200 lines
7.2 KiB
Plaintext
200 lines
7.2 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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" de Bruijn sequences in Google CP Solver.\n",
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"\n",
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" Implementation of de Bruijn sequences in Minizinc, both 'classical' and\n",
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" 'arbitrary'.\n",
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" The 'arbitrary' version is when the length of the sequence (m here) is <\n",
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" base**n.\n",
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"\n",
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"\n",
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" Compare with the the web based programs:\n",
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" http://www.hakank.org/comb/debruijn.cgi\n",
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" http://www.hakank.org/comb/debruijn_arb.cgi\n",
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"\n",
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" Compare with the following models:\n",
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" * Tailor/Essence': http://hakank.org/tailor/debruijn.eprime\n",
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" * MiniZinc: http://hakank.org/minizinc/debruijn_binary.mzn\n",
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" * SICStus: http://hakank.org/sicstus/debruijn.pl\n",
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" * Zinc: http://hakank.org/minizinc/debruijn_binary.zinc\n",
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" * Choco: http://hakank.org/choco/DeBruijn.java\n",
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" * Comet: http://hakank.org/comet/debruijn.co\n",
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" * ECLiPSe: http://hakank.org/eclipse/debruijn.ecl\n",
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" * Gecode: http://hakank.org/gecode/debruijn.cpp\n",
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" * Gecode/R: http://hakank.org/gecode_r/debruijn_binary.rb\n",
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" * JaCoP: http://hakank.org/JaCoP/DeBruijn.java\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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"# converts a number (s) <-> an array of numbers (t) in the specific base.\n",
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"\n",
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"\n",
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"def toNum(solver, t, s, base):\n",
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" tlen = len(t)\n",
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" solver.Add(\n",
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" s == solver.Sum([(base**(tlen - i - 1)) * t[i] for i in range(tlen)]))\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(\"de Bruijn sequences\")\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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"# base = 2 # the base to use, i.e. the alphabet 0..n-1\n",
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"# n = 3 # number of bits to use (n = 4 -> 0..base^n-1 = 0..2^4 -1, i.e. 0..15)\n",
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"# m = base**n # the length of the sequence. For \"arbitrary\" de Bruijn\n",
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"# sequences\n",
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"\n",
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"# base = 4\n",
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"# n = 4\n",
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"# m = base**n\n",
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"\n",
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"# harder problem\n",
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"#base = 13\n",
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"#n = 4\n",
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"#m = 52\n",
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"\n",
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"# for n = 4 with different value of base\n",
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"# base = 2 0.030 seconds 16 failures\n",
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"# base = 3 0.041 108\n",
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"# base = 4 0.070 384\n",
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"# base = 5 0.231 1000\n",
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"# base = 6 0.736 2160\n",
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"# base = 7 2.2 seconds 4116\n",
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"# base = 8 6 seconds 7168\n",
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"# base = 9 16 seconds 11664\n",
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"# base = 10 42 seconds 18000\n",
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"# base = 6\n",
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"# n = 4\n",
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"# m = base**n\n",
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"\n",
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"# if True then ensure that the number of occurrences of 0..base-1 is\n",
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"# the same (and if m mod base = 0)\n",
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"check_same_gcc = True\n",
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"\n",
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"print(\"base: %i n: %i m: %i\" % (base, n, m))\n",
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"if check_same_gcc:\n",
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" print(\"Checks gcc\")\n",
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"\n",
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"# declare variables\n",
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"x = [solver.IntVar(0, (base**n) - 1, \"x%i\" % i) for i in range(m)]\n",
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"binary = {}\n",
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"for i in range(m):\n",
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" for j in range(n):\n",
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" binary[(i, j)] = solver.IntVar(0, base - 1, \"x_%i_%i\" % (i, j))\n",
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"\n",
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"bin_code = [solver.IntVar(0, base - 1, \"bin_code%i\" % i) for i in range(m)]\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(solver.AllDifferent([x[i] for i in range(m)]))\n",
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"solver.Add(solver.AllDifferent(x))\n",
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"\n",
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"# converts x <-> binary\n",
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"for i in range(m):\n",
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" t = [solver.IntVar(0, base - 1, \"t_%i\" % j) for j in range(n)]\n",
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" toNum(solver, t, x[i], base)\n",
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" for j in range(n):\n",
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" solver.Add(binary[(i, j)] == t[j])\n",
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"\n",
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"# the de Bruijn condition\n",
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"# the first elements in binary[i] is the same as the last\n",
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"# elements in binary[i-i]\n",
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"for i in range(1, m - 1):\n",
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" for j in range(1, n - 1):\n",
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" solver.Add(binary[(i - 1, j)] == binary[(i, j - 1)])\n",
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"\n",
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"# ... and around the corner\n",
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"for j in range(1, n):\n",
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" solver.Add(binary[(m - 1, j)] == binary[(0, j - 1)])\n",
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"\n",
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"# converts binary -> bin_code\n",
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"for i in range(m):\n",
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" solver.Add(bin_code[i] == binary[(i, 0)])\n",
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"\n",
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"# extra: ensure that all the numbers in the de Bruijn sequence\n",
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"# (bin_code) has the same occurrences (if check_same_gcc is True\n",
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"# and mathematically possible)\n",
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"gcc = [solver.IntVar(0, m, \"gcc%i\" % i) for i in range(base)]\n",
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"solver.Add(solver.Distribute(bin_code, list(range(base)), gcc))\n",
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"if check_same_gcc and m % base == 0:\n",
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" for i in range(1, base):\n",
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" solver.Add(gcc[i] == gcc[i - 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[i] for i in range(m)])\n",
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"solution.Add([bin_code[i] for i in range(m)])\n",
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"# solution.Add([binary[(i,j)] for i in range(m) for j in range(n)])\n",
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"solution.Add([gcc[i] for i in range(base)])\n",
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"\n",
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"db = solver.Phase([x[i] for i in range(m)] + [bin_code[i] for i in range(m)],\n",
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" solver.CHOOSE_MIN_SIZE_LOWEST_MAX, solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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"num_solutions = 0\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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" num_solutions += 1\n",
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" print(\"\\nSolution %i\" % num_solutions)\n",
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" print(\"x:\", [int(x[i].Value()) for i in range(m)])\n",
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" print(\"gcc:\", [int(gcc[i].Value()) for i in range(base)])\n",
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" print(\"de Bruijn sequence:\", [int(bin_code[i].Value()) for i in range(m)])\n",
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" # for i in range(m):\n",
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" # for j in range(n):\n",
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" # print binary[(i,j)].Value(),\n",
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" # print\n",
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" # print\n",
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"solver.EndSearch()\n",
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"\n",
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"if num_solutions == 0:\n",
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" print(\"No solution found\")\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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"base = 2\n",
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"n = 3\n",
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"m = base**n\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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