SDSL 3.0.1
Succinct Data Structure Library
k2_tree.hpp
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1// Copyright (c) 2016, the SDSL Project Authors. All rights reserved.
2// Please see the AUTHORS file for details. Use of this source code is governed
3// by a BSD license that can be found in the LICENSE file.
8#ifndef INCLUDED_SDSL_K2_TREE
9#define INCLUDED_SDSL_K2_TREE
10
11#include <deque>
12#include <queue>
13#include <stdexcept>
14#include <tuple>
15
16#include <sdsl/bit_vectors.hpp>
18#include <sdsl/io.hpp>
20
22namespace sdsl
23{
25
36template <uint8_t k, typename t_bv = bit_vector, typename t_rank = typename t_bv::rank_1_type>
38{
39 public:
42
43 private:
46 t_bv k_t;
48 t_bv k_l;
49
50 t_rank k_t_rank;
51
52 uint8_t k_k;
53 uint16_t k_height;
54
55 protected:
56 void build_from_matrix(const std::vector<std::vector<int>> & matrix)
57 {
58 // Makes the size a power of k.
59 int simulated_size = std::pow(k, k_height);
60 std::vector<std::deque<bit_vector>> acc(k_height + 1);
61
62 k2_tree_ns::_build_from_matrix<bit_vector>(matrix, k, simulated_size, k_height, 1, 0, 0, acc);
63
64 size_type t_size = 0;
65 size_type l_size = 0;
66 for (int i = 1; i < k_height; i++)
67 for (auto it = acc[i].begin(); it != acc[i].end(); it++) t_size += (*it).size();
68
69 for (auto it = acc[k_height].begin(); it != acc[k_height].end(); it++) l_size += (*it).size();
70
71 bit_vector k_t_(t_size, 0);
72 bit_vector k_l_(l_size, 0);
73
74 int n = 0;
75 for (int j = 1; j < k_height; j++)
76 for (auto it = acc[j].begin(); it != acc[j].end(); it++)
77 for (unsigned i = 0; i < (*it).size(); i++)
78 {
79 // TODO there should be a better way to do this
80 k_t_.set_int(n, (*it).get_int(i, 1), 1);
81 n++;
82 }
83 n = 0;
84 for (auto it = acc[k_height].begin(); it != acc[k_height].end(); it++)
85 for (unsigned i = 0; i < (*it).size(); i++)
86 {
87 // TODO there should be a better way to do this
88 k_l_.set_int(n * 1, (*it).get_int(i, 1), 1);
89 n++;
90 }
91
92 k2_tree_ns::build_template_vector<t_bv>(k_t_, k_l_, k_t, k_l);
93 }
94
106 void _neigh(size_type n, idx_type row, idx_type col, size_type level, std::vector<idx_type> & acc) const
107 {
108 if (level >= k_t.size())
109 { // Last level
110 if (k_l[level - k_t.size()] == 1) acc.push_back(col);
111 return;
112 }
113
114 if (k_t[level] == 1)
115 {
116 idx_type y = k_t_rank(level + 1) * std::pow(k_k, 2) + k_k * std::floor(row / static_cast<double>(n));
117 for (unsigned j = 0; j < k_k; j++) _neigh(n / k_k, row % n, col + n * j, y + j, acc);
118 }
119 }
120
132 void _reverse_neigh(size_type n, idx_type row, idx_type col, size_type level, std::vector<idx_type> & acc) const
133 {
134 if (level >= k_t.size())
135 { // Last level
136 if (k_l[level - k_t.size()] == 1) { acc.push_back(row); }
137 return;
138 }
139
140 if (k_t[level] == 1)
141 {
142 idx_type y = k_t_rank(level + 1) * std::pow(k_k, 2) + std::floor(col / static_cast<double>(n));
