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
|
#include "vektor.h"
#include <stdio.h>
#include "printer.h"
void outOfRange(int i, int n)
{
fprintf(Stderr,"Index out of range: index=%i vector lenght=%i\n",i,n);
assert(0);
}
IntegerVectorList transposeIntegerVectorList(IntegerVectorList const &l)
{
int n=l.size();
assert(n);
int m=l.begin()->size();
IntegerVectorList r;
for(int i=0;i<m;i++)
{
IntegerVector column(n);
int j=0;
for(IntegerVectorList::const_iterator J=l.begin();J!=l.end();J++)
{
column[j]=(*J)[i];
j++;
}
r.push_back(column);
}
return r;
}
IntegerVectorList multiplyIntegerVectorList(IntegerVectorList const &A, IntegerVectorList const &B)
{
int s1=A.size();
assert(s1);
int r=A.begin()->size();
int t=B.size();
assert(t);
int s2=B.begin()->size();
assert(s1==s2);
IntegerVectorList C;
for(IntegerVectorList::const_iterator I=B.begin();I!=B.end();I++)
{
IntegerVector column(r);
int j=0;
for(IntegerVectorList::const_iterator J=A.begin();J!=A.end();J++)
{
column+=(*I)[j]*(*J);
j++;
}
C.push_back(column);
}
return C;
}
/* Computes the greatest common divisor of two integers.
The result is always positive.
Asserts if both integers are zero.
*/
int gcdGFAN(int r, int s)
{
if(r<0)r=-r;
if(s<0)s=-s;
if(s<r)
{
int t;
t=r;
r=s;
s=t;
}
while(r!=0)
{
int t=s%r;
s=r;
r=t;
}
assert(s!=0);
return s;
}
/* Returns positive gcd of elements in the vector.
The result is always positive.
Asserts if the vector is the zero-vector.
*/
int gcdOfVector(IntegerVector const &v)
{
int ret=0;
for(int i=0;i<v.size();i++)if(ret=v[i])break;
if(ret<0)ret=-ret;
assert(ret!=0);
for(int i=0;i<v.size();i++)ret=gcdGFAN(ret,v[i]);
return ret;
}
int gcdOfVectorCandidate(IntegerVector const &v, int ret)
{
for(int i=0;i<v.size();i++)
{
ret=gcdGFAN(ret,v[i]);
if(ret==1)break;
}
return ret;
}
/* Uses gcd to put (the direction given by) the vector in a unique form by scaling.
Only positive scaling is applied.
If the input is the zero-vector so is the output.
Otherwise, the common divisor of the output is 1.
*/
void normalizedLowLevel(IntegerVector const &v, IntegerVector &dest)
{
int a;
int n=v.size();
assert(n==dest.size());
int smallest=0x7fffffff;
int zeroTest=0;
for(int i=0;i<n;i++)
{
int vv=v.UNCHECKEDACCESS(i);
if(vv>0)
{
if(vv<smallest)smallest=vv;
}
else if(vv<0)
{
if(-vv<smallest)smallest=-vv;
}
zeroTest|=vv;
}
if(smallest==1)goto returnv;
if(zeroTest==0)goto returnv;
a=gcdOfVectorCandidate(v,smallest);
for(int i=0;i<n;i++)dest[i]=v.UNCHECKEDACCESS(i)/a;
return;
returnv:
for(int i=0;i<n;i++)dest[i]=v.UNCHECKEDACCESS(i);
}
IntegerVector normalized(IntegerVector const &v)
{
int n=v.size();
int smallest=0x7fffffff;
for(int i=0;i<n;i++)
{
if(v[i]>0)
{
if(v[i]<smallest)smallest=v[i];
}
else if(v[i]<0)
{
if(-(v[i])<smallest)smallest=-(v[i]);
}
}
if(smallest==1)return v;
if(v.isZero())return v;
int a=gcdOfVectorCandidate(v,smallest);
// int a=gcdOfVector(v);
IntegerVector V(n);
for(int i=0;i<n;i++)V[i]=v[i]/a;
return V;
}
IntegerVectorList subvectorsOfIntegerVectorList(IntegerVectorList const &l, list<int> const &chosen)
{
IntegerVectorList ret;
for(IntegerVectorList::const_iterator i=l.begin();i!=l.end();i++)
ret.push_back(i->subvector(chosen));
return ret;
}
void removeDuplicates(IntegerVectorList &l)
{
l.sort();
l.unique();
}
|