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
|
#include <iostream>
#include <string>
#include <cstdlib>
#include <cstdint>
#include <cassert>
using namespace std;
class Board{
int8_t *bd;
inline int8_t& operator[](int i){return bd[i];}
inline int8_t& at(int x,int y,bool tr=false){
if(tr)return bd[S*x+y];
else return bd[S*y+x];
}
string row(int i,bool tr){return (tr?"column ":"row ")+to_string(i+1);}
string column(int i,bool tr){return (tr?"row ":"column ")+to_string(i+1);}
string pos(int x,int y,bool tr){return "("+to_string(tr?y+1:x+1)+","+to_string(tr?x+1:y+1)+")";}
bool solvefullrows(bool tr){
bool changed=false;
for(int y=0;y<S;y++){
int n0=0,n1=0,ex=-1;
for(int x=0;x<S;x++){
switch(at(x,y,tr)){
case -1: ex=x; break;
case 0: n0++; break;
case 1: n1++; break;
}
}
if(ex!=-1&&n0+n1==S-1){
bool v=n0<S/2?0:1;
at(ex,y,tr)=v;
cerr<<"Fill "<<row(y,tr)<<": "<<pos(ex,y,tr)<<" -> "<<v<<endl<<*this<<endl<<endl;
changed=true;
}
}
return changed;
}
bool solvefullrows(){return solvefullrows(false)|solvefullrows(true);}
bool completerows(bool tr){
bool changed=false;
for(int y=0;y<S;y++){
int n0=0,n1=0;
for(int x=0;x<S;x++){
switch(at(x,y,tr)){
case 0: n0++; break;
case 1: n1++; break;
}
}
if(n0==S/2&&n1<S/2){
cerr<<"Complete "<<row(y,tr)<<" with ones:";
for(int x=0;x<S;x++)if(at(x,y,tr)==-1){
at(x,y,tr)=1;
cerr<<' '<<pos(x,y,tr)<<" -> 1";
}
cerr<<endl<<*this<<endl<<endl;
changed=true;
} else if(n1==S/2&&n0<S/2){
cerr<<"Complete "<<row(y,tr)<<" with zeros:";
for(int x=0;x<S;x++)if(at(x,y,tr)==-1){
at(x,y,tr)=0;
cerr<<' '<<pos(x,y,tr)<<" -> 0";
}
cerr<<endl<<*this<<endl<<endl;
changed=true;
}
}
return changed;
}
bool completerows(){return completerows(false)|completerows(true);}
bool solveequalrows(bool tr){
bool changed=false;
for(int y1=0;y1<S;y1++){
for(int y2=y1+1;y2<S;y2++){
int x,n1=0,n2=0,exa=-1,exb=-1;
for(x=0;x<S;x++){
int v1=at(x,y1,tr),v2=at(x,y2,tr);
n1+=v1!=-1; n2+=v2!=-1;
if(v1==-1||v2==-1){
exa=exb;
exb=x;
}
if(v1!=-1&&v2!=-1&&v1!=v2)break;
}
if(x==S){
if(n1==S&&n2==S-2){
at(exa,y2,tr)=!at(exa,y1,tr);
at(exb,y2,tr)=!at(exb,y1,tr);
cerr<<"Prevent "<<row(y2,tr)<<" from matching "<<row(y1,tr)
<<": "<<pos(exa,y2,tr)<<" -> "<<!at(exa,y1,tr)
<<", "<<pos(exb,y2,tr)<<" -> "<<!at(exb,y1,tr)<<endl<<*this<<endl<<endl;
changed=true;
} else if(n1==S-2&&n2==S){
at(exa,y1,tr)=!at(exa,y2,tr);
at(exb,y1,tr)=!at(exb,y2,tr);
cerr<<"Prevent "<<row(y1,tr)<<" from matching "<<row(y2,tr)
<<": "<<pos(exa,y1,tr)<<" -> "<<!at(exa,y2,tr)
<<", "<<pos(exb,y1,tr)<<" -> "<<!at(exb,y2,tr)<<endl<<*this<<endl<<endl;
changed=true;
}
}
}
}
return changed;
}
bool solveequalrows(){return solveequalrows(false)|solveequalrows(true);}
bool solvetrits(bool tr){
bool changed=false;
for(int y=0;y<S;y++){
