120 lines
3.6 KiB
Plaintext
120 lines
3.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com\n",
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"#\n",
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"# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"# you may not use this file except in compliance with the License.\n",
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"# You may obtain a copy of the License at\n",
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"#\n",
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"# http://www.apache.org/licenses/LICENSE-2.0\n",
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"#\n",
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"# Unless required by applicable law or agreed to in writing, software\n",
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"# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"# See the License for the specific language governing permissions and\n",
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"# limitations under the License.\n",
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"\"\"\"\n",
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"\n",
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" Magic squares in Google CP Solver.\n",
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"\n",
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" Magic square problem.\n",
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"\n",
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" This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
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" Also see my other Google CP Solver models:\n",
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" http://www.hakank.org/google_or_tools/\n",
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"\"\"\"\n",
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"from __future__ import print_function\n",
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"import sys\n",
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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"\n",
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"# Create the solver.\n",
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"solver = pywrapcp.Solver(\"n-queens\")\n",
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"\n",
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"#\n",
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"# data\n",
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"#\n",
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"\n",
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"#\n",
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"# declare variables\n",
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"#\n",
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"x = {}\n",
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"for i in range(n):\n",
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" for j in range(n):\n",
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" x[(i, j)] = solver.IntVar(1, n * n, \"x(%i,%i)\" % (i, j))\n",
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"x_flat = [x[(i, j)] for i in range(n) for j in range(n)]\n",
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"\n",
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"# the sum\n",
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"# s = ( n * (n*n + 1)) / 2\n",
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"s = solver.IntVar(1, n * n * n, \"s\")\n",
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"\n",
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"#\n",
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"# constraints\n",
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"#\n",
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"# solver.Add(s == ( n * (n*n + 1)) / 2)\n",
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"\n",
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"solver.Add(solver.AllDifferent(x_flat))\n",
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"\n",
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"[solver.Add(solver.Sum([x[(i, j)] for j in range(n)]) == s) for i in range(n)]\n",
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"[solver.Add(solver.Sum([x[(i, j)] for i in range(n)]) == s) for j in range(n)]\n",
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"\n",
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"solver.Add(solver.Sum([x[(i, i)] for i in range(n)]) == s) # diag 1\n",
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"solver.Add(solver.Sum([x[(i, n - i - 1)] for i in range(n)]) == s) # diag 2\n",
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"\n",
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"# symmetry breaking\n",
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"# solver.Add(x[(0,0)] == 1)\n",
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"\n",
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"#\n",
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"# solution and search\n",
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"#\n",
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"solution = solver.Assignment()\n",
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"solution.Add(x_flat)\n",
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"solution.Add(s)\n",
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"\n",
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"# db: DecisionBuilder\n",
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"db = solver.Phase(\n",
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" x_flat,\n",
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" # solver.INT_VAR_DEFAULT,\n",
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" solver.CHOOSE_FIRST_UNBOUND,\n",
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" # solver.CHOOSE_MIN_SIZE_LOWEST_MAX,\n",
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"\n",
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" # solver.ASSIGN_MIN_VALUE\n",
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" solver.ASSIGN_CENTER_VALUE)\n",
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"\n",
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"solver.NewSearch(db)\n",
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"num_solutions = 0\n",
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"while solver.NextSolution():\n",
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" print(\"s:\", s.Value())\n",
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" for i in range(n):\n",
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" for j in range(n):\n",
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" print(\"%2i\" % x[(i, j)].Value(), end=\" \")\n",
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" print()\n",
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"\n",
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" print()\n",
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" num_solutions += 1\n",
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" if num_solutions > limit:\n",
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" break\n",
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"solver.EndSearch()\n",
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"\n",
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"print()\n",
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"print(\"num_solutions:\", num_solutions)\n",
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"print(\"failures:\", solver.Failures())\n",
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"print(\"branches:\", solver.Branches())\n",
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"print(\"WallTime:\", solver.WallTime())\n",
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"\n",
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"n = 4\n",
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"limit=100\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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