fix

examples/cpp/magic_square_sat.cc

@@ -33,46 +33,52 @@ namespace sat {
 void MagicSquare(int size) {
   CpModelBuilder builder;
 
-  std::vector<std::vector<IntVar> > square(size);
-  std::vector<std::vector<IntVar> > transposed(size);
-  std::vector<IntVar> diag1;
-  std::vector<IntVar> diag2;
+  std::vector<std::vector<IntVar>> square(size);
   std::vector<IntVar> all_variables;
-  Domain domain(1, size * size);
+  const Domain domain(1, size * size);
   for (int i = 0; i < size; ++i) {
     for (int j = 0; j < size; ++j) {
       const IntVar var = builder.NewIntVar(domain);
       square[i].push_back(var);
-      transposed[j].push_back(var);
       all_variables.push_back(var);
-      if (i == j) {
-        diag1.push_back(var);
-      }
-      if (i + j == size) {
-        diag2.push_back(var);
-      }
     }
   }
 
-  // All Diff.
+  // All cells take different values.
   for (int i = 0; i < size; ++i) {
     builder.AddAllDifferent(all_variables);
   }
 
-  const int sum = size * (size * size + 1) / 2;
+  // The sum on each row, columns and two main diagonals.
+  const int magic_value = size * (size * size + 1) / 2;
+
   // Sum on rows.
   for (int i = 0; i < size; ++i) {
-    builder.AddEquality(LinearExpr::Sum(square[i]), sum);
+    LinearExpr sum;
+    for (int j = 0; j < size; ++j) {
+      sum += square[i][j];
+    }
+    builder.AddEquality(sum, magic_value);
   }
 
   // Sum on columns.
-  for (int i = 0; i < size; ++i) {
-    builder.AddEquality(LinearExpr::Sum(transposed[i]), sum);
+  for (int j = 0; j < size; ++j) {
+    LinearExpr sum;
+    for (int i = 0; i < size; ++i) {
+      sum += square[i][j];
+    }
+    builder.AddEquality(sum, magic_value);
   }
 
   // Sum on diagonals.
-  builder.AddEquality(LinearExpr::Sum(diag1), sum);
-  builder.AddEquality(LinearExpr::Sum(diag2), sum);
+  LinearExpr diag1_sum;
+  LinearExpr diag2_sum;
+  for (int i = 0; i < size; ++i) {
+    diag1_sum += square[i][i];
+    diag2_sum += square[i][size - 1 - i];
+  }
+  builder.AddEquality(diag1_sum, magic_value);
+  builder.AddEquality(diag2_sum, magic_value);
 
   Model model;
   model.Add(NewSatParameters(absl::GetFlag(FLAGS_params)));