/usr/include/sdsl/sd_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) 2012-2014 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 sd_vector.hpp
\brief sd_vector.hpp contains the sdsl::sd_vector class, and
classes which support rank and select for sd_vector.
\author Simon Gog
*/
#ifndef INCLUDED_SDSL_SD_VECTOR
#define INCLUDED_SDSL_SD_VECTOR
#include "int_vector.hpp"
#include "select_support_mcl.hpp"
#include "util.hpp"
#include "iterators.hpp"
//! Namespace for the succinct data structure library
namespace sdsl
{
// forward declaration needed for friend declaration
template<uint8_t t_b = 1,
class t_hi_bit_vector= bit_vector,
class t_select_1 = typename t_hi_bit_vector::select_1_type,
class t_select_0 = typename t_hi_bit_vector::select_0_type>
class rank_support_sd; // in sd_vector
// forward declaration needed for friend declaration
template<uint8_t t_b = 1,
class t_hi_bit_vector= bit_vector,
class t_select_1 = typename t_hi_bit_vector::select_1_type,
class t_select_0 = typename t_hi_bit_vector::select_0_type>
class select_support_sd; // in sd_vector
//! A bit vector which compresses very sparse populated bit vectors by
// representing the positions of 1 by the Elias-Fano representation for non-decreasing sequences
/*!
* \par Other implementations of this data structure:
* - the sdarray of Okanohara and Sadakane
* - Sebastiano Vigna implemented a elias_fano class in this sux library.
*
* \par References
* - P. Elias: ,,Efficient storage and retrieval by content and address of static files'',
* Journal of the ACM, 1974
* - R. Fano: ,,On the number of bits required to implement an associative memory''.
* Memorandum 61. Computer Structures Group, Project MAC, MIT, 1971
* - D. Okanohara, K. Sadakane: ,,Practical Entropy-Compressed Rank/Select Dictionary'',
* Proceedings of ALENEX 2007.
*
* \tparam t_hi_bit_vector Type of the bitvector used for the unary decoded differences of
* the high part of the positions of the 1s.
* \tparam t_select_1 Type of the select structure which is used to select ones in HI.
* \tparam t_select_0 Type of the select structure which is used to select zeros in HI.
*/
template<class t_hi_bit_vector = bit_vector,
class t_select_1 = typename t_hi_bit_vector::select_1_type,
class t_select_0 = typename t_hi_bit_vector::select_0_type>
class sd_vector
{
public:
typedef bit_vector::size_type size_type;
typedef size_type value_type;
typedef bit_vector::difference_type difference_type;
typedef random_access_const_iterator<sd_vector> iterator;
typedef bv_tag index_category;
typedef t_select_0 select_0_support_type;
typedef t_select_1 select_1_support_type;
typedef rank_support_sd<0, t_hi_bit_vector, select_1_support_type, select_0_support_type> rank_0_type;
typedef rank_support_sd<1, t_hi_bit_vector, select_1_support_type, select_0_support_type> rank_1_type;
typedef select_support_sd<0, t_hi_bit_vector, select_1_support_type, select_0_support_type> select_0_type;
typedef select_support_sd<1, t_hi_bit_vector, select_1_support_type, select_0_support_type> select_1_type;
typedef t_hi_bit_vector hi_bit_vector_type;
private:
// we need this variables to represent the m ones of the original bit vector of size n
size_type m_size = 0; // length of the original bit vector
uint8_t m_wl = 0; // log n - log m, where n is the length of the original bit vector
// and m is the number of ones in the bit vector, wl is the abbreviation
// for ,,width (of) low (part)''
int_vector<> m_low; // vector for the least significant bits of the positions of the m ones
hi_bit_vector_type m_high; // bit vector that represents the most significant bit in permuted order
select_1_support_type m_high_1_select; // select support for the ones in m_high
select_0_support_type m_high_0_select; // select support for the zeros in m_high
void copy(const sd_vector& v) {
m_size = v.m_size;
m_wl = v.m_wl;
m_low = v.m_low;
