{
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   "source": [
    "# Copyright 2010-2018 Google LLC\n",
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "#     http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License.\n",
    "\"\"\"Implements a step function.\"\"\"\n",
    "\n",
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "from ortools.sat.python import cp_model\n",
    "\n",
    "\n",
    "class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):\n",
    "    \"\"\"Print intermediate solutions.\"\"\"\n",
    "\n",
    "    def __init__(self, variables):\n",
    "        cp_model.CpSolverSolutionCallback.__init__(self)\n",
    "        self.__variables = variables\n",
    "        self.__solution_count = 0\n",
    "\n",
    "    def on_solution_callback(self):\n",
    "        self.__solution_count += 1\n",
    "        for v in self.__variables:\n",
    "            print('%s=%i' % (v, self.Value(v)), end=' ')\n",
    "        print()\n",
    "\n",
    "    def solution_count(self):\n",
    "        return self.__solution_count\n",
    "\n",
    "\n",
    "def step_function_sample_sat():\n",
    "    \"\"\"Encode the step function.\"\"\"\n",
    "\n",
    "    # Model.\n",
    "    model = cp_model.CpModel()\n",
    "\n",
    "    # Declare our primary variable.\n",
    "    x = model.NewIntVar(0, 20, 'x')\n",
    "\n",
    "    # Create the expression variable and implement the step function\n",
    "    # Note it is not defined for x == 2.\n",
    "    #\n",
    "    #        -               3\n",
    "    # -- --      ---------   2\n",
    "    #                        1\n",
    "    #      -- ---            0\n",
    "    # 0 ================ 20\n",
    "    #\n",
    "    expr = model.NewIntVar(0, 3, 'expr')\n",
    "\n",
    "    # expr == 0 on [5, 6] U [8, 10]\n",
    "    b0 = model.NewBoolVar('b0')\n",
    "    model.AddLinearExpressionInDomain(\n",
    "        x, cp_model.Domain.FromIntervals([(5, 6), (8, 10)])).OnlyEnforceIf(b0)\n",
    "    model.Add(expr == 0).OnlyEnforceIf(b0)\n",
    "\n",
    "    # expr == 2 on [0, 1] U [3, 4] U [11, 20]\n",
    "    b2 = model.NewBoolVar('b2')\n",
    "    model.AddLinearExpressionInDomain(\n",
    "        x, cp_model.Domain.FromIntervals([(0, 1), (3, 4),\n",
    "                                          (11, 20)])).OnlyEnforceIf(b2)\n",
    "    model.Add(expr == 2).OnlyEnforceIf(b2)\n",
    "\n",
    "    # expr == 3 when x == 7\n",
    "    b3 = model.NewBoolVar('b3')\n",
    "    model.Add(x == 7).OnlyEnforceIf(b3)\n",
    "    model.Add(expr == 3).OnlyEnforceIf(b3)\n",
    "\n",
    "    # At least one bi is true. (we could use a sum == 1).\n",
    "    model.AddBoolOr([b0, b2, b3])\n",
    "\n",
    "    # Search for x values in increasing order.\n",
    "    model.AddDecisionStrategy([x], cp_model.CHOOSE_FIRST,\n",
    "                              cp_model.SELECT_MIN_VALUE)\n",
    "\n",
    "    # Create a solver and solve with a fixed search.\n",
    "    solver = cp_model.CpSolver()\n",
    "\n",
    "    # Force the solver to follow the decision strategy exactly.\n",
    "    solver.parameters.search_branching = cp_model.FIXED_SEARCH\n",
    "\n",
    "    # Search and print out all solutions.\n",
    "    solution_printer = VarArraySolutionPrinter([x, expr])\n",
    "    solver.SearchForAllSolutions(model, solution_printer)\n",
    "\n",
    "\n",
    "step_function_sample_sat()\n",
    "\n"
   ]
  }
 ],
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