for(int x=0;x<S;x++){
if(at(x,y,tr)!=-1)continue;
bool opp;
if(x>0&&x<S-1&&at(x-1,y,tr)!=-1&&at(x-1,y,tr)==at(x+1,y,tr))opp=at(x-1,y,tr);
else if(x>1&&at(x-2,y,tr)!=-1&&at(x-2,y,tr)==at(x-1,y,tr))opp=at(x-1,y,tr);
else if(x<S-2&&at(x+2,y,tr)!=-1&&at(x+2,y,tr)==at(x+1,y,tr))opp=at(x+1,y,tr);
else continue;
at(x,y,tr)=!opp;
cerr<<"Prevent trit: "<<pos(x,y,tr)<<" -> "<<!opp<<endl<<*this<<endl<<endl;
changed=true;
}
}
return changed;
}
bool solvetrits(){return solvetrits(false)|solvetrits(true);}
bool verifycounts(bool tr){
for(int y=0;y<S;y++){
int n0=0,n1=0;
for(int x=0;x<S;x++){
switch(at(x,y,tr)){
case 0: n0++; break;
case 1: n1++; break;
}
}
if(n0!=S/2||n1!=S/2){
cerr<<"Count verification failure at "<<row(y,tr)<<endl;
return false;
}
}
return true;
}
bool verifycounts(){return verifycounts(false)&&verifycounts(true);}
bool verifytrits(bool tr){
for(int y=0;y<S;y++){
int pr=-1,n=0;
for(int x=0;x<S;x++){
int v=at(x,y,tr);
if(pr==v){
n++;
if(pr!=-1&&n>=3){
cerr<<"Trit verification failure at "<<pos(x,y,tr)<<endl;
return false;
}
} else {
pr=v;
n=0;
}
}
}
return true;
}
bool verifytrits(){return verifytrits(false)&&verifytrits(true);}
bool verifyequalrows(bool tr){
for(int y1=0;y1<S;y1++){
for(int y2=y1+1;y2<S;y2++){
int x;
for(x=0;x<S;x++){
if(at(x,y1,tr)!=at(x,y2,tr))break;
}
if(x==S){
cerr<<"Equal row verification failure on "<<row(y1,tr)<<" and "<<row(y2,tr)<<endl;
return false;
}
}
}
return true;
}
bool verifyequalrows(){return verifyequalrows(false)&&verifyequalrows(true);}
public:
const int S;
Board(int S):S(S){
if(S<2||S%2==1){
cerr<<"Invalid board size "<<S<<endl;
exit(1);
}
bd=new int8_t[S*S];
}
~Board(){
delete[] bd;
}
inline int8_t operator[](int i) const {return bd[i];}
inline int8_t at(int x,int y) const {return bd[S*y+x];}
void solve(){
while(solvefullrows()
|completerows()
|solveequalrows()
|solvetrits());
}
bool verify(){
return verifycounts()&&verifytrits()&&verifyequalrows();
}
friend istream& operator>>(istream &is,Board &bd);
friend ostream& operator<<(ostream &os,const Board &bd);
};
istream& operator>>(istream &is,Board &bd){
char c;
for(int i=0;i<bd.S*bd.S;i++){
is>>c;
if(c=='0')bd[i]=0;
else if(c=='1')bd[i]=1;
else if(c=='.'||c=='_')bd[i]=-1;
else {
cerr<<"Invalid char inputted: '"<<c<<'\''<<endl;
exit(1);
}
}
return is;
}
ostream& operator<<(ostream &os,const Board &bd){
for(int y=0;y<bd.S;y++){
if(y!=0)os<<'\n';
for(int x=0;x<bd.S;x++){
if(x!=0)os<<' ';
switch(bd.at(x,y)){
case -1: os<<'.'; break;
case 0: os<<'0'; break;
case 1: os<<'1'; break;
default: os<<'?'; break;
}
}
}
return os;
}
int main(){
int S;
cin>>S;
Board bd(S);
cin>>bd;
cerr<<bd<<endl<<endl;
bd.solve();
if(!bd.verify()){
cerr<<"VERIFICATION FAILURE!"<<endl;
return 1;
}
cout<<bd<<endl;
return 0;
}
|
