python/snakecube/snakecube.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "107384c9",
   "metadata": {
    "id": "107384c9"
   },
   "source": [
    "# Le [Cube-Serpent](https://fr.wikipedia.org/wiki/Cube_serpent) ou Snake Cube"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a367e02f",
   "metadata": {
    "id": "a367e02f"
   },
   "source": [
    "## Objet du problème"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edeb3226",
   "metadata": {
    "id": "edeb3226"
   },
   "source": [
    "Un *Cube-Serpent* est un casse-tête constitué de $3\\times3\\times3=27$ \n",
    "petits cubes de côté $1$ (pour fixer les idées) reliés entre eux par un élastique, un peu comme un collier\n",
    "de perles. \n",
    "Chacun des 27 cubes est de l'un des trois types suivants représentés ci-dessous,\n",
    "*bout*, *droit* ou  *coin* :\n",
    "\n",
    "![fig1.png](data:image/png;base64,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)\n",
    "* Il y a 2 cubes bouts. Chacune des deux extrémités de l'elastique est fixée\n",
    "  au centre d'une face d'un bout.\n",
    "* Les cubes droits et les cubes coins sont transpercés par un trou dans lequel coulisse \n",
    "  l'élastique. Dans un cube droit le trou relie deux faces opposées\n",
    "  et, dans un cube coin, il relie deux faces contiguës.\n",
    "  \n",
    "L'élastique est suffisamment tendu pour que deux cubes successifs du serpent soient\n",
    "appuyés l'un contre l'autre ; il est assez lâche pour que l'on puisse \n",
    "le manipuler. Le but est de former, si possible, un gros cube de côté $3$ :\n",
    "\n",
    "![fig2.png](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "347539fe",
   "metadata": {
    "id": "347539fe"
   },
   "source": [
    "## Représentation des données et des solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8829a64e",
   "metadata": {
    "id": "8829a64e"
   },
   "source": [
    "Un exemple de serpent est le *cobra bleu* représenté\n",
    "par la chaîne de 25 caractères \n",
    "\n",
    "$+-+-+-+----+-+---+--+---+$\n",
    "\n",
    "dans laquelle les $+$ symbolisent les cubes droits et les $-$ les coins \n",
    "(les bouts ne sont pas représentés) :\n",
    "\n",
    "![fig3.png](data:image/png;base64,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)\n",
    "\n",
    "Une solution (essentiellement la seule) du cobra bleu\n",
    "est donnée par la figure située à la fin de cette page.\n",
    "\n",
    "On définit un *graphe non orienté*   $CUBE=(S,A)$ par l'ensemble $S$\n",
    "de ses *sommets* et l'ensemble $A$ de ses *arcs* :\n",
    "* Les sommets sont les $27$ points  $P=(x,y,z)$ de l'espace dont\n",
    "  les coordonnées $x$, $y$ et $z$ valent soit $0$, soit $1$, soit $2$ ; \n",
    "  autrement dit, $S=\\{0,1,2\\}^3$.\n",
    "* Un arc est une paire de sommets $\\{P,Q\\}$ où $Q$ s'obtient à partir \n",
    "  de $P$ en ajoutant ou en retranchant $1$ à une et une seule des \n",
    "  trois coordonnées de $P$. Ainsi $\\{(1,2,0),(1,1,0)\\}$ est un arc mais \n",
    "  $\\{(1,2,0),(1,0,0)\\}$ et $\\{(1,2,0),(1,1,1)\\}$ n'en sont pas. \n",
    "  \n",
    "Le graphe $CUBE$ est représenté ci-dessous \n",
    "\n",
