diff --git a/examples/c++/example.cpp b/examples/c++/example.cpp index b348e7d362e..750933cba13 100644 --- a/examples/c++/example.cpp +++ b/examples/c++/example.cpp @@ -974,6 +974,83 @@ void substitute_example() { std::cout << new_f << std::endl; } +void sudoku_example() { + std::cout << "sudoku example\n"; + + context c; + + // 9x9 matrix of integer variables + expr_vector x(c); + for (unsigned i = 0; i < 9; ++i) + for (unsigned j = 0; j < 9; ++j) { + std::stringstream x_name; + + x_name << "x_" << i << '_' << j; + x.push_back(c.int_const(x_name.str().c_str())); + } + + solver s(c); + + // each cell contains a value in {1, ..., 9} + for (unsigned i = 0; i < 9; ++i) + for (unsigned j = 0; j < 9; ++j) { + s.add(x[i * 9 + j] >= 1 && x[i * 9 + j] <= 9); + } + + // each row contains a digit at most once + for (unsigned i = 0; i < 9; ++i) { + expr_vector t(c); + for (unsigned j = 0; j < 9; ++j) + t.push_back(x[i * 9 + j]); + s.add(distinct(t)); + } + + // each column contains a digit at most once + for (unsigned j = 0; j < 9; ++j) { + expr_vector t(c); + for (unsigned i = 0; i < 9; ++i) + t.push_back(x[i * 9 + j]); + s.add(distinct(t)); + } + + // each 3x3 square contains a digit at most once + for (unsigned i0 = 0; i0 < 3; i0++) { + for (uint j0 = 0; j0 < 3; j0++) { + expr_vector t(c); + for (unsigned i = 0; i < 3; i++) + for (unsigned j = 0; j < 3; j++) + t.push_back(x[(i0 * 3 + i) * 9 + j0 * 3 + j]); + s.add(distinct(t)); + } + } + + // sudoku instance, we use '0' for empty cells + int instance[9][9] = {{0,0,0,0,9,4,0,3,0}, + {0,0,0,5,1,0,0,0,7}, + {0,8,9,0,0,0,0,4,0}, + {0,0,0,0,0,0,2,0,8}, + {0,6,0,2,0,1,0,5,0}, + {1,0,2,0,0,0,0,0,0}, + {0,7,0,0,0,0,5,2,0}, + {9,0,0,0,6,5,0,0,0}, + {0,4,0,9,7,0,0,0,0}}; + + for (unsigned i = 0; i < 9; i++) + for (unsigned j = 0; j < 9; j++) + if (instance[i][j] != 0) + s.add(x[i * 9 + j] == instance[i][j]); + + std::cout << s.check() << std::endl; + std::cout << s << std::endl; + + model m = s.get_model(); + for (unsigned i = 0; i < 9; ++i) { + for (unsigned j = 0; j < 9; ++j) + std::cout << m.eval(x[i * 9 + j]); + std::cout << '\n'; + } +} + int main() { try { demorgan(); std::cout << "\n"; @@ -1012,6 +1089,7 @@ int main() { expr_vector_example(); std::cout << "\n"; exists_expr_vector_example(); std::cout << "\n"; substitute_example(); std::cout << "\n"; + sudoku_example(); std::cout << "\n"; std::cout << "done\n"; } catch (exception & ex) {