{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2025 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# mip_var_array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/linear_solver/mip_var_array.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/ortools/linear_solver/samples/mip_var_array.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "MIP example that uses a variable array.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "\n",
    "def create_data_model():\n",
    "    \"\"\"Stores the data for the problem.\"\"\"\n",
    "    data = {}\n",
    "    data[\"constraint_coeffs\"] = [\n",
    "        [5, 7, 9, 2, 1],\n",
    "        [18, 4, -9, 10, 12],\n",
    "        [4, 7, 3, 8, 5],\n",
    "        [5, 13, 16, 3, -7],\n",
    "    ]\n",
    "    data[\"bounds\"] = [250, 285, 211, 315]\n",
    "    data[\"obj_coeffs\"] = [7, 8, 2, 9, 6]\n",
    "    data[\"num_vars\"] = 5\n",
    "    data[\"num_constraints\"] = 4\n",
    "    return data\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def main():\n",
    "    data = create_data_model()\n",
    "    # Create the mip solver with the SCIP backend.\n",
    "    solver = pywraplp.Solver.CreateSolver(\"SCIP\")\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    infinity = solver.infinity()\n",
    "    x = {}\n",
    "    for j in range(data[\"num_vars\"]):\n",
    "        x[j] = solver.IntVar(0, infinity, \"x[%i]\" % j)\n",
    "    print(\"Number of variables =\", solver.NumVariables())\n",
    "\n",
    "    for i in range(data[\"num_constraints\"]):\n",
    "        constraint = solver.RowConstraint(0, data[\"bounds\"][i], \"\")\n",
    "        for j in range(data[\"num_vars\"]):\n",
    "            constraint.SetCoefficient(x[j], data[\"constraint_coeffs\"][i][j])\n",
    "    print(\"Number of constraints =\", solver.NumConstraints())\n",
    "    # In Python, you can also set the constraints as follows.\n",
    "    # for i in range(data['num_constraints']):\n",
    "    #  constraint_expr = \\\n",
    "    # [data['constraint_coeffs'][i][j] * x[j] for j in range(data['num_vars'])]\n",
    "    #  solver.Add(sum(constraint_expr) <= data['bounds'][i])\n",
    "\n",
    "    objective = solver.Objective()\n",
    "    for j in range(data[\"num_vars\"]):\n",
    "        objective.SetCoefficient(x[j], data[\"obj_coeffs\"][j])\n",
    "    objective.SetMaximization()\n",
    "    # In Python, you can also set the objective as follows.\n",
    "    # obj_expr = [data['obj_coeffs'][j] * x[j] for j in range(data['num_vars'])]\n",
    "    # solver.Maximize(solver.Sum(obj_expr))\n",
    "\n",
    "    print(f\"Solving with {solver.SolverVersion()}\")\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        print(\"Objective value =\", solver.Objective().Value())\n",
    "        for j in range(data[\"num_vars\"]):\n",
    "            print(x[j].name(), \" = \", x[j].solution_value())\n",
    "        print()\n",
    "        print(f\"Problem solved in {solver.wall_time():d} milliseconds\")\n",
    "        print(f\"Problem solved in {solver.iterations():d} iterations\")\n",
    "        print(f\"Problem solved in {solver.nodes():d} branch-and-bound nodes\")\n",
    "    else:\n",
    "        print(\"The problem does not have an optimal solution.\")\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}