replace magic_square by magic_square_sat with much improved performance

examples/cpp/magic_square_sat.cc

@@ -0,0 +1,96 @@
+// Copyright 2010-2018 Google LLC
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <string>
+#include <vector>
+
+#include "ortools/base/commandlineflags.h"
+#include "ortools/base/stringprintf.h"
+#include "ortools/sat/cp_model.h"
+#include "ortools/sat/model.h"
+
+DEFINE_int32(size, 7, "Size of the magic square");
+DEFINE_string(params, "", "Sat paramters");
+
+namespace operations_research {
+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<IntVar> all_variables;
+  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.
+  for (int i = 0; i < size; ++i) {
+    builder.AddAllDifferent(all_variables);
+  }
+
+  const int sum = size * (size * size + 1) / 2;
+  // Sum on rows.
+  for (int i = 0; i < size; ++i) {
+    builder.AddEquality(LinearExpr::Sum(square[i]), sum);
+  }
+
+  // Sum on columns.
+  for (int i = 0; i < size; ++i) {
+   builder.AddEquality(LinearExpr::Sum(transposed[i]), sum);
+  }
+
+  // Sum on diagonals.
+  builder.AddEquality(LinearExpr::Sum(diag1), sum);
+  builder.AddEquality(LinearExpr::Sum(diag2), sum);
+  
+  const CpSolverResponse response = Solve(builder);
+  if (response.status() == CpSolverStatus::FEASIBLE) {
+    for (int n = 0; n < size; ++n) {
+      std::string output;
+      for (int m = 0; m < size; ++m) {
+        StringAppendF(&output, "%3lld ",
+                      SolutionIntegerValue(response, square[n][m]));
+      }
+      LOG(INFO) << output;
+    } 
+  } else {
+    LOG(INFO) << "No solution found!";
+  }
+  LOG(INFO) << CpSolverResponseStats(response);  
+}
+
+} // namespace sat
+} // namespace sat
+
+int main(int argc, char **argv) {
+  base::SetFlag(&FLAGS_logtostderr, true);
+  gflags::ParseCommandLineFlags(&argc, &argv, true);
+  operations_research::sat::MagicSquare(FLAGS_size);
+  return EXIT_SUCCESS;
+}