1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
|
#include <cstdlib>
#include <list>
#include <vector>
#include <algorithm>
#include <queue>
#include "../utility.h"
namespace meow{
////////////////////////////////////////////////////////////////////
// **# Node #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::Node::Node(Vector __vector,
ssize_t __lChild, ssize_t __rChild):
_vector(__vector), _lChild(__lChild), _rChild(__rChild){
}
////////////////////////////////////////////////////////////////////
// **# Sorter #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::Sorter::Sorter(Nodes const* __nodes, size_t __cmp):
_nodes(__nodes), _cmp(__cmp){
}
template<class Vector, class Scalar>
inline bool
KD_Tree<Vector, Scalar>::Sorter::operator()(size_t const& __a,
size_t const& __b) const{
if((*_nodes)[__a]._vector[_cmp] != (*_nodes)[__b]._vector[_cmp]){
return ((*_nodes)[__a]._vector[_cmp] < (*_nodes)[__b]._vector[_cmp]);
}
return ((*_nodes)[__a]._vector < (*_nodes)[__b]._vector);
}
////////////////////////////////////////////////////////////////////
// **# Answer / Answer's Compare class #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::Answer::Answer(ssize_t __index, Scalar __dist2):
_index(__index), _dist2(__dist2){
}
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::Answer::Answer(Answer const& __answer2):
_index(__answer2._index), _dist2(__answer2._dist2){
}
//
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::AnswerCompare::AnswerCompare(Nodes const* __nodes,
bool __cmpValue):
_nodes(__nodes), _cmpValue(__cmpValue){
}
template<class Vector, class Scalar>
inline bool
KD_Tree<Vector, Scalar>::AnswerCompare::operator()(Answer const& __a,
Answer const& __b) const{
if(_cmpValue == true && __a._dist2 == __b._dist2){
return ((*_nodes)[__a._index]._vector < (*_nodes)[__b._index]._vector);
}
return (__a._dist2 < __b._dist2);
}
////////////////////////////////////////////////////////////////////
// **# distance2() #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline Scalar
KD_Tree<Vector, Scalar>::distance2(Vector const& __v1,
Vector const& __v2) const{
Scalar ret(0);
for(size_t i = 0; i < _dimension; i++){
ret += squ(__v1[i] - __v2[i]);
}
return ret;
}
////////////////////////////////////////////////////////////////////
// **# query() #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline void
KD_Tree<Vector, Scalar>::query(Vector const& __vector,
size_t __nearestNumber,
AnswerCompare const& __answerCompare,
size_t __index,
int __depth,
std::vector<Scalar>& __dist2Vector,
Scalar __dist2Minimum,
Answers *__out) const{
if(__index == _NIL) return ;
size_t cmp = __depth % _dimension;
ssize_t this_side, that_side;
if(!(_nodes[__index]._vector[cmp] < __vector[cmp])){
this_side = _nodes[__index]._lChild;
that_side = _nodes[__index]._rChild;
}else{
this_side = _nodes[__index]._rChild;
that_side = _nodes[__index]._lChild;
}
query(__vector, __nearestNumber, __answerCompare,
this_side, __depth + 1,
__dist2Vector, __dist2Minimum,
__out);
Answer my_ans(__index, distance2(_nodes[__index]._vector, __vector));
if(__out->size() < __nearestNumber ||
__answerCompare(my_ans, __out->top())){
__out->push(my_ans);
if(__out->size() > __nearestNumber) __out->pop();
}
Scalar dist2_old = __dist2Vector[cmp];
__dist2Vector[cmp] = squ(_nodes[__index]._vector[cmp] - __vector[cmp]);
Scalar dist2Minimum = __dist2Minimum + __dist2Vector[cmp] - dist2_old;
if(__out->size() < __nearestNumber ||
!(__out->top()._dist2 < dist2Minimum)){
query(__vector, __nearestNumber, __answerCompare,
that_side, __depth + 1,
__dist2Vector, dist2Minimum,
__out);
}
__dist2Vector[cmp] = dist2_old;
}
////////////////////////////////////////////////////////////////////
// **# build() #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline ssize_t
KD_Tree<Vector, Scalar>::build(ssize_t __beg,
