241 lines
7.2 KiB
Plaintext
241 lines
7.2 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "google",
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"metadata": {},
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"source": [
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"##### Copyright 2025 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "apache",
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"metadata": {},
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"source": [
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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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]
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},
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{
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"cell_type": "markdown",
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"id": "basename",
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"metadata": {},
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"source": [
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"# futoshiki"
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]
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},
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{
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"cell_type": "markdown",
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"id": "link",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/futoshiki.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/futoshiki.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "doc",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "install",
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"metadata": {},
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"outputs": [],
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"source": [
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"%pip install ortools"
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]
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},
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{
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"cell_type": "markdown",
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"id": "description",
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"metadata": {},
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"source": [
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"\n",
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"\n",
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" Futoshiki problem in Google CP Solver.\n",
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"\n",
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" From http://en.wikipedia.org/wiki/Futoshiki\n",
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" '''\n",
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" The puzzle is played on a square grid, such as 5 x 5. The objective\n",
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" is to place the numbers 1 to 5 (or whatever the dimensions are)\n",
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" such that each row, and column contains each of the digits 1 to 5.\n",
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" Some digits may be given at the start. In addition, inequality\n",
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" constraints are also initially specifed between some of the squares,\n",
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" such that one must be higher or lower than its neighbour. These\n",
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" constraints must be honoured as the grid is filled out.\n",
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" '''\n",
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"\n",
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" Also see\n",
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" http://www.guardian.co.uk/world/2006/sep/30/japan.estheraddley\n",
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"\n",
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"\n",
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" This Google CP Solver model is inspired by the Minion/Tailor\n",
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" example futoshiki.eprime.\n",
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"\n",
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"\n",
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" Compare with the following models:\n",
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" * MiniZinc: http://hakank.org/minizinc/futoshiki.mzn\n",
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" * ECLiPSe: http://hakank.org/eclipse/futoshiki.ecl\n",
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" * Gecode: http://hakank.org/gecode/futoshiki.cpp\n",
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" * SICStus: http://hakank.org/sicstus/futoshiki.pl\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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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "code",
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"metadata": {},
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"outputs": [],
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"source": [
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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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"def main(values, lt):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"Futoshiki problem\")\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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" size = len(values)\n",
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" RANGE = list(range(size))\n",
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" NUMQD = list(range(len(lt)))\n",
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"\n",
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" #\n",
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" # variables\n",
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" #\n",
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" field = {}\n",
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" for i in RANGE:\n",
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" for j in RANGE:\n",
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" field[i, j] = solver.IntVar(1, size, \"field[%i,%i]\" % (i, j))\n",
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" field_flat = [field[i, j] for i in RANGE for j in RANGE]\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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" # set initial values\n",
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" for row in RANGE:\n",
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" for col in RANGE:\n",
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" if values[row][col] > 0:\n",
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" solver.Add(field[row, col] == values[row][col])\n",
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"\n",
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" # all rows have to be different\n",
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" for row in RANGE:\n",
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" solver.Add(solver.AllDifferent([field[row, col] for col in RANGE]))\n",
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"\n",
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" # all columns have to be different\n",
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" for col in RANGE:\n",
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" solver.Add(solver.AllDifferent([field[row, col] for row in RANGE]))\n",
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"\n",
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" # all < constraints are satisfied\n",
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" # Also: make 0-based\n",
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" for i in NUMQD:\n",
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" solver.Add(\n",
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" field[lt[i][0] - 1, lt[i][1] - 1] < field[lt[i][2] - 1, lt[i][3] - 1])\n",
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"\n",
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" #\n",
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" # search and result\n",
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" #\n",
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" db = solver.Phase(field_flat, solver.CHOOSE_FIRST_UNBOUND,\n",
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" solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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" solver.NewSearch(db)\n",
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"\n",
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" num_solutions = 0\n",
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" while solver.NextSolution():\n",
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" num_solutions += 1\n",
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" for i in RANGE:\n",
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" for j in RANGE:\n",
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" print(field[i, j].Value(), end=\" \")\n",
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" print()\n",
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" print()\n",
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"\n",
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" solver.EndSearch()\n",
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"\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",
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"#\n",
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"# Example from Tailor model futoshiki.param/futoshiki.param\n",
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"# Solution:\n",
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"# 5 1 3 2 4\n",
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"# 1 4 2 5 3\n",
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"# 2 3 1 4 5\n",
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"# 3 5 4 1 2\n",
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"# 4 2 5 3 1\n",
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"#\n",
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"# Futoshiki instance, by Andras Salamon\n",
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"# specify the numbers in the grid\n",
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"#\n",
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"values1 = [[0, 0, 3, 2, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0],\n",
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" [0, 0, 0, 0, 0]]\n",
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"\n",
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"# [i1,j1, i2,j2] requires that values[i1,j1] < values[i2,j2]\n",
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"# Note: 1-based\n",
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"lt1 = [[1, 2, 1, 1], [1, 4, 1, 5], [2, 3, 1, 3], [3, 3, 2, 3], [3, 4, 2, 4],\n",
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" [2, 5, 3, 5], [3, 2, 4, 2], [4, 4, 4, 3], [5, 2, 5, 1], [5, 4, 5, 3],\n",
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" [5, 5, 4, 5]]\n",
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"\n",
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"#\n",
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"# Example from http://en.wikipedia.org/wiki/Futoshiki\n",
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"# Solution:\n",
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"# 5 4 3 2 1\n",
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"# 4 3 1 5 2\n",
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"# 2 1 4 3 5\n",
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"# 3 5 2 1 4\n",
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"# 1 2 5 4 3\n",
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"#\n",
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"values2 = [[0, 0, 0, 0, 0], [4, 0, 0, 0, 2], [0, 0, 4, 0, 0], [0, 0, 0, 0, 4],\n",
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" [0, 0, 0, 0, 0]]\n",
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"\n",
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"# Note: 1-based\n",
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"lt2 = [[1, 2, 1, 1], [1, 4, 1, 3], [1, 5, 1, 4], [4, 4, 4, 5], [5, 1, 5, 2],\n",
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" [5, 2, 5, 3]]\n",
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"\n",
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"print(\"Problem 1\")\n",
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"main(values1, lt1)\n",
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"print(\"\\nProblem 2\")\n",
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"main(values2, lt2)\n",
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"\n"
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]
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}
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],
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"metadata": {
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"language_info": {
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"name": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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