#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
class SpecificPolyominoCovering
{
public:
vector <string> findCovering(vector <string> region)
{
try {
rec(0, 0, region);
} catch( vector<string>& r ) {
return r;
}
return vector<string>();
}
bool nextX(int &y, int &x, vector<string>& r)
{
while( r[y][x] != 'X' ) {
++x;
if( x == r[y].size() ) {
x=0, ++y;
if( y == r.size() )
return false;
}
}
return true;
}
bool canFill( vector<string> r )
{
return canFill_rec(0, 0, r);
}
bool canFill_rec(int y, int x, vector<string>& r)
{
if( !nextX(y, x, r) )
return true;
// if it was the pattern fillable both by B and A,
// XX?X
// XXXX
// then, if we can fill starting from A it implies ?=X
// In this case, we must have been able to fill starting
// from B. Thus, we never need to try A if we've failed
// filling by B. The "lexicographically first" will by
// considered elsewhere.
if( x+1 < r[y].size() && r[y][x+1]=='X' )
{
r[y][x] = r[y][x+1] = 'B';
return canFill_rec(y, x, r);
}
if( x+3 < r[y].size() && y+1 < r.size() )
{
int py[] = {0,0,1,1,1,1};
int px[] = {0,3,0,1,2,3};
for(int i=0; i<6; ++i)
if( r[y+py[i]][x+px[i]]!='X' )
return false;
else
r[y+py[i]][x+px[i]] = 'A';
return canFill_rec(y, x, r);
}
return false;
}
void rec(int y, int x, vector<string>& r)
{
if( !nextX(y, x, r) )
throw r;
// try to fill by A
if( x+3 < r[y].size() && y+1 < r.size() )
{
int py[] = {0,0,1,1,1,1};
int px[] = {0,3,0,1,2,3};
bool bad = false;
for(int i=0; i<6; ++i)
if( r[y+py[i]][x+px[i]]!='X' )
bad = true;
if( !bad )
{
for(int i=0; i<6; ++i)
r[y+py[i]][x+px[i]] = 'A';
if( canFill(r) )
rec(y, x, r);
for(int i=0; i<6; ++i)
r[y+py[i]][x+px[i]] = 'X';
}
}
// try to fill by B
if( x+1 < r[y].size() && r[y][x+1]=='X' )
{
r[y][x] = r[y][x+1] = 'B';
rec(y, x, r);
r[y][x] = r[y][x+1] = 'X';
}
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time;string timer() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
int verify_case(const vector <string> &Expected, const vector <string> &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: " << print_array(Expected) << endl; cerr << "\tReceived: " << print_array(Received) << endl; } return 0;}
template<int N> struct Case_ { Case_(){start_time=clock();} };
char Test_(...);
int Test_(Case_<0>) {
string region_[] = {"XXXX",
"XXXX"};
vector <string> region(region_, region_+sizeof(region_)/sizeof(*region_));
string RetVal_[] = {"ABBA", "AAAA" };
vector <string> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, SpecificPolyominoCovering().findCovering(region)); }
int Test_(Case_<1>) {
string region_[] = {"X..XXXX..X",
"XXXX..XXXX"};
vector <string> region(region_, region_+sizeof(region_)/sizeof(*region_));
string RetVal_[] = {"A..ABBA..A", "AAAA..AAAA" };
vector <string> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, SpecificPolyominoCovering().findCovering(region)); }
int Test_(Case_<2>) {
string region_[] = {"XXXXXX",
"XXXXXX",
"XXXXXX"};
vector <string> region(region_, region_+sizeof(region_)/sizeof(*region_));
string RetVal_[] = {"ABBABB", "AAAABB", "BBBBBB" };
vector <string> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, SpecificPolyominoCovering().findCovering(region)); }
int Test_(Case_<3>) {
string region_[] = {"X..XX",
"XXXXX"};
vector <string> region(region_, region_+sizeof(region_)/sizeof(*region_));
vector <string> RetVal;
return verify_case(RetVal, SpecificPolyominoCovering().findCovering(region)); }
int Test_(Case_<4>) {
string region_[] = {"XXXXXXXXXX",
"XXXXXXXXXX",
"XXXXXXXXXX",
"XXXXX..XXX",
"XXXXXXXXXX",
"XXXXXXXXXX",
"XXXXXXXXXX"};
vector <string> region(region_, region_+sizeof(region_)/sizeof(*region_));
string RetVal_[] = {"ABBAABBABB", "AAAAAAAABB", "ABBABBBBBB", "AAAAA..ABB", "ABBAAAAABB", "AAAAABBABB", "BBBBAAAABB" };
vector <string> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, SpecificPolyominoCovering().findCovering(region)); }
template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
template<> void Run_<-1>() {}
int main() { Run_<0>(); }
// END CUT HERE