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
|
/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* 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 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* 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 <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include "link/link.h"
#include <cassert>
#include <climits>
#include <cstdlib>
#include <iterator>
namespace {
// Computes abs(a-b) without using negative numbers.
size_t absdiff(size_t a, size_t b) {
return (a >= b ? a - b : b - a);
}
}
namespace regina {
std::string Link::dt(bool alpha) const {
std::ostringstream out;
dt(out, alpha);
return out.str();
}
void Link::dt(std::ostream& out, bool alpha) const {
if (components_.size() != 1)
throw NotImplemented("Dowker-Thistlethwaite notation is "
"only implemented for single-component links");
if (crossings_.empty())
return;
if (alpha && size() > 26)
throw NotImplemented("Alphabetical Dowker-Thistlethwaite notation is "
"only implemented for links with at most 26 crossings");
if (! isClassical())
throw NotImplemented("Dowker-Thistlethwaite notation is only "
"implemented for classical link diagrams, not virtual diagrams");
// Dowker-Thistlethwaite notation requires us to start on the lower strand.
StrandRef start = components_.front();
if (start.strand() == 1)
start.jump();
size_t n = size();
// Work with the largest signed integer type that we could possibly need.
using Int = std::make_signed_t<size_t>;
// Odd steps in traversal -> crossing index
FixedArray<size_t> oddCrossing(n);
// Crossing index -> even steps in traversal, negated if passing under
FixedArray<Int> evenStep(n);
StrandRef s = start;
Int step = 0;
do {
++step;
if (step % 2 == 1) {
oddCrossing[step >> 1] = s.crossing()->index();
} else {
// TODO: It would be kind to do some sanity checking here,
// to make sure that every crossing is seen here exactly once.
evenStep[s.crossing()->index()] = (s.strand() == 1 ? step : -step);
}
++s;
} while (s != start);
assert(static_cast<size_t>(step) == 2 * n);
if (alpha) {
for (size_t i = 0; i < n; ++i)
out << (evenStep[oddCrossing[i]] > 0 ?
(char('a' + evenStep[oddCrossing[i]] / 2 - 1)) :
(char('A' - evenStep[oddCrossing[i]] / 2 - 1)));
} else {
for (size_t i = 0; i < n; ++i) {
if (i > 0)
out << ' ';
out << evenStep[oddCrossing[i]];
}
}
}
std::vector<int> Link::dtData() const {
if (components_.size() != 1)
throw NotImplemented("Dowker-Thistlethwaite notation is "
"only implemented for single-component links");
if (crossings_.empty())
return {};
if (2 * size() > INT_MAX)
throw NotImplemented("This Dowker-Thistlethwaite notation has "
"entries that cannot fit into a C++ int");
if (! isClassical())
throw NotImplemented("Dowker-Thistlethwaite notation is only "
"implemented for classical link diagrams, not virtual diagrams");
// Dowker-Thistlethwaite notation requires us to start on the lower strand.
StrandRef start = components_.front();
if (start.strand() == 1)
start.jump();
int n = static_cast<int>(size());
// Odd steps in traversal -> crossing index
FixedArray<int> oddCrossing(n);
// Crossing index -> even steps in traversal, negated if passing under
FixedArray<int> evenStep(n);
StrandRef s = start;
int step = 0;
do {
++step;
if (step % 2 == 1) {
oddCrossing[step >> 1] = static_cast<int>(s.crossing()->index());
} else {
evenStep[s.crossing()->index()] = (s.strand() == 1 ? step : -step);
}
++s;
} while (s != start);
assert(step == 2 * n);
std::vector<int> ans;
ans.reserve(n);
for (int i = 0; i < n; ++i)
ans.push_back(evenStep[oddCrossing[i]]);
return ans;
}
Link Link::fromDT(const std::string& s) {
// Do we have an alphabetical or numerical string?
auto it = s.begin();
while (it != s.end() && ::isspace(*it))
++it;
if (it == s.end()) {
// Empty string, so return the unknot.
return { 1 };
}
// Work with the largest integer type that we could possibly need.
using Int = std::make_signed_t<size_t>;
std::vector<Int> terms;
if ((*it >= 'a' && *it <= 'z') || (*it >= 'A' && *it <= 'Z')) {
// We have the alphabetical variant.
for ( ; it != s.end(); ++it) {
if (*it >= 'a' && *it <= 'z')
terms.push_back(2 * (*it - 'a' + 1));
else if (*it >= 'A' && *it <= 'Z')
terms.push_back(-2 * (*it - 'A' + 1));
else if (! ::isspace(*it)) {
// Invalid character.
throw InvalidArgument(
"fromDT(): invalid alphabetical character");
}
}
} else if ((*it >= '0' && *it <= '9') || *it == '-') {
// We have the numerical variant.
std::istringstream in(s);
Int i;
while (true) {
in >> i;
if (! in) {
if (in.eof())
break;
throw InvalidArgument("fromDT(): invalid numerical character");
}
terms.push_back(i);
}
} else
throw InvalidArgument("fromDT(): invalid character");
return fromDT(terms.begin(), terms.end());
}
} // namespace regina
|