143 for (unsigned j = 0; j < k_k; j++) _reverse_neigh(n / k_k, row + n * j, col % n, y + j * k_k, acc);
144 }
145 }
146
148
156 void build_from_edges(std::vector<std::tuple<idx_type, idx_type>> & edges, const size_type size)
157 {
158
159 typedef std::tuple<idx_type, idx_type, size_type, idx_type, idx_type> t_part_tuple;
160
161 k_k = k;
162 k_height = std::ceil(std::log(size) / std::log(k_k));
163 k_height = k_height > 1 ? k_height : 1; // If size == 0
164 size_type k_2 = std::pow(k_k, 2);
165 bit_vector k_t_ = bit_vector(k_2 * k_height * edges.size(), 0);
166 bit_vector k_l_;
167
168 std::queue<t_part_tuple> q;
169 idx_type t = 0, last_level = 0;
170 idx_type i, j, r_0, c_0, it, c, r;
171 size_type l = std::pow(k_k, k_height - 1);
172 std::vector<idx_type> pos_by_chunk(k_2 + 1, 0);
173
174 q.push(t_part_tuple(0, edges.size(), l, 0, 0));
175
176 while (!q.empty())
177 {
178 std::vector<idx_type> amount_by_chunk(k_2, 0);
179 std::tie(i, j, l, r_0, c_0) = q.front();
180 q.pop();
181 // Get size for each chunk
182 for (it = i; it < j; it++)
183 amount_by_chunk[k2_tree_ns::get_chunk_idx(std::get<0>(edges[it]),
184 std::get<1>(edges[it]),
185 c_0,
186 r_0,
187 l,
188 k_k)] += 1;
189 if (l == 1)
190 {
191 if (last_level == 0)
192 {
193 last_level = t;
194 k_l_ = bit_vector(k_t_.size() - last_level, 0);
195 k_t_.resize(last_level);
196 k_t_.shrink_to_fit();
197 last_level = 1; // if t was 0
198 t = 0; // Restart counter as we're storing at k_l_ now.
199 }
200 for (it = 0; it < k_2; it++, t++)
201 if (amount_by_chunk[it] != 0) k_l_[t] = 1;
202 // At l == 1 we do not put new elements at the queue.
203 continue;
204 }
205
206 // Set starting position in the vector for each chunk
207 pos_by_chunk[0] = i;
208 for (it = 1; it < k_2; it++) pos_by_chunk[it] = pos_by_chunk[it - 1] + amount_by_chunk[it - 1];
209 // To handle the last case when it = k_2 - 1
210 pos_by_chunk[k_2] = j;
211 // Push to the queue every non zero elements chunk
212 for (it = 0; it < k_2; it++, t++)
213 // If not empty chunk, set bit to 1
214 if (amount_by_chunk[it] != 0)
215 {
216 r = it / k_k;
217 c = it % k_k;
218 k_t_[t] = 1;
219 q.push(t_part_tuple(pos_by_chunk[it], pos_by_chunk[it + 1], l / k_k, r_0 + r * l, c_0 + c * l));
220 }
221 idx_type chunk;
222
223 // Sort edges' vector
224 for (unsigned ch = 0; ch < k_2; ch++)
225 {
226 idx_type be = ch == 0 ? i : pos_by_chunk[ch - 1];
227 for (it = pos_by_chunk[ch]; it < be + amount_by_chunk[ch];)
228 {
229 chunk = k2_tree_ns::get_chunk_idx(std::get<0>(edges[it]), std::get<1>(edges[it]), c_0, r_0, l, k_k);
230
231 if (pos_by_chunk[chunk] != it)
232 std::iter_swap(edges.begin() + it, edges.begin() + pos_by_chunk[chunk]);
233 else
234 it++;
235 pos_by_chunk[chunk]++;
236 }
237 }
238 }
239 k_l_.resize(t);
240 k_l_.shrink_to_fit();
241 k2_tree_ns::build_template_vector<t_bv>(k_t_, k_l_, k_t, k_l);
242
243 k_t_rank = t_rank(&k_t);
244 }
245
246 public:
247 k2_tree() = default;
248
250