ssize_t __end,
std::vector<size_t>* __orders,
int __depth){
if(__beg > __end) return _NIL;
size_t tmp_order = _dimension;
size_t which_side = _dimension + 1;
ssize_t mid = (__beg + __end) / 2;
size_t cmp = __depth % _dimension;
for(ssize_t i = __beg; i <= mid; i++){
__orders[which_side][__orders[cmp][i]] = 0;
}
for(ssize_t i = mid + 1; i <= __end; i++){
__orders[which_side][__orders[cmp][i]] = 1;
}
for(int i = 0; i < _dimension; i++){
if(i == cmp) continue;
size_t left = __beg, right = mid + 1;
for(int j = __beg; j <= __end; j++){
size_t ask = __orders[i][j];
if(ask == __orders[cmp][mid]){
__orders[tmp_order][mid] = ask;
}else if(__orders[which_side][ask] == 1){
__orders[tmp_order][right++] = ask;
}else{
__orders[tmp_order][left++] = ask;
}
}
for(int j = __beg; j <= __end; j++){
__orders[i][j] = __orders[tmp_order][j];
}
}
_nodes[__orders[cmp][mid]]._lChild=build(__beg,mid-1,__orders,__depth+1);
_nodes[__orders[cmp][mid]]._rChild=build(mid+1,__end,__orders,__depth+1);
return __orders[cmp][mid];
}
////////////////////////////////////////////////////////////////////
// **# constructures/destructures #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::KD_Tree():
_NIL(-1), _root(_NIL), _needRebuild(false), _dimension(1){
}
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::KD_Tree(size_t __dimension):
_NIL(-1), _root(_NIL), _needRebuild(false), _dimension(__dimension){
}
template<class Vector, class Scalar>
inline
KD_Tree<Vector, Scalar>::~KD_Tree(){
}
////////////////////////////////////////////////////////////////////
// **# insert, build #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline void
KD_Tree<Vector, Scalar>::insert(Vector const& __vector){
_nodes.push_back(Node(__vector, _NIL, _NIL));
_needRebuild = true;
}
template<class Vector, class Scalar>
inline bool
KD_Tree<Vector, Scalar>::erase(Vector const& __vector){
for(size_t i = 0, I = _nodes.size(); i < I; i++){
if(_nodes[i] == __vector){
if(i != I - 1){
std::swap(_nodes[i], _nodes[I - 1]);
}
_needRebuild = true;
return true;
}
}
return false;
}
template<class Vector, class Scalar>
inline void
KD_Tree<Vector, Scalar>::build(){
if(_needRebuild){
forceBuild();
}
}
template<class Vector, class Scalar>
inline void
KD_Tree<Vector, Scalar>::forceBuild(){
std::vector<size_t> *orders = new std::vector<size_t>[_dimension + 2];
for(int j = 0; j < _dimension + 2; j++){
orders[j].resize(_nodes.size());
}
for(int j = 0; j < _dimension; j++){
for(size_t i = 0, I = _nodes.size(); i < I; i++){
orders[j][i] = i;
}
std::sort(orders[j].begin(), orders[j].end(), Sorter(&_nodes, j));
}
_root = build(0, (ssize_t)_nodes.size() - 1, orders, 0);
delete [] orders;
_needRebuild = false;
}
////////////////////////////////////////////////////////////////////
// **# query #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline typename KD_Tree<Vector, Scalar>::Vectors
KD_Tree<Vector, Scalar>::query(Vector const& __vector,
size_t __nearestNumber,
bool __compareWholeVector) const{
((KD_Tree*)this)->build();
AnswerCompare answer_compare(&_nodes, __compareWholeVector);
Answers answer_set(answer_compare);
std::vector<Scalar> tmp(_dimension, 0);
query(__vector, __nearestNumber,
answer_compare,
_root, 0,
tmp, Scalar(0),
&answer_set);
Vectors ret(answer_set.size());
for(int i = (ssize_t)answer_set.size() - 1; i >= 0; i--){
ret[i] = _nodes[answer_set.top()._index]._vector;
answer_set.pop();
}
return ret;
}
////////////////////////////////////////////////////////////////////
// **# clear, reset #** //
////////////////////////////////////////////////////////////////////
template<class Vector, class Scalar>
inline void
KD_Tree<Vector, Scalar>::clear(){
_root = _NIL;
_nodes.clear();
_needRebuild = false;
}
template<class Vector, class Scalar>
inline void
KD_Tree<Vector, Scalar>::reset(size_t __dimension){
clear();
_dimension = __dimension;
}
}
|
