Add Sudoku example.

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) {