256 k2_tree(std::vector<std::vector<int>> & matrix)
257 {
258 if (matrix.size() < 1) { throw std::logic_error("Matrix has no elements"); }
259 std::vector<bit_vector> t;
260 k_k = k;
261 if (matrix.size() < k_k)
262 k_height = 1;
263 else // height = log_k n
264 k_height = std::ceil(std::log(matrix.size()) / std::log(k_k));
265
266 build_from_matrix(matrix);
267
268 k_t_rank = t_rank(&k_t);
269 }
270
272
280 k2_tree(std::vector<std::tuple<idx_type, idx_type>> & edges, const size_type size)
281 {
282 assert(size > 0);
283 assert(edges.size() > 0);
284
285 build_from_edges(edges, size);
286 }
287
289
301 k2_tree(std::string filename, size_type size = 0)
302 {
303 int_vector_buffer<> buf_x(filename + ".x", std::ios::in);
304 int_vector_buffer<> buf_y(filename + ".y", std::ios::in);
305
306 assert(buf_x.size() == buf_y.size());
307 assert(buf_x.size() > 0);
308
309 std::vector<std::tuple<idx_type, idx_type>> edges;
310 edges.reserve(buf_x.size());
311
312 if (size == 0)
313 {
314 size_type max = 0;
315 for (auto v : buf_x) max = std::max(static_cast<size_type>(v), max);
316 for (auto v : buf_y) max = std::max(static_cast<size_type>(v), max);
317 size = max + 1;
318 }
319
320 for (uint64_t i = 0; i < buf_x.size(); i++)
321 edges.push_back(std::tuple<idx_type, idx_type>{ buf_x[i], buf_y[i] });
322
323 build_from_edges(edges, size);
324 }
325
326 k2_tree(const k2_tree & tr)
327 : k_t(tr.k_t)
328 , k_l(tr.k_l)
329 , k_k(tr.k_k)
330 , k_height(tr.k_height)
331 , k_t_rank(tr.k_t_rank)
332 {
333 k_t_rank.set_vector(&k_t);
334 }
335
336 k2_tree(k2_tree && tr) { *this = std::move(tr); }
337
340 {
341 if (this != &tr)
342 {
343 k_t = std::move(tr.k_t);
344 k_l = std::move(tr.k_l);
345 k_k = std::move(tr.k_k);
346 k_height = std::move(tr.k_height);
347 k_t_rank = std::move(tr.k_t_rank);
348 k_t_rank.set_vector(&k_t);
349 }
350 return *this;
351 }
352
355 {
356 if (this != &tr)
357 {
358 k2_tree tmp(tr);
359 *this = std::move(tmp);
360 }
361 return *this;
362 }
363
365 bool operator==(const k2_tree & tr) const
366 {
367 // TODO check the rank support equality?
368 if (k_k != tr.k_k || k_height != tr.k_height) return false;
369 if (k_t.size() != tr.k_t.size() || k_l.size() != tr.k_l.size()) return false;
370 for (unsigned i = 0; i < k_t.size(); i++)
371 if (k_t[i] != tr.k_t[i]) return false;
372 for (unsigned i = 0; i < k_l.size(); i++)
373 if (k_l[i] != tr.k_l[i]) return false;
374 return true;
375 }
376
377 t_bv get_t() { return k_t; }
378
379 t_bv get_l() { return k_l; }
380
382
388 bool adj(idx_type i, idx_type j) const
389 {
390 if (k_t.size() == 0 && k_l.size() == 0) return false;
391 size_type n = std::pow(k_k, k_height - 1);
392 size_type k_2 = std::pow(k_k, 2);
393 idx_type col, row;
394
395 // This is duplicated to avoid an extra if at the loop. As idx_type
396 // is unsigned and rank has an offset of one, is not possible to run
397 // k_t_rank with zero as parameter at the first iteration.
