ortools-clone/examples/notebook/contrib/broken_weights.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com\n",
    "#\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",
    "\"\"\"\n",
    "\n",
    "  Broken weights problem in Google CP Solver.\n",
    "\n",
    "  From http://www.mathlesstraveled.com/?p=701\n",
    "  '''\n",
    "  Here's a fantastic problem I recently heard. Apparently it was first\n",
    "  posed by Claude Gaspard Bachet de Meziriac in a book of arithmetic problems\n",
    "  published in 1612, and can also be found in Heinrich Dorrie's 100\n",
    "  Great Problems of Elementary Mathematics.\n",
    "\n",
    "      A merchant had a forty pound measuring weight that broke\n",
    "      into four pieces as the result of a fall. When the pieces were\n",
    "      subsequently weighed, it was found that the weight of each piece\n",
    "      was a whole number of pounds and that the four pieces could be\n",
    "      used to weigh every integral weight between 1 and 40 pounds. What\n",
    "      were the weights of the pieces?\n",
    "\n",
    "  Note that since this was a 17th-century merchant, he of course used a\n",
    "  balance scale to weigh things. So, for example, he could use a 1-pound\n",
    "  weight and a 4-pound weight to weigh a 3-pound object, by placing the\n",
    "  3-pound object and 1-pound weight on one side of the scale, and\n",
    "  the 4-pound weight on the other side.\n",
    "  '''\n",
    "\n",
    "  Compare with the following problems:\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/broken_weights.mzn\n",
    "  * ECLiPSE: http://www.hakank.org/eclipse/broken_weights.ecl\n",
    "  * Gecode: http://www.hakank.org/gecode/broken_weights.cpp\n",
    "  * Comet: http://hakank.org/comet/broken_weights.co\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n",
    "\"\"\"\n",
    "from __future__ import print_function\n",
    "import sys\n",
    "\n",
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "\n",
    "# Create the solver.\n",
    "solver = pywrapcp.Solver('Broken weights')\n",
    "\n",
    "#\n",
    "# data\n",
    "#\n",
    "print('total weight (m):', m)\n",
    "print('number of pieces (n):', n)\n",
    "print()\n",
    "\n",
    "#\n",
    "# variables\n",
    "#\n",
    "weights = [solver.IntVar(1, m, 'weights[%i]' % j) for j in range(n)]\n",
    "x = {}\n",
    "for i in range(m):\n",
    "  for j in range(n):\n",
    "    x[i, j] = solver.IntVar(-1, 1, 'x[%i,%i]' % (i, j))\n",
    "x_flat = [x[i, j] for i in range(m) for j in range(n)]\n",
    "\n",
    "#\n",
    "# constraints\n",
    "#\n",
    "\n",
    "# symmetry breaking\n",
    "for j in range(1, n):\n",
    "  solver.Add(weights[j - 1] < weights[j])\n",
    "\n",
    "solver.Add(solver.SumEquality(weights, m))\n",
    "\n",
    "# Check that all weights from 1 to 40 can be made.\n",
    "#\n",
    "# Since all weights can be on either side\n",
    "# of the side of the scale we allow either\n",
    "# -1, 0, or 1 or the weights, assuming that\n",
    "# -1 is the weights on the left and 1 is on the right.\n",
    "#\n",
    "for i in range(m):\n",
    "  solver.Add(i + 1 == solver.Sum([weights[j] * x[i, j] for j in range(n)]))\n",
    "\n",
    "# objective\n",
    "objective = solver.Minimize(weights[n - 1], 1)\n",
    "\n",
    "#\n",
    "# search and result\n",
    "#\n",
    "db = solver.Phase(weights + x_flat, solver.CHOOSE_FIRST_UNBOUND,\n",
    "                  solver.ASSIGN_MIN_VALUE)\n",
    "\n",
    "search_log = solver.SearchLog(1)\n",
    "\n",
    "solver.NewSearch(db, [objective])\n",
    "\n",
    "num_solutions = 0\n",
    "while solver.NextSolution():\n",
    "  num_solutions += 1\n",
    "  print('weights:   ', end=' ')\n",
    "  for w in [weights[j].Value() for j in range(n)]:\n",
    "    print('%3i ' % w, end=' ')\n",
    "  print()\n",
    "  print('-' * 30)\n",
    "  for i in range(m):\n",
    "    print('weight  %2i:' % (i + 1), end=' ')\n",
    "    for j in range(n):\n",
    "      print('%3i ' % x[i, j].Value(), end=' ')\n",
    "    print()\n",
    "  print()\n",
    "print()\n",
    "solver.EndSearch()\n",
    "\n",
    "print('num_solutions:', num_solutions)\n",
    "print('failures :', solver.Failures())\n",
    "print('branches :', solver.Branches())\n",
    "print('WallTime:', solver.WallTime(), 'ms')\n",
    "\n",
    "m = 40\n",
    "n = 4\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 4
}