From c597820746d61e8c20f2a67d018cfce18d4f56f3 Mon Sep 17 00:00:00 2001
From: Andrea Spadaccini <andrea.spadaccini@microsoft.com>
Date: Wed, 16 Oct 2019 13:59:32 +0100
Subject: [PATCH 1/2] Fix typo: an -> a.

---
 ortools/sat/csharp/IntegerExpressions.cs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ortools/sat/csharp/IntegerExpressions.cs b/ortools/sat/csharp/IntegerExpressions.cs
index 82345d314b..43b7a6e51c 100644
--- a/ortools/sat/csharp/IntegerExpressions.cs
+++ b/ortools/sat/csharp/IntegerExpressions.cs
@@ -45,7 +45,7 @@ namespace Google.OrTools.Sat
     int GetIndex();
   }
 
-  // Holds an linear expression.
+  // Holds a linear expression.
   public class LinearExpr
   {
 

From a24c7904ab4f7fb8f1d84649ccaf6f63562ac44d Mon Sep 17 00:00:00 2001
From: Paul <ptrow@google.com>
Date: Tue, 19 Nov 2019 17:02:48 -0500
Subject: [PATCH 2/2] Create mip_var_array.py

New MIP example for documentation.
---
 .../linear_solver/samples/mip_var_array.py    | 103 ++++++++++++++++++
 1 file changed, 103 insertions(+)
 create mode 100644 ortools/linear_solver/samples/mip_var_array.py

diff --git a/ortools/linear_solver/samples/mip_var_array.py b/ortools/linear_solver/samples/mip_var_array.py
new file mode 100644
index 0000000000..fdd751c965
--- /dev/null
+++ b/ortools/linear_solver/samples/mip_var_array.py
@@ -0,0 +1,103 @@
+# 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.
+"""Integer programming examples that show how to use the APIs."""
+# [START program]
+# [START import]
+from __future__ import print_function
+from ortools.linear_solver import pywraplp
+# [END import]
+
+
+# [START data_model]
+def create_data_model():
+  """Stores the data for the problem."""
+  data = {}
+  # Locations in block units
+  data['constraint_coeffs'] = [
+      [5, 7, 9, 2, 1],
+      [18, 4, -9, 10, 12],
+      [4, 7, 3, 8, 5],
+      [5, 13, 16, 3, -7],
+  ]
+  data['bounds'] = [250, 285, 211, 315]
+  data['obj_coeffs'] = [7, 8, 2, 9, 6]
+  data['num_vars'] = 5
+  data['num_constraints'] = 4
+  return data
+# [END data_model]
+
+
+def main():
+  # [START data]
+  data = create_data_model()
+  # [END data]
+
+  # [START solver]
+  # MOE:begin_strip
+  # Create the mip solver with the CBC backend.
+  solver = pywraplp.Solver(
+      'simple_mip_program',
+      pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
+  # [END solver]
+  # [START variables]
+  infinity = solver.infinity()
+  x = {}
+  for j in range(data['num_vars']):
+    x[j] = solver.IntVar(0, infinity, 'x[%i]' % j)
+  print('Number of variables =', solver.NumVariables())
+  # [END variables]
+
+  # [START constraints]
+  for i in range(data['num_constraints']):
+    constraint = solver.RowConstraint(0, data['bounds'][i], '')
+    for j in range(data['num_vars']):
+      constraint.SetCoefficient(x[j], data['constraint_coeffs'][i][j])
+  print('Number of constraints =', solver.NumConstraints())
+  # In Python, you can also set the constraints as follows.
+  # for i in range(data['num_constraints']):
+  #  constraint_expr = \
+  # [data['constraint_coeffs'][i][j] * x[j] for j in range(data['num_vars'])]
+  #  solver.Add(sum(constraint_expr) <= data['bounds'][i])
+  # [END constraints]
+
+  # [START objective]
+  objective = solver.Objective()
+  for j in range(data['num_vars']):
+    objective.SetCoefficient(x[j], data['obj_coeffs'][j])
+  objective.SetMaximization()
+  # In Python, you can also set the objective as follows.
+  # obj_expr = [data['obj_coeffs'][j] * x[j] for j in range(data['num_vars'])]
+  # solver.Maximize(solver.Sum(obj_expr))
+  # [END objective]
+
+  # [START solve]
+  status = solver.Solve()
+  # [END solve]
+
+  # [START print_solution]
+  if status == pywraplp.Solver.OPTIMAL:
+    print('Objective value =', solver.Objective().Value())
+    for j in range(data['num_vars']):
+      print(x[j].name(), ' = ', x[j].solution_value())
+    print()
+    print('Problem solved in %f milliseconds' % solver.wall_time())
+    print('Problem solved in %d iterations' % solver.iterations())
+    print('Problem solved in %d branch-and-bound nodes' % solver.nodes())
+  else:
+    print('The problem does not have an optimal solution.')
+  # [END print_solution]
+
+
+if __name__ == '__main__':
+  main()
+# [END program]