap which contains the 10 first items of
* each binary search could increase performance.
* Experiments on select_support_interleaved showed about
* 25%.
*/
template<uint8_t t_b, uint16_t t_bs, class t_rac, uint16_t t_k>
class select_support_rrr
{
static_assert(t_b == 1u or t_b == 0u , "select_support_rrr: bit pattern must be `0` or `1`");
public:
typedef rrr_vector<t_bs, t_rac, t_k> bit_vector_type;
typedef typename bit_vector_type::size_type size_type;
typedef typename bit_vector_type::rrr_helper_type rrr_helper_type;
typedef typename rrr_helper_type::number_type number_type;
enum { bit_pat = t_b };
private:
const bit_vector_type* m_v; //!< Pointer to the rank supported rrr_vector
size_type select1(size_type i)const {
if (m_v->m_rank[m_v->m_rank.size()-1] < i)
return size();
// (1) binary search for the answer in the rank_samples
size_type begin=0, end=m_v->m_rank.size()-1; // min included, max excluded
size_type idx, rank;
// invariant: m_rank[end] >= i
// m_rank[begin] < i
while (end-begin > 1) {
idx = (begin+end) >> 1; // idx in [0..m_rank.size()-1]
rank = m_v->m_rank[idx];
if (rank >= i)
end = idx;
else { // rank < i
begin = idx;
}
}
// (2) linear search between the samples
rank = m_v->m_rank[begin]; // now i>rank
idx = begin * t_k; // initialize idx for select result
size_type diff_rank = m_v->m_rank[end] - rank;
#ifndef RRR_NO_OPT
if (diff_rank == (size_type)t_bs*t_k) {// optimisation for select<1>
return idx*t_bs + i-rank -1;
}
#endif
const bool inv = m_v->m_invert[ begin ];
size_type btnrp = m_v->m_btnrp[ begin ];
uint16_t bt = 0, btnrlen = 0; // temp variables for block_type and space for block type
while (i > rank) {
bt = m_v->m_bt[idx++]; bt = inv ? t_bs-bt : bt;
rank += bt;
btnrp += (btnrlen=rrr_helper_type::space_for_bt(bt));
}
rank -= bt;
number_type btnr = rrr_helper_type::decode_btnr(m_v->m_btnr, btnrp-btnrlen, btnrlen);
return (idx-1) * t_bs + rrr_helper_type::decode_select(bt, btnr, i-rank);
}
size_type select0(size_type i)const {
if ((size() - m_v->m_rank[m_v->m_rank.size()-1]) < i) {
return size();
}
// (1) binary search for the answer in the rank_samples
size_type begin=0, end=m_v->m_rank.size()-1; // min included, max excluded
size_type idx, rank;
// invariant: m_rank[end] >= i
// m_rank[begin] < i
while (end-begin > 1) {
idx = (begin+end) >> 1; // idx in [0..m_rank.size()-1]
rank = idx*t_bs*t_k - m_v->m_rank[idx];
if (rank >= i)
end = idx;
else { // rank < i
begin = idx;
}
}
// (2) linear search between the samples
rank = begin*t_bs*t_k - m_v->m_rank[begin]; // now i>rank
idx = begin * t_k; // initialize idx for select result
if (m_v->m_rank[end] == m_v->m_rank[begin]) { // only for select<0>
return idx*t_bs + i-rank -1;
}
const bool inv = m_v->m_invert[ begin ];
size_type btnrp = m_v->m_btnrp[ begin ];
uint16_t bt = 0, btnrlen = 0; // temp variables for block_type and space for block type
while (i > rank) {
bt = m_v->m_bt[idx++]; bt = inv ? t_bs-bt : bt;
rank += (t_bs-bt);
btnrp += (btnrlen=rrr_helper_type::space_for_bt(bt));
}
rank -= (t_bs-bt);
number_type btnr = rrr_helper_type::decode_btnr(m_v->m_btnr, btnrp-btnrlen, btnrlen);
return (idx-1) * t_bs + rrr_helper_type::template decode_select_bitpattern<0, 1>(bt, btnr, i-rank);
}
public:
explicit select_support_rrr(const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Answers select queries
size_type select(size_type i)const {
return t_b ? select1(i) : select0(i);
}
const size_type operator()(size_type i)const {
return select(i);
}
const size_type size()const {
return m_v->size();
}
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
select_support_rrr& operator=(const select_support_rrr& rs) {
if (this != &rs) {
set_vector(rs.m_v);
}
return *this;
}
void swap(select_support_rrr&) { }
void load(std::istream&, const bit_vector_type* v=nullptr) {
set_vector(v);
}
size_type serialize(std::ostream&, structure_tree_node* v=nullptr, std::string name="")const {
structure_tree_node* child = structure_tree::add_child(v, name, util::class_name(*this));
structure_tree::add_size(child, 0);
return 0;
}
};
}// end namespace sdsl
#include "rrr_vector_15.hpp" // include specialization
#endif
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