398 row = std::floor(i / static_cast<double>(n));
399 col = std::floor(j / static_cast<double>(n));
400 i = i % n;
401 j = j % n;
402 idx_type level = k_k * row + col;
403 n = n / k_k;
404
405 while (level < k_t.size())
406 {
407 if (k_t[level] == 0) return false;
408 row = std::floor(i / static_cast<double>(n));
409 col = std::floor(j / static_cast<double>(n));
410 i = i % n;
411 j = j % n;
412 level = k_t_rank(level + 1) * k_2 + k_k * row + col;
413 n = n / k_k;
414 }
415
416 return k_l[level - k_t.size()] == 1;
417 }
418
420
424 std::vector<idx_type> neigh(idx_type i) const
425 {
426 std::vector<idx_type> acc{};
427 if (k_l.size() == 0 && k_t.size() == 0) return acc;
428 size_type n = static_cast<size_type>(std::pow(k_k, k_height)) / k_k;
429 idx_type y = k_k * std::floor(i / static_cast<double>(n));
430 for (unsigned j = 0; j < k_k; j++) _neigh(n / k_k, i % n, n * j, y + j, acc);
431 return acc;
432 }
433
435
439 std::vector<idx_type> reverse_neigh(idx_type i) const
440 {
441 std::vector<idx_type> acc{};
442 if (k_l.size() == 0 && k_t.size() == 0) return acc;
443 // Size of the first square division
444 size_type n = static_cast<size_type>(std::pow(k_k, k_height)) / k_k;
445 idx_type y = std::floor(i / static_cast<double>(n));
446 for (unsigned j = 0; j < k_k; j++) _reverse_neigh(n / k_k, n * j, i % n, y + j * k_k, acc);
447
448 return acc;
449 }
450
452
458 size_type serialize(std::ostream & out, structure_tree_node * v = nullptr, std::string name = "") const
459 {
460 structure_tree_node * child = structure_tree::add_child(v, name, util::class_name(*this));
461 size_type written_bytes = 0;
462
463 written_bytes += k_t.serialize(out, child, "t");
464 written_bytes += k_l.serialize(out, child, "l");
465 written_bytes += k_t_rank.serialize(out, child, "t_rank");
466 written_bytes += write_member(k_k, out, child, "k");
467 written_bytes += write_member(k_height, out, child, "height");
468 structure_tree::add_size(child, written_bytes);
469 return written_bytes;
470 }
471
473
476 void load(std::istream & in)
477 {
478 k_t.load(in);
479 k_l.load(in);
480 k_t_rank.load(in);
481 k_t_rank.set_vector(&k_t);
482 read_member(k_k, in);
483 read_member(k_height, in);
484 }
485
487 template <typename archive_t>
488 void CEREAL_SAVE_FUNCTION_NAME(archive_t & ar) const
489 {
490 ar(CEREAL_NVP(k_k));
491 ar(CEREAL_NVP(k_height));
492 ar(CEREAL_NVP(k_t));
493 ar(CEREAL_NVP(k_l));
494 ar(CEREAL_NVP(k_t_rank));
495 }
496
498 template <typename archive_t>
499 typename std::enable_if<cereal::traits::is_output_serializable<k2_tree, archive_t>::value, void>::type
501 {
502 ar(CEREAL_NVP(k_k));
503 ar(CEREAL_NVP(k_height));
504 ar(CEREAL_NVP(k_t));
505 ar(CEREAL_NVP(k_l));
506 ar(CEREAL_NVP(k_t_rank));
507 k_t_rank.set_vector(&k_t);
508 }
509};
510} // namespace sdsl
511
512#endif
bit_vectors.hpp contains classes for uncompressed and compressed bit vector representations.
#define CEREAL_NVP(X)
Definition: cereal.hpp:31
uint64_t size() const
Returns the number of elements currently stored.
void shrink_to_fit()
Free unused allocated memory.
Definition: int_vector.hpp:506
size_type size() const noexcept
The number of elements in the int_vector.
void push_back(value_type value)
Insert element at the end.
Definition: int_vector.hpp:448
void resize(const size_type size)
Resize the int_vector in terms of elements.
Definition: int_vector.hpp:521
void set_int(size_type idx, value_type x, const uint8_t len=64)
Set the bits from position idx to idx+len-1 to the binary representation of integer x.
A k^2-tree.
Definition: k2_tree.hpp:38
bool adj(idx_type i, idx_type j) const
Indicates wheter node j is adjacent to node i or not.
