constexpr Cell next(const Sudoku& s)
{
for(size_t i=0; i<s.dimension(); ++i)
for(size_t j=0; j<s.dimension(); ++j)
if (s(i,j) == 0) return {i,j};
return {std::numeric_limits<Cell::first_type>::max(),std::numeric_limits<Cell::second_type>::max()};
}
constexpr bool finished(const Sudoku& s)
{
for(size_t i=0; i<s.dimension(); ++i)
for(size_t j=0; j<s.dimension(); ++j)
if (s(i,j) == 0) return false;
return true;
}
constexpr bool colValid(const Sudoku& s, size_t col, size_t pos = 0)
{
if (pos > s.dimension()) return true;
else if (s(pos,col) == 0) return colValid(s,col,pos+1);
else {
for(size_t i=pos+1;i<s.dimension();++i)
if (s(i,col) == s(pos,col)) return false;
return colValid(s,col,pos+1);
}
}
constexpr bool rowValid(const Sudoku& s, size_t row, size_t pos = 0)
{
if (pos > s.dimension()) return true;
else if (s(row,pos) == 0) return rowValid(s,row,pos+1);
else {
for(size_t i=pos+1;i<s.dimension();++i)
if (s(row,i) == s(row,pos)) return false;
return rowValid(s,row,pos+1);
}
}
constexpr bool quadrantValid(const Sudoku& s, size_t x, size_t y, size_t pos = 0)
{
if (pos > s.dimension()) return true;
else if (qVal(s, x,y,pos) == 0) return quadrantValid(s, x, y, pos+1);
else {
for(size_t i=pos+1;i<s.dimension();++i)
if (qVal(s, x,y,i) == qVal(s, x,y,pos)) return false;
return quadrantValid(s,x,y,pos+1);
}
}
constexpr bool valid(const Sudoku& s)
{
for(size_t x=0;x<s.dimension();++x) {
if (!rowValid(s,x)) return false;
if (!colValid(s,x)) return false;
}
size_t qsize = sqrt(s.dimension());
for(size_t i=0; i<qsize; ++i)
for(size_t j=0; j<qsize; ++j)
if (!quadrantValid(s,i,j)) return false;
return true;
}
constexpr Sudoku solve(const Sudoku& s)
{
if (!valid(s)) return s;
else {
const Cell n{next(s)};
if (n.first == std::numeric_limits<Cell::first_type>::max()) return s;
for(unsigned i=1;i<=s.dimension();++i) {
const auto ns = s.replace(n.first,n.second,i);
const Sudoku res = solve(ns);
if (finished(res) && valid(res)) return res;
}
return s;
}
}
// return the value at offset in quadrant(x,y)
constexpr unsigned qVal(const Sudoku& s, size_t x,size_t y, size_t offset = 0)
{
size_t qsize = sqrt(s.dimension());
return s(qsize*x + offset/qsize, qsize*y + offset % qsize);
}