261 lines
8.2 KiB
Plaintext
261 lines
8.2 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Copyright 2020 Google LLC."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"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",
|
|
"metadata": {},
|
|
"source": [
|
|
"# magic_square_mip"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<table align=\"left\">\n",
|
|
"<td>\n",
|
|
"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/master/examples/notebook/contrib/magic_square_mip.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
|
|
"</td>\n",
|
|
"<td>\n",
|
|
"<a href=\"https://github.com/google/or-tools/blob/master/examples/contrib/magic_square_mip.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
|
|
"</td>\n",
|
|
"</table>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"!pip install ortools"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Copyright 2011 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",
|
|
" Magic square (integer programming) in Google or-tools.\n",
|
|
"\n",
|
|
" Translated from GLPK:s example magic.mod\n",
|
|
" '''\n",
|
|
" MAGIC, Magic Square\n",
|
|
"\n",
|
|
" Written in GNU MathProg by Andrew Makhorin <mao@mai2.rcnet.ru>\n",
|
|
"\n",
|
|
" In recreational mathematics, a magic square of order n is an\n",
|
|
" arrangement of n^2 numbers, usually distinct integers, in a square,\n",
|
|
" such that n numbers in all rows, all columns, and both diagonals sum\n",
|
|
" to the same constant. A normal magic square contains the integers\n",
|
|
" from 1 to n^2.\n",
|
|
"\n",
|
|
" (From Wikipedia, the free encyclopedia.)\n",
|
|
" '''\n",
|
|
"\n",
|
|
" Compare to the CP version:\n",
|
|
" http://www.hakank.org/google_or_tools/magic_square.py\n",
|
|
"\n",
|
|
" Here we also experiment with how long it takes when\n",
|
|
" using an output_matrix (much longer).\n",
|
|
"\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",
|
|
"from ortools.linear_solver import pywraplp\n",
|
|
"\n",
|
|
"#\n",
|
|
"# main(n, use_output_matrix)\n",
|
|
"# n: size of matrix\n",
|
|
"# use_output_matrix: use the output_matrix\n",
|
|
"#\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"# Create the solver.\n",
|
|
"\n",
|
|
"print('Solver: ', sol)\n",
|
|
"\n",
|
|
"# using GLPK\n",
|
|
"if sol == 'GLPK':\n",
|
|
" solver = pywraplp.Solver('CoinsGridGLPK',\n",
|
|
" pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)\n",
|
|
"else:\n",
|
|
" # Using CLP\n",
|
|
" solver = pywraplp.Solver('CoinsGridCLP',\n",
|
|
" pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
|
|
"\n",
|
|
"#\n",
|
|
"# data\n",
|
|
"#\n",
|
|
"print('n = ', n)\n",
|
|
"\n",
|
|
"# range_n = range(1, n+1)\n",
|
|
"range_n = list(range(0, n))\n",
|
|
"\n",
|
|
"N = n * n\n",
|
|
"range_N = list(range(1, N + 1))\n",
|
|
"\n",
|
|
"#\n",
|
|
"# variables\n",
|
|
"#\n",
|
|
"\n",
|
|
"# x[i,j,k] = 1 means that cell (i,j) contains integer k\n",
|
|
"x = {}\n",
|
|
"for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" for k in range_N:\n",
|
|
" x[i, j, k] = solver.IntVar(0, 1, 'x[%i,%i,%i]' % (i, j, k))\n",
|
|
"\n",
|
|
"# For output. Much slower....\n",
|
|
"if use_output_matrix == 1:\n",
|
|
" print('Using an output matrix')\n",
|
|
" square = {}\n",
|
|
" for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" square[i, j] = solver.IntVar(1, n * n, 'square[%i,%i]' % (i, j))\n",
|
|
"\n",
|
|
"# the magic sum\n",
|
|
"s = solver.IntVar(1, n * n * n, 's')\n",
|
|
"\n",
|
|
"#\n",
|
|
"# constraints\n",
|
|
"#\n",
|
|
"\n",
|
|
"# each cell must be assigned exactly one integer\n",
|
|
"for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" solver.Add(solver.Sum([x[i, j, k] for k in range_N]) == 1)\n",
|
|
"\n",
|
|
"# each integer must be assigned exactly to one cell\n",
|
|
"for k in range_N:\n",
|
|
" solver.Add(solver.Sum([x[i, j, k] for i in range_n for j in range_n]) == 1)\n",
|
|
"\n",
|
|
"# # the sum in each row must be the magic sum\n",
|
|
"for i in range_n:\n",
|
|
" solver.Add(\n",
|
|
" solver.Sum([k * x[i, j, k] for j in range_n for k in range_N]) == s)\n",
|
|
"\n",
|
|
"# # the sum in each column must be the magic sum\n",
|
|
"for j in range_n:\n",
|
|
" solver.Add(\n",
|
|
" solver.Sum([k * x[i, j, k] for i in range_n for k in range_N]) == s)\n",
|
|
"\n",
|
|
"# # the sum in the diagonal must be the magic sum\n",
|
|
"solver.Add(\n",
|
|
" solver.Sum([k * x[i, i, k] for i in range_n for k in range_N]) == s)\n",
|
|
"\n",
|
|
"# # the sum in the co-diagonal must be the magic sum\n",
|
|
"if range_n[0] == 1:\n",
|
|
" # for range_n = 1..n\n",
|
|
" solver.Add(\n",
|
|
" solver.Sum([k * x[i, n - i + 1, k]\n",
|
|
" for i in range_n\n",
|
|
" for k in range_N]) == s)\n",
|
|
"else:\n",
|
|
" # for range_n = 0..n-1\n",
|
|
" solver.Add(\n",
|
|
" solver.Sum([k * x[i, n - i - 1, k]\n",
|
|
" for i in range_n\n",
|
|
" for k in range_N]) == s)\n",
|
|
"\n",
|
|
"# for output\n",
|
|
"if use_output_matrix == 1:\n",
|
|
" for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" solver.Add(\n",
|
|
" square[i, j] == solver.Sum([k * x[i, j, k] for k in range_N]))\n",
|
|
"\n",
|
|
"#\n",
|
|
"# solution and search\n",
|
|
"#\n",
|
|
"solver.Solve()\n",
|
|
"\n",
|
|
"print()\n",
|
|
"\n",
|
|
"print('s: ', int(s.SolutionValue()))\n",
|
|
"if use_output_matrix == 1:\n",
|
|
" for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" print(int(square[i, j].SolutionValue()), end=' ')\n",
|
|
" print()\n",
|
|
" print()\n",
|
|
"else:\n",
|
|
" for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" print(\n",
|
|
" sum([int(k * x[i, j, k].SolutionValue()) for k in range_N]),\n",
|
|
" ' ',\n",
|
|
" end=' ')\n",
|
|
" print()\n",
|
|
"\n",
|
|
"print('\\nx:')\n",
|
|
"for i in range_n:\n",
|
|
" for j in range_n:\n",
|
|
" for k in range_N:\n",
|
|
" print(int(x[i, j, k].SolutionValue()), end=' ')\n",
|
|
" print()\n",
|
|
"\n",
|
|
"print()\n",
|
|
"print('walltime :', solver.WallTime(), 'ms')\n",
|
|
"if sol == 'CBC':\n",
|
|
" print('iterations:', solver.Iterations())\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|