Definition: k2_tree.hpp:388
void load(std::istream &in)
Load from istream.
Definition: k2_tree.hpp:476
void _neigh(size_type n, idx_type row, idx_type col, size_type level, std::vector< idx_type > &acc) const
Recursive function to retrieve list of neighbors.
Definition: k2_tree.hpp:106
void build_from_edges(std::vector< std::tuple< idx_type, idx_type > > &edges, const size_type size)
Build a tree from an edges collection.
Definition: k2_tree.hpp:156
void CEREAL_SAVE_FUNCTION_NAME(archive_t &ar) const
Serialise (save) via cereal.
Definition: k2_tree.hpp:488
k2_tree & operator=(k2_tree &&tr)
Move assignment operator.
Definition: k2_tree.hpp:339
k2_tree_ns::idx_type idx_type
Definition: k2_tree.hpp:40
void _reverse_neigh(size_type n, idx_type row, idx_type col, size_type level, std::vector< idx_type > &acc) const
Recursive function to retrieve list of reverse neighbors.
Definition: k2_tree.hpp:132
k2_tree(std::vector< std::tuple< idx_type, idx_type > > &edges, const size_type size)
Constructor.
Definition: k2_tree.hpp:280
t_bv get_l()
Definition: k2_tree.hpp:379
bool operator==(const k2_tree &tr) const
Equal operator.
Definition: k2_tree.hpp:365
std::vector< idx_type > neigh(idx_type i) const
Returns a list of neighbors of node i.
Definition: k2_tree.hpp:424
t_bv get_t()
Definition: k2_tree.hpp:377
void build_from_matrix(const std::vector< std::vector< int > > &matrix)
Definition: k2_tree.hpp:56
std::vector< idx_type > reverse_neigh(idx_type i) const
Returns a list of reverse neighbors of node i.
Definition: k2_tree.hpp:439
std::enable_if< cereal::traits::is_output_serializable< k2_tree, archive_t >::value, void >::type CEREAL_LOAD_FUNCTION_NAME(archive_t &ar)
Load via cereal.
Definition: k2_tree.hpp:500
k2_tree(const k2_tree &tr)
Definition: k2_tree.hpp:326
k2_tree & operator=(k2_tree &tr)
Assignment operator.
Definition: k2_tree.hpp:354
k2_tree_ns::size_type size_type
Definition: k2_tree.hpp:41
k2_tree(k2_tree &&tr)
Definition: k2_tree.hpp:336
k2_tree(std::vector< std::vector< int > > &matrix)
Constructor.
Definition: k2_tree.hpp:256
k2_tree()=default
k2_tree(std::string filename, size_type size=0)
Constructor.
Definition: k2_tree.hpp:301
size_type serialize(std::ostream &out, structure_tree_node *v=nullptr, std::string name="") const
Serialize to a stream.
Definition: k2_tree.hpp:458
static structure_tree_node * add_child(structure_tree_node *v, const std::string &name, const std::string &type)
static void add_size(structure_tree_node *v, uint64_t value)
int_vector_buffer.hpp contains the sdsl::int_vector_buffer class.
io.hpp contains some methods for reading/writing sdsl structures.
k2_tree_helper.hpp contains helper functions and definitions for a k^2-tree implementation.
uint16_t get_chunk_idx(idx_type v, idx_type u, idx_type c_0, idx_type r_0, size_type l, uint8_t k)
Get the chunk index ([0, k^2[) of a submatrix point.
int_vector ::size_type size_type
int_vector ::size_type idx_type
Namespace for the succinct data structure library.
size_t write_member(const T &t, std::ostream &out, sdsl::structure_tree_node *v=nullptr, std::string name="")
Definition: io.hpp:84
void read_member(T &t, std::istream &in)
Definition: io.hpp:111
int_vector< 1 > bit_vector
bit_vector is a specialization of the int_vector.
Definition: int_vector.hpp:53
int_vector ::size_type size(const range_type &r)
Size of a range.
Definition: wt_helper.hpp:787