    "![fig4.png](data:image/png;base64,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)\n",
    "\n",
    "On se propose d'écrire une fonction \"calcSols\" qui prend en argument un Cube-Serpent\n",
    "et qui affiche les solutions aux isométries près.\n",
    "\n",
    "Un Cube-Serpent sera appelé un *jeu*\n",
    "et représenté par une chaîne de caractères de longueur 25 sur l'alphabet $\\{+,-\\}$ ;\n",
    "par exemple, *Cobra Bleu* $= +-+-+-+----+-+---+--+---+$\n",
    "\n",
    "Une solution est un ordonnancement $(p_0,...,p_{26})$ des 27 sommets de $CUBE$.\n",
    "Elle sera représentée par : $p_0,p_1-p_0,...,p_{26}-p_{25}$.\n",
    "Comme les $p_i-p_{i-1}$ sont soit des vecteurs de la base \n",
    "canonique $i$, $j$, $k$, soit $-i$, $-j$ ou $-k$, on représentera ces vecteurs\n",
    "respectivement par les lettres $X, Y, Z, x, y, z$.\n",
    "    \n",
    " Ainsi calcSols(*Cobra Bleu*) affichera $000XXYYxxZZXzXyyxxZYzzXZZyXYY$\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb362ca1",
   "metadata": {
    "id": "eb362ca1"
   },
   "source": [
    "## Méthode"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cbee29b",
   "metadata": {
    "id": "0cbee29b"
   },
   "source": [
    " \n",
    "Voir le code (backtraking classique).\n",
    "    \n",
    "Si $(x,y,z)\\in\\{0,1,2\\}^3$ est soit un sommet de $CUBE$, soit un vecteur \n",
    "de la base canonique, il est représenté par l'entier \n",
    "$x + 3y + 9z\\in[|0,26|]$.\n",
    " \n",
    "Pour élaguer l'arbre des appels récursifs en utilisant\n",
    "les isométries de $CUBE$, on n'autorise que certains débuts (voir la fonction calc);\n",
    "et si $p_0,..,p_k$ sont dans le plan $x = 1$ ($k$ maximum), \n",
    "on impose $p_{k+1} = p_k - i$ (on coupe la branche     $p_{k+1} = p_k + i$).\n",
    " \n",
    "### Limitations\n",
    "    \n",
    "Si jeu est un palindrome, l'inverse d'une solution \n",
    "est aussi une solution. La fonction calcSols affiche\n",
    "les deux solutions. Ainsi calcSols(cubraPurple) affiche\n",
    "12 solutions alors qu'il n'y en a fondamentalement que 6.\n",
    " \n",
    "En fait il est possible (et pas plus difficile) de calculer \n",
    "une fois pour toutes les solutions de tous les jeux possibles.\n",
    "Il suffit de calculer tous les [chemins hamiltoniens](https://fr.wikipedia.org/wiki/Graphe_hamiltonien#:~:text=En%20math%C3%A9matiques%2C%20dans%20le%20cadre,qui%20poss%C3%A8de%20un%20cycle%20hamiltonien.)\n",
    "du graphe CUBE et de considérer chacun de ces chemins\n",
    "comme une solution du jeu correspondant.\n",
    "Néanmoins un tel procédé est coûteux. Voir par exemple la page très complète de [Jaap Scherphuis](https://www.jaapsch.net/puzzles/snakecube.htm)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "100cd0ec",
   "metadata": {
    "id": "100cd0ec"
   },
   "source": [
    "## Implémentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f47c578",
   "metadata": {
    "id": "6f47c578"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def addVect(p,v): # p = un sommet du CUBE, v = + ou - un vect de la b.c.\n",
    "\n",
    "  aux = p // abs(v)\n",
    "  if v > 0: aux += 1\n",
    "  if aux % 3 == 0: return None # p + v en dehors du CUBE\n",
    "  else: return p + v\n",
    "\n",