m_high = v.m_high;
m_high_1_select = v.m_high_1_select;
m_high_1_select.set_vector(&m_high);
m_high_0_select = v.m_high_0_select;
m_high_0_select.set_vector(&m_high);
}
public:
const uint8_t& wl = m_wl;
const hi_bit_vector_type& high = m_high;
const int_vector<>& low = m_low;
const select_1_support_type& high_1_select = m_high_1_select;
const select_0_support_type& high_0_select = m_high_0_select;
sd_vector() { }
sd_vector(const sd_vector& sd) {
copy(sd);
}
sd_vector(sd_vector&& sd) {
*this = std::move(sd);
}
sd_vector(const bit_vector& bv) {
m_size = bv.size();
size_type m = util::cnt_one_bits(bv);
uint8_t logm = bits::hi(m)+1;
uint8_t logn = bits::hi(m_size)+1;
if (logm == logn) {
--logm; // to ensure logn-logm > 0
}
m_wl = logn - logm;
m_low = int_vector<>(m, 0, m_wl);
bit_vector high = bit_vector(m + (1ULL<<logm), 0); //
const uint64_t* bvp = bv.data();
for (size_type i=0, mm=0,last_high=0,highpos=0; i < (bv.size()+63)/64; ++i, ++bvp) {
size_type position = 64*i;
uint64_t w = *bvp;
while (w) { // process bit_vector word by word
uint8_t offset = bits::lo(w);
w >>= offset; // note: w >>= (offset+1) can not be applied for offset=63!
position += offset;
if (position >= bv.size()) // check that we have not reached the end of the bitvector
break;
// (1) handle high part
size_type cur_high = position >> m_wl;
highpos += (cur_high - last_high); // write cur_high-last_high 0s
last_high = cur_high;
// (2) handle low part
m_low[mm++] = position; // int_vector truncates the most significant logm bits
high[highpos++] = 1; // write 1 for the entry
position += 1;
w >>= 1;
}
}
util::assign(m_high, high);
util::init_support(m_high_1_select, &m_high);
util::init_support(m_high_0_select, &m_high);
}
//! Accessing the i-th element of the original bit_vector
/*! \param i An index i with \f$ 0 \leq i < size() \f$.
* \return The i-th bit of the original bit_vector
* \par Time complexity
* \f$ \Order{t_{select0} + n/m} \f$, where m equals the number of zeros
* \par Remark
* The time complexity can be easily improved to
* \f$\Order{t_{select0}+\log(n/m)}\f$
* by using binary search in the second step.
*/
value_type operator[](size_type i)const {
size_type high_val = (i >> (m_wl));
size_type sel_high = m_high_0_select(high_val + 1);
size_type rank_low = sel_high - high_val;
if (0 == rank_low)
return 0;
size_type val_low = i & bits::lo_set[ m_wl ]; // extract the low m_wl = log n -log m bits
--sel_high; --rank_low;
while (m_high[sel_high] and m_low[rank_low] > val_low) {
if (sel_high > 0) {
--sel_high; --rank_low;
} else
return 0;
}
return m_high[sel_high] and m_low[rank_low] == val_low;
}
//! 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, const uint8_t len=64) const {
uint64_t i = idx+len-1;
uint64_t high_val = (i >> (m_wl));
uint64_t sel_high = m_high_0_select(high_val + 1);
uint64_t rank_low = sel_high - high_val;
if (0 == rank_low)
return 0;
size_type val_low = i & bits::lo_set[ m_wl ]; // extract the low m_wl = log n -log m bits
--sel_high; --rank_low;
while (m_high[sel_high] and m_low[rank_low] > val_low) {
if (sel_high > 0) {
--sel_high; --rank_low;
} else
return 0;
}
uint64_t res = 0;
while (true) {
while (!m_high[sel_high]) {
if (sel_high > 0 and(high_val << m_wl) >=idx) {
--sel_high; --high_val;
} else {
return res;
}
}
while (m_high[sel_high]) {
uint64_t val = (high_val << m_wl) + m_low[rank_low];
if (val >= idx) {
res |= 1ULL<<(val-idx);
} else {
return res;
}
if (sel_high > 0) {
--sel_high; --rank_low;
} else {
return res;
}
}
}
}
//! Swap method
void swap(sd_vector& v) {
if (this != &v) {
std::swap(m_size, v.m_size);
std::swap(m_wl, v.m_wl);
m_low.swap(v.m_low);
m_high.swap(v.m_high);
util::swap_support(m_high_1_select, v.m_high_1_select, &m_high, &v.m_high);
util::swap_support(m_high_0_select, v.m_high_0_select, &m_high, &v.m_high);
}
}
//! Returns the size of the original bit vector.
