{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# De Bruijn Sequences with NetworkX" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "De Bruijn sequences are an interesting concept to study, with many real life applications.\n", "\n", "One interesting application is related to PIN code cracking. For a code to be cracked (in this example), only the last 4 digits must be correct, which means that all the digits typed before will be ignored. In other words: given a stream of digits, a code is cracked when the last 4 digits of the stream match the code.\n", "\n", "If we want to crack such a 4-digit PIN code, one possible way would be to enumerate all the different combinations and try them one by one. In that case, there would be 10000 combinations to try (from 0000 to 9999), and for each combination, 4 digits must be typed. This results in a total of 40000 digits to type in order to bruteforce the code with this naive approach.\n", "\n", "As we might guess, there must be a clever way to produce a list of digits, such that if entered sequentially, would cover all the possible codes in the minimal amount of digits.\n", "\n", "And the answer is yes, there exists such a way, thanks to **De Bruijn sequences**. De Bruijn sequences are used in many different domains ranging from computer science to neuroscience. More in-depth information can be found on external websites:\n", "1. De Bruijn Sequences on [Wikipedia](https://en.wikipedia.org/wiki/De_Bruijn_sequence)\n", "2. De Bruijn Sequences on [Datagenetics](http://www.datagenetics.com/blog/october22013/index.html)\n", "\n", "The article on Datagenetics provides a (the only?) 10003 digits long solution to the code cracking problem. It also explains the basic idea of these sequences and how to get to that solution.\n", "\n", "Alright, let's get started and copy the solution below to use it as a reference. \n", "\n", "## Reference" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "REF = '0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350036003700380039004100420043004400450046004700480049005100520053005400550056005700580059006100620063006400650066006700680069007100720073007400750076007700780079008100820083008400850086008700880089009100920093009400950096009700980099010102010301040105010601070108010901110112011301140115011601170118011901210122012301240125012601270128012901310132013301340135013601370138013901410142014301440145014601470148014901510152015301540155015601570158015901610162016301640165016601670168016901710172017301740175017601770178017901810182018301840185018601870188018901910192019301940195019601970198019902020302040205020602070208020902110212021302140215021602170218021902210222022302240225022602270228022902310232023302340235023602370238023902410242024302440245024602470248024902510252025302540255025602570258025902610262026302640265026602670268026902710272027302740275027602770278027902810282028302840285028602870288028902910292029302940295029602970298029903030403050306030703080309031103120313031403150316031703180319032103220323032403250326032703280329033103320333033403350336033703380339034103420343034403450346034703480349035103520353035403550356035703580359036103620363036403650366036703680369037103720373037403750376037703780379038103820383038403850386038703880389039103920393039403950396039703980399040405040604070408040904110412041304140415041604170418041904210422042304240425042604270428042904310432043304340435043604370438043904410442044304440445044604470448044904510452045304540455045604570458045904610462046304640465046604670468046904710472047304740475047604770478047904810482048304840485048604870488048904910492049304940495049604970498049905050605070508050905110512051305140515051605170518051905210522052305240525052605270528052905310532053305340535053605370538053905410542054305440545054605470548054905510552055305540555055605570558055905610562056305640565056605670568056905710572057305740575057605770578057905810582058305840585058605870588058905910592059305940595059605970598059906060706080609061106120613061406150616061706180619062106220623062406250626062706280629063106320633063406350636063706380639064106420643064406450646064706480649065106520653065406550656065706580659066106620663066406650666066706680669067106720673067406750676067706780679068106820683068406850686068706880689069106920693069406950696069706980699070708070907110712071307140715071607170718071907210722072307240725072607270728072907310732073307340735073607370738073907410742074307440745074607470748074907510752075307540755075607570758075907610762076307640765076607670768076907710772077307740775077607770778077907810782078307840785078607870788078907910792079307940795079607970798079908080908110812081308140815081608170818081908210822082308240825082608270828082908310832083308340835083608370838083908410842084308440845084608470848084908510852085308540855085608570858085908610862086308640865086608670868086908710872087308740875087608770878087908810882088308840885088608870888088908910892089308940895089608970898089909091109120913091409150916091709180919092109220923092409250926092709280929093109320933093409350936093709380939094109420943094409450946094709480949095109520953095409550956095709580959096109620963096409650966096709680969097109720973097409750976097709780979098109820983098409850986098709880989099109920993099409950996099709980999111121113111411151116111711181119112211231124112511261127112811291132113311341135113611371138113911421143114411451146114711481149115211531154115511561157115811591162116311641165116611671168116911721173117411751176117711781179118211831184118511861187118811891192119311941195119611971198119912121312141215121612171218121912221223122412251226122712281229123212331234123512361237123812391242124312441245124612471248124912521253125412551256125712581259126212631264126512661267126812691272127312741275127612771278127912821283128412851286128712881289129212931294129512961297129812991313141315131613171318131913221323132413251326132713281329133213331334133513361337133813391342134313441345134613471348134913521353135413551356135713581359136213631364136513661367136813691372137313741375137613771378137913821383138413851386138713881389139213931394139513961397139813991414151416141714181419142214231424142514261427142814291432143314341435143614371438143914421443144414451446144714481449145214531454145514561457145814591462146314641465146614671468146914721473147414751476147714781479148214831484148514861487148814891492149314941495149614971498149915151615171518151915221523152415251526152715281529153215331534153515361537153815391542154315441545154615471548154915521553155415551556155715581559156215631564156515661567156815691572157315741575157615771578157915821583158415851586158715881589159215931594159515961597159815991616171618161916221623162416251626162716281629163216331634163516361637163816391642164316441645164616471648164916521653165416551656165716581659166216631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9000'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One might wonder why look at that problem if it is already largely covered online by many great resources?