    "def calcSols(jeu):\n",
    "\n",
    "  code = {1 : 'X', -1 : 'x', 3 : 'Y', -3 : 'y', 9 : 'Z', -9 : 'z'}\n",
    "  i = None                       # sommet initial\n",
    "  s = np.zeros(26,dtype='int8')  # + ou - vecteurs de la base canonique => la solution partielle courante s_0,..,s_{n-1}\n",
    "  c = np.zeros(27,dtype='bool')  # cubes placés\n",
    "  n = 0                          # nombre de cubes placés\n",
    "  p = None                       # dernier cube placé\n",
    "  b = np.zeros(27,dtype='bool')  # b[0],..,b[n-1] = True si les n cubes placés sont dans le plan x = 1\n",
    "  e = 0                          # nombre d'essais avant d'aboutir à la solution\n",
    "  t = 0                          # nombre total d'essais  \n",
    "\n",
    "  def avancer(q): # placer q\n",
    "    nonlocal s, c, n, p, b, e\n",
    "    e += 1\n",
    "    c[q] = True\n",
    "    if n == 0: \n",
    "      b[0] = q % 3 == 1\n",
    "    else:\n",
    "      s[n-1] = q - p\n",
    "      b[n] = b[n-1] and q % 3 == 1 \n",
    "    n += 1\n",
    "    p = q\n",
    "\n",
    "  def reculer():\n",
    "    nonlocal s, c, n, p\n",
    "    c[p] = False\n",
    "    n -= 1\n",
    "    if n != 0: p -= s[n-1] \n",
    "\n",
    "  def parcourir(): # fonction récursive principale (backtraking)\n",
    "    nonlocal i, s, c, n, p, b, e, t\n",
    "    if n == 27: \n",
    "      print('{}{} {:5} essais'.format(i,''.join([code[v] for v in s]),e)) # solution trouvée\n",
    "      t += e\n",
    "      e = 0\n",
    "    else:\n",
    "      v = s[n-2] # vecteur joignant l'avant-dernier et le dernier (p) cube placé\n",
    "      l = []     # liste des vecteurs \"ajoutables\" à p pour obtenir le suivant\n",
    "      if jeu[n-2] == '+': l.append(v)\n",
    "      else:\n",
    "        for w in [1,3,9]:\n",
    "          if w != abs(v): # w,v orthogonaux\n",
    "            l.append(w)\n",
    "            if not(b[n-1] and w == 1): l.append(-w)\n",
    "      for w in l:\n",
    "        q = addVect(p,w)\n",
    "        if q != None and not c[q]:\n",
    "          avancer(q)\n",
    "          parcourir()\n",
    "          reculer()\n",
    "\n",
    "  def calc(s,debut): \n",
    "    nonlocal i\n",
    "    if jeu[:len(s)] == s:\n",
    "      j = debut[0] \n",
    "      i = str(j % 3)+str((j // 3) % 3)+str((j // 9) % 3)\n",
    "      for q in debut: avancer(q)\n",
    "      parcourir()\n",
    "      for q in debut: reculer()\n",
    "            \n",
    "  calc('+-',[0,1,2,5])    # coin\n",
    "  calc('-',[0,1,4])       # coin\n",
    "  calc('-',[1,0,3])       # milieu arête (inutile en fait)\n",
    "  calc('',[1,4])          # milieu arête (inutile en fait)\n",
    "  calc('',[4,1])          # centre face\n",
    "  calc('-',[4,13,10])     # centre face\n",
    "  calc('+-',[4,13,22,19]) # centre face\n",
    "  calc('-',[13,4,1])      # centre cube  (inutile en fait)\n",
    "\n",
    "  print('{} essais'.format(t + e))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91b8603c",
   "metadata": {
    "id": "91b8603c"
   },
   "source": [
    "### Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8708868f",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 966,
     "status": "ok",