size_type size()const {
return m_size;
}
sd_vector& operator=(const sd_vector& v) {
if (this != &v) {
copy(v);
}
return *this;
}
sd_vector& operator=(sd_vector&& v) {
if (this != &v) {
m_size = v.m_size;
m_wl = v.m_wl;
m_low = std::move(v.m_low);
m_high = std::move(v.m_high);
m_high_1_select = std::move(v.m_high_1_select);
m_high_1_select.set_vector(&m_high);
m_high_0_select = std::move(v.m_high_0_select);
m_high_0_select.set_vector(&m_high);
}
return *this;
}
//! 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 += write_member(m_wl, out, child, "wl");
written_bytes += m_low.serialize(out, child, "low");
written_bytes += m_high.serialize(out, child, "high");
written_bytes += m_high_1_select.serialize(out, child, "high_1_select");
written_bytes += m_high_0_select.serialize(out, child, "high_0_select");
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);
read_member(m_wl, in);
m_low.load(in);
m_high.load(in);
m_high_1_select.load(in, &m_high);
m_high_0_select.load(in, &m_high);
}
iterator begin() const {
return iterator(this, 0);
}
iterator end() const {
return iterator(this, size());
}
};
template<uint8_t t_b>
struct rank_support_sd_trait {
typedef bit_vector::size_type size_type;
static size_type adjust_rank(size_type r,size_type) {
return r;
}
};
template<>
struct rank_support_sd_trait<0> {
typedef bit_vector::size_type size_type;
static size_type adjust_rank(size_type r, size_type n) {
return n - r;
}
};
//! Rank data structure for sd_vector
/*! \tparam t_b Bit pattern.
* \tparam t_hi_bit_vector Type of the bitvector used for the unary decoded differences of
* the high part of the positions of the 1s.
* \tparam t_select_1 Type of the select structure which is used to select ones in HI.
* \tparam t_select_0 Type of the select structure which is used to select zeros in HI.
*/
template<uint8_t t_b, class t_hi_bit_vector, class t_select_1, class t_select_0>
class rank_support_sd
{
static_assert(t_b == 1u or t_b == 0u , "rank_support_sd: bit pattern must be `0` or `1`");
public:
typedef bit_vector::size_type size_type;
typedef sd_vector<t_hi_bit_vector, t_select_1, t_select_0> bit_vector_type;
enum { bit_pat = t_b };
private:
const bit_vector_type* m_v;
public:
explicit rank_support_sd(const bit_vector_type* v=nullptr) {
set_vector(v);
}
size_type rank(size_type i)const {
assert(m_v != nullptr);
assert(i <= m_v->size());
// split problem in two parts:
// (1) find >=
size_type high_val = (i >> (m_v->wl));
size_type sel_high = m_v->high_0_select(high_val + 1);
size_type rank_low = sel_high - high_val; //
if (0 == rank_low)
return rank_support_sd_trait<t_b>::adjust_rank(0, i);
size_type val_low = i & bits::lo_set[ m_v->wl ];
// now since rank_low > 0 => sel_high > 0
do {
if (!sel_high)
return rank_support_sd_trait<t_b>::adjust_rank(0, i);
--sel_high; --rank_low;
} while (m_v->high[sel_high] and m_v->low[rank_low] >= val_low);
return rank_support_sd_trait<t_b>::adjust_rank(rank_low+1, i);
}
size_type operator()(size_type i)const {
return rank(i);
}
size_type size()const {
return m_v->size();
}
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
rank_support_sd& operator=(const rank_support_sd& rs) {
if (this != &rs) {
set_vector(rs.m_v);
}
return *this;
}
void swap(rank_support_sd&) { }
void load(std::istream&, const bit_vector_type* v=nullptr) {
set_vector(v);
}
size_type serialize(std::ostream& out, structure_tree_node* v=nullptr, std::string name="")const {
return serialize_empty_object(out, v, name, this);
}
};
template<uint8_t t_b, class t_sd_vec>
struct select_support_sd_trait {
typedef bit_vector::size_type size_type;
static size_type select(size_type i, const t_sd_vec* v) {
return v->low[i-1] + // lower part of the number
((v->high_1_select(i) + 1 - i) << (v->wl)); // upper part