\n", "\n", "Well, I thought it would be interesting to try to find a solution, but with a different approach.\n", "\n", "First, let's look at the (trimmed) code provided on the Wikipedia page generating a De Bruijn sequence for the given parameters k and n." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def de_bruijn(k, n):\n", " alphabet = list(map(str, range(k)))\n", " \n", " a = [0] * k * n\n", " sequence = []\n", " \n", " def db(t, p):\n", " if t > n:\n", " if n % p == 0:\n", " sequence.extend(a[1:p + 1])\n", " else:\n", " a[t] = a[t - p]\n", " db(t + 1, p)\n", " for j in range(a[t - p] + 1, k):\n", " a[t] = j\n", " db(t + 1, t)\n", " \n", " db(1, 1)\n", " return ''.join(alphabet[i] for i in sequence)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's verify this code produces an optimal solution. A solution is valid if it contains all the different codes from 0000 to 9999. And it's optimal if its length is not greater than the reference solution (considered as the best solution)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from itertools import product" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def check_solution(k, n, sol):\n", " '''Check against the solution sol'''\n", " for p in product(''.join(map(str, range(k))), repeat=n):\n", " code = ''.join(p)\n", " if code not in sol:\n", " return False\n", " return True" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Good solution? True\n" ] } ], "source": [ "ls = de_bruijn(10, 4)\n", "ls += ls[:3] # wrap around\n", "print('Good solution?', check_solution(10, 4, ls))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At least we find the same result, which is comforting.\n", "\n", "But let's be honest. This code snippet from Wikipedia is quite opaque. It would be nice to develop a more intuitive feeling of the problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## With NetworkX\n", "\n", "Representing this problem as a graph problems makes it more intuitive to understand. It is possible to represent the codes as the nodes and the digits (typed one by one) as the edges of a graph:\n", "\n", "\n", "\n", "De Bruijn sequences have this great property of being generated by finding an **Eulerian cycle** from a De Bruijn graph.\n", "\n", "The De Bruijn sequence corresponding to the De Bruijn graph above is: 0000111101100101.\n", "\n", "Why does the Eulerian cycle give a valid sequence? A few observations can be made without entering into too much details and proofs:\n", "\n", "- Each node represents a distinct code.\n", "- All the codes must be tried at least once, so each node has to be visited at least once.\n", "- One code can be created from another by entering a new digit (edge between two nodes).\n", "\n", "With these points in mind, the problem is reduced to the implementation of the Eulerian cycle algorithm on the De Bruijn graph. This can be done from scratch, but we can also speed-up the process and use the existing NetworkX graph library." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def create_de_bruijn_graph(k, n):\n", " g = nx.DiGraph()\n", " for p in product(tuple(map(str, range(k))), repeat=n):\n", " code = ''.join(p)\n", " u = str(code).zfill(n)\n", " tmp = u[1:]\n", " for i in range(k):\n", " v = tmp + str(i)\n", " g.add_edge(u, v, weight=i)\n", " return g\n", " \n", "def de_bruijn_nx(k, n):\n", " g = create_de_bruijn_graph(k, n)\n", " ls = nx.eulerian_circuit(g)\n", " res = ''.join(map(str, (g.get_edge_data(*e)['weight'] for e in ls)))\n", " return res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the De Bruijn graph corresponding to the image above to visually verify its correctness." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def draw_de_bruijn_graph(g):\n", " plt.figure(figsize=(20,20), dpi=80)\n", " nx.draw_networkx(\n", " g, pos=nx.circular_layout(g),\n", " node_shape='o', node_size=4000, font_size=20,\n", " edge_color='#555555', width=3.0\n", " )\n", " nx.draw_networkx_edge_labels(\n", " g, pos=nx.circular_layout(g), \n", " edge_labels=nx.get_edge_attributes(g, 'weight'),\n", " font_size=24, label_pos=0.25, rotate=False\n", " )\n", " plt.axis('off')\n", " plt.show() " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AAFgsQQUAAGCXEFUAAGBxBBUAAIBdRFQBAIDFEFQAAAB2GVEFAABOP0EFAABg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\nAMB84AwVAABYgPrpTJW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_de_bruijn_graph(create_de_bruijn_graph(2, 3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The circular_layout is in that case more suited than the default spring layout. And even though this plot is quite simple (and doesn't show the loop for node 000), we can still visually verify the graph against the one above.\n", "\n", "Now with the real values k = 10 and n = 4:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution (overview): 16255004019983523821923269393645738058512587270874...21029426911638198665010844534159683130383134958162\n", "Good solution? True\n" ] } ], "source": [ "res = de_bruijn_nx(10, 4)\n", "res += res[:3] # wrap around\n", "print('Solution (overview): %s...%s' % (res[:50], res[-50:]))\n", "print('Good solution?', check_solution(10, 4, res))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution contains all the codes. However it looks different than the reference." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Is circular permutation? False\n" ] } ], "source": [ "is_circular_permutation = res in (REF + REF)\n", "print('Is circular permutation?', is_circular_permutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's a practical way to notice that given a De Bruijn graph, the corresponding De Bruijn sequences are not unique." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wrap up\n", "\n", "There are many more things to learn from De Bruijn sequences. At least now we know that NetworkX is handy for some of the applications!" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }