270 lines
8.8 KiB
Plaintext
270 lines
8.8 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"##### Copyright 2020 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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"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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"metadata": {},
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"source": [
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"# nonogram_default_search"
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]
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},
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{
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"cell_type": "markdown",
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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/master/examples/notebook/contrib/nonogram_default_search.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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/master/examples/contrib/nonogram_default_search.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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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"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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"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": "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, lperron@google.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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" Nonogram (Painting by numbers) in Google CP Solver.\n",
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"\n",
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" http://en.wikipedia.org/wiki/Nonogram\n",
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" '''\n",
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" Nonograms or Paint by Numbers are picture logic puzzles in which cells in a\n",
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" grid have to be colored or left blank according to numbers given at the\n",
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" side of the grid to reveal a hidden picture. In this puzzle type, the\n",
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" numbers measure how many unbroken lines of filled-in squares there are\n",
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" in any given row or column. For example, a clue of '4 8 3' would mean\n",
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" there are sets of four, eight, and three filled squares, in that order,\n",
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" with at least one blank square between successive groups.\n",
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"\n",
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" '''\n",
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"\n",
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" See problem 12 at http://www.csplib.org/.\n",
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"\n",
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" http://www.puzzlemuseum.com/nonogram.htm\n",
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"\n",
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" Haskell solution:\n",
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" http://twan.home.fmf.nl/blog/haskell/Nonograms.details\n",
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"\n",
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" Brunetti, Sara & Daurat, Alain (2003)\n",
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" 'An algorithm reconstructing convex lattice sets'\n",
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" http://geodisi.u-strasbg.fr/~daurat/papiers/tomoqconv.pdf\n",
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"\n",
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"\"\"\"\n",
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"import sys\n",
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"\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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"#\n",
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"# Make a transition (automaton) list of tuples from a\n",
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"# single pattern, e.g. [3,2,1]\n",
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"#\n",
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"def make_transition_tuples(pattern):\n",
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" p_len = len(pattern)\n",
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" num_states = p_len + sum(pattern)\n",
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"\n",
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" tuples = []\n",
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"\n",
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" # this is for handling 0-clues. It generates\n",
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" # just the minimal state\n",
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" if num_states == 0:\n",
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" tuples.append((1, 0, 1))\n",
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" return (tuples, 1)\n",
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"\n",
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" # convert pattern to a 0/1 pattern for easy handling of\n",
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" # the states\n",
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" tmp = [0]\n",
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" c = 0\n",
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" for pattern_index in range(p_len):\n",
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" tmp.extend([1] * pattern[pattern_index])\n",
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" tmp.append(0)\n",
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"\n",
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" for i in range(num_states):\n",
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" state = i + 1\n",
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" if tmp[i] == 0:\n",
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" tuples.append((state, 0, state))\n",
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" tuples.append((state, 1, state + 1))\n",
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" else:\n",
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" if i < num_states - 1:\n",
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" if tmp[i + 1] == 1:\n",
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" tuples.append((state, 1, state + 1))\n",
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" else:\n",
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" tuples.append((state, 0, state + 1))\n",
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" tuples.append((num_states, 0, num_states))\n",
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" return (tuples, num_states)\n",
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"\n",
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"\n",
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"#\n",
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"# check each rule by creating an automaton and transition constraint.\n",
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"#\n",
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"def check_rule(rules, y):\n",
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" cleaned_rule = [rules[i] for i in range(len(rules)) if rules[i] > 0]\n",
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" (transition_tuples, last_state) = make_transition_tuples(cleaned_rule)\n",
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"\n",
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" initial_state = 1\n",
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" accepting_states = [last_state]\n",
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"\n",
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" solver = y[0].solver()\n",
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" solver.Add(\n",
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" solver.TransitionConstraint(y, transition_tuples, initial_state,\n",
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" accepting_states))\n",
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"\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('Nonogram')\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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"board = {}\n",
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"for i in range(rows):\n",
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" for j in range(cols):\n",
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" board[i, j] = solver.IntVar(0, 1, 'board[%i, %i]' % (i, j))\n",
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"\n",
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"board_flat = [board[i, j] for i in range(rows) for j in range(cols)]\n",
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"\n",
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"# Flattened board for labeling.\n",
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"# This labeling was inspired by a suggestion from\n",
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"# Pascal Van Hentenryck about my (hakank's) Comet\n",
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"# nonogram model.\n",
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"board_label = []\n",
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"if rows * row_rule_len < cols * col_rule_len:\n",
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" for i in range(rows):\n",
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" for j in range(cols):\n",
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" board_label.append(board[i, j])\n",
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"else:\n",
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" for j in range(cols):\n",
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" for i in range(rows):\n",
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" board_label.append(board[i, j])\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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"for i in range(rows):\n",
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" check_rule(row_rules[i], [board[i, j] for j in range(cols)])\n",
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"\n",
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"for j in range(cols):\n",
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" check_rule(col_rules[j], [board[i, j] for i in range(rows)])\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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"parameters = pywrapcp.DefaultPhaseParameters()\n",
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"parameters.heuristic_period = 200000\n",
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"\n",
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"db = solver.DefaultPhase(board_label, parameters)\n",
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"\n",
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"print('before solver, wall time = ', solver.WallTime(), 'ms')\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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" print()\n",
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" num_solutions += 1\n",
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" for i in range(rows):\n",
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" row = [board[i, j].Value() for j in range(cols)]\n",
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" row_pres = []\n",
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" for j in row:\n",
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" if j == 1:\n",
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" row_pres.append('#')\n",
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" else:\n",
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" row_pres.append(' ')\n",
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" print(' ', ''.join(row_pres))\n",
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"\n",
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" print()\n",
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" print(' ', '-' * cols)\n",
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"\n",
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" if num_solutions >= 2:\n",
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" print('2 solutions is enough...')\n",
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" break\n",
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"\n",
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"solver.EndSearch()\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(), 'ms')\n",
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"\n",
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"\n",
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"#\n",
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"# Default problem\n",
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"#\n",
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"# From http://twan.home.fmf.nl/blog/haskell/Nonograms.details\n",
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"# The lambda picture\n",
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"#rows = 12\n",
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"row_rule_len = 3\n",
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"row_rules = [[0, 0, 2], [0, 1, 2], [0, 1, 1], [0, 0, 2], [0, 0, 1], [0, 0, 3],\n",
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" [0, 0, 3], [0, 2, 2], [0, 2, 1], [2, 2, 1], [0, 2, 3], [0, 2, 2]]\n",
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"\n",
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"cols = 10\n",
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"col_rule_len = 2\n",
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"col_rules = [[2, 1], [1, 3], [2, 4], [3, 4], [0, 4], [0, 3], [0, 3], [0, 3],\n",
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" [0, 2], [0, 2]]\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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"nbformat": 4,
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"nbformat_minor": 4
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}
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