//^-number of 0 before the i-th 1-^ ^-shift by wl
}
};
template<class t_sd_vec>
struct select_support_sd_trait<0, t_sd_vec> {
typedef bit_vector::size_type size_type;
static size_type select(size_type i, const t_sd_vec* v) {
auto ones = v->low.size();
assert(0 < i and i <= v->size() - ones);
size_type lb = 1, rb = ones+1;
size_type r0 = 0;
size_type pos = (size_type)-1;
// rb exclusive
// invariant: rank0(select_1(rb)) >= i
while (lb < rb) {
auto mid = lb + (rb-lb)/2;
auto x = select_support_sd_trait<1, t_sd_vec>::select(mid, v);
auto rank0 = x + 1 - mid;
if (rank0 >= i) {
rb = mid;
} else {
r0 = rank0;
pos = x;
lb = mid + 1;
}
}
return pos + i - r0;
}
};
//! Select data structure for sd_vector
/*! \tparam t_b Bit pattern.
* \tparam t_hi_bit_vector Type of the bitvector used for the unary decoded differences of
* the high part of the positions of the 1s.
* \tparam t_select_1 Type of the select structure which is used to select ones in HI.
* \tparam t_select_0 Type of the select structure which is used to select zeros in HI.
*/
template<uint8_t t_b, class t_hi_bit_vector, class t_select_1, class t_select_0>
class select_support_sd
{
public:
typedef bit_vector::size_type size_type;
typedef sd_vector<t_hi_bit_vector, t_select_1, t_select_0> bit_vector_type;
enum { bit_pat = t_b };
private:
const bit_vector_type* m_v;
public:
explicit select_support_sd(const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Returns the position of the i-th occurrence in the bit vector.
size_type select(size_type i)const {
return select_support_sd_trait<t_b, bit_vector_type>::select(i, m_v);
}
size_type operator()(size_type i)const {
return select(i);
}
size_type size()const {
return m_v->size();
}
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
select_support_sd& operator=(const select_support_sd& ss) {
if (this != &ss) {
set_vector(ss.m_v);
}
return *this;
}
void swap(select_support_sd&) { }
void load(std::istream&, const bit_vector_type* v=nullptr) {
set_vector(v);
}
size_type serialize(std::ostream& out, structure_tree_node* v=nullptr, std::string name="")const {
return serialize_empty_object(out, v, name, this);
}
};
//! Select_0 data structure for sd_vector
/*! \tparam t_sd_vector sd_vector type
* \tparam t_rank_1 Rank support for high part of sd_vector
*/
template<typename t_sd_vector=sd_vector<>>
class select_0_support_sd
{
public:
typedef bit_vector::size_type size_type;
typedef t_sd_vector bit_vector_type;
using rank_1 = typename t_sd_vector::rank_1_type;
using sel0_type = typename t_sd_vector::select_0_type;
typedef bit_vector y_high_type;
enum { bit_pat = 0 };
private:
const bit_vector_type* m_v;
int_vector<> m_pointer;
int_vector<> m_rank1;
public:
explicit select_0_support_sd(const bit_vector_type* v=nullptr) {
set_vector(v);
if (nullptr != m_v) {
size_type rank_0 = 0; // rank0 in H
const size_type bs = 1ULL << (m_v->wl);
size_type z = 0;
size_type rank1 = 0;// rank1 in H
size_type zeros = m_v->size() - rank_1(m_v)(m_v->size()); // zeros in B
m_pointer = int_vector<>(zeros/(64*bs)+1, 0, bits::hi(m_v->high.size()/64)+1);
m_rank1 = int_vector<>(m_pointer.size(), 0, bits::hi(m_v->high.size())+1);
uint64_t w=0;
for (size_type i=0, sel0=1; i < m_v->high.size(); i+=64) {
size_type old_rank1 = rank1;
w = m_v->high.get_int(i, 64);
rank1 += bits::cnt(w);
rank_0 = (i+64)-rank1;
if (rank1 > 0 and (w>>63)&1) {
uint64_t pos = rank_0*bs + m_v->low[rank1-1]; // pos of last one (of previous block in B
z = pos + 1 - rank1;
} else {
z = rank_0*bs - rank1;
}
while (sel0 <= z and sel0 <= zeros) {
m_pointer[(sel0-1)/(64*bs)] = i/64;
m_rank1[(sel0-1)/(64*bs)] = old_rank1;
sel0 += 64*bs;
}
}
}
}
//! Returns the position of the i-th occurrence in the bit vector.
