271 lines
9.0 KiB
Plaintext
271 lines
9.0 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 2024 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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"# debruijn_binary"
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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/debruijn_binary.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/debruijn_binary.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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" 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 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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]
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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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"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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"def main(base=2, n=3, m=8):\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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"\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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"if len(sys.argv) > 1:\n",
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" base = int(sys.argv[1])\n",
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"if len(sys.argv) > 2:\n",
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" n = int(sys.argv[2])\n",
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"if len(sys.argv) > 3:\n",
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" m = int(sys.argv[3])\n",
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"\n",
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"main(base, n, m)\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": 5
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}
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