size_type select(size_type i)const {
const size_type bs = 1ULL << (m_v->wl);
size_type j = m_pointer[(i-1)/(64*bs)]*64;// index into m_high
size_type rank1 = m_rank1[(i-1)/(64*bs)]; // rank_1(j*bs*64) in B
size_type pos = 0;
size_type rank0 = 0;
if (rank1 > 0 and (m_v->high[j-1])&1) {
pos = (j-rank1)*bs + m_v->low[rank1-1]; // starting position of current block
rank0 = pos+1-rank1;
} else {
pos = (j-rank1)*bs;// starting position of current block
rank0 = pos-rank1;
}
uint64_t w = m_v->high.get_int(j, 64);
do {
uint64_t _rank1 = rank1 + bits::cnt(w);
uint64_t _rank0 = 0;
if (_rank1 > 0 and (w>>63)&1) {
pos = (j+64-_rank1)*bs + m_v->low[_rank1-1];
_rank0 = pos+1-_rank1;
} else {
pos = (j+64-_rank1)*bs;
_rank0 = pos-_rank1;
}
if (_rank0 < i) {
j+=64;
w = m_v->high.get_int(j, 64);
rank1 = _rank1;
} else {
break;
}
} while (true);
// invariant i >zeros
do {
uint64_t _rank1 = rank1 + bits::lt_cnt[w&0xFFULL];
uint64_t _rank0 = 0;
if (_rank1 > 0 and (w>>7)&1) {
pos = (j+8-_rank1)*bs + m_v->low[_rank1-1];
_rank0 = pos+1-_rank1;
} else {
pos = (j+8-_rank1)*bs;
_rank0 = pos-_rank1;
}
if (_rank0 < i) {
j+=8;
w >>= 8;
rank1 = _rank1;
} else {
break;
}
} while (true);
do {
bool b = w&1ULL;
w >>= 1; // zeros are shifted in
++j;
if (0 == b) {
pos = (j-rank1)*bs;
size_type zeros = pos-rank1;
if (zeros >= i) {
pos = pos - (zeros-i) - 1;
break;
}
} else {
pos = (j-1-rank1)*bs;
size_type one_pos = pos + m_v->low[rank1];
++rank1;
size_type zeros = one_pos + 1 - rank1;
if (zeros >= i) {
pos = one_pos - (zeros-i) - 1;
break;
}
}
if (j%64==0) {
w = m_v->high.get_int(j,64);
}
} while (true);
return pos;
}
size_type operator()(size_type i)const {
return select(i);
}
size_type size()const {
return m_v->size();
}
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
select_0_support_sd& operator=(const select_0_support_sd& ss) {
if (this != &ss) {
m_pointer = ss.m_pointer;
m_rank1 = ss.m_rank1;
set_vector(ss.m_v);
}
return *this;
}
void swap(select_0_support_sd& ss) {
m_pointer.swap(ss.m_pointer);
m_rank1.swap(ss.m_rank1);
}
void load(std::istream& in, const bit_vector_type* v=nullptr) {
m_pointer.load(in);
m_rank1.load(in);
set_vector(v);
}
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 += m_pointer.serialize(out, child, "pointer");
written_bytes += m_rank1.serialize(out, child, "rank1");
structure_tree::add_size(child, written_bytes);
return written_bytes;
}
};
} // end namespace
#endif
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