     "timestamp": 1670626076105,
     "user": {
      "displayName": "Yves Lemaire",
      "userId": "04690556979859113270"
     },
     "user_tz": -60
    },
    "id": "8708868f",
    "outputId": "d971b6d9-0f01-4ec1-fb9b-08a3fdabe4b5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Cubra Blue\n",
      "   +-+-+-+----+-+---+--+---+\n",
      "000XXYYxxZZXzXyyxxZYzzXZZyXYY    68 essais\n",
      "275 essais\n",
      "\n",
      "Cubra Red\n",
      "   +---------+-------+-+----\n",
      "000XXYxYXZxZXyyzYxZyxYYzzyZyX   333 essais\n",
      "000XXYZyxYZxYzzXyxZyZXXYYxzXz 13071 essais\n",
      "000XXYZyxYzxYZZXyxzyZXXYYzxzX   389 essais\n",
      "000XXYZyxZXYxzzxYZXzXZZxxyzyZ   255 essais\n",
      "000XXYZyZxzxZYYXzyZXYzzxxZyzX  1609 essais\n",
      "000XXYZyZxzxZYYzXZyXYzzxxyXZx   101 essais\n",
      "000XXYZyZxzxZYYzXZyXYzzxxyZXz     3 essais\n",
      "000XXYZyZxzxZYYzyXzxYXXZZyxYz    91 essais\n",
      "000XXYZyZYxYXzzxZyzxYZZyyXzxY   259 essais\n",
      "000XXYZyZYxyzYYxzyXYXZZxxyzyZ   721 essais\n",
      "25291 essais\n",
      "\n",
      "Cubra Green\n",
      "   +-+-+--+-+-+----+--+--+-+\n",
      "000XXYYxxZXXyyxxZXYzzxZZYXXyy    82 essais\n",
      "210 essais\n",
      "\n",
      "Cubra Orange\n",
      "   +-+----+--------+---+---+\n",
      "000XXYYxZXyyxZxzYZYzzyXZZYXyy  1496 essais\n",
      "4179 essais\n",
      "\n",
      "Cubra Purple\n",
      "   ----+-+-----------+-+----\n",
      "000XYXyZZxxYXYxzXyXZYzzxxyZyX  6771 essais\n",
      "000XYXyZZxxYXzYzXZyZYxxzzyZyX   342 essais\n",
      "000XYxYXXZZyxYxzXyXzyZZxxYzyX  8925 essais\n",
      "000XYxYXXZZyxYzxZyzyZXXzzYZxy   137 essais\n",
      "000XYxYZZXXyxzxZyzXZXzzYYxZXy  1634 essais\n",
      "000XYxYZZXXyxzYzXZyzyZZxxYzyX    53 essais\n",
      "110yZXZxxYYzXZXyxzxyzYYXXZyzy 10331 essais\n",
      "110yZXZYYxxzXyZyxYzyzYYXXZyzy  1759 essais\n",
      "110yZXzYYxxZXyZyXYzYZxxyyzYzy  2127 essais\n",
      "110yZXzYYxxZXZxyXzXYZyyxxzYzy   173 essais\n",
      "110yZXzYYxxZXZxyXzxzyZZXXYzYZ    31 essais\n",
      "110ZyXzxxYYXZxZXyxzyZXXYYzyzY  2954 essais\n",
      "40069 essais\n",
      "\n",
      "Kev 9B\n",
      "   +---+-+-------------+-+--\n",
      "110ZZyXzzYYZxzxZyzyXZxZYYXXyz  2886 essais\n",
      "2938 essais\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for nom,jeu in [\n",
    "                ('Cubra Blue'  ,'+-+-+-+----+-+---+--+---+'),\n",
    "                ('Cubra Red'   ,'+---------+-------+-+----'),\n",
    "                ('Cubra Green' ,'+-+-+--+-+-+----+--+--+-+'),\n",
    "                ('Cubra Orange','+-+----+--------+---+---+'),\n",
    "                ('Cubra Purple','----+-+-----------+-+----'),\n",
    "                ('Kev 9B'      ,'+---+-+-------------+-+--')]: \n",
    "      print('\\n' + nom + '\\n   ' + jeu)\n",
    "      calcSols(jeu)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "uX_bVb3MTq03",
   "metadata": {
    "id": "uX_bVb3MTq03"
   },
   "source": [
    "## Affichage graphique des solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ee028858",
   "metadata": {
    "id": "ee028858"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "alpha = 0.4\n",
    "beta = 0.6\n",
    "    \n",
    "def plot3d(ax,x,y,z,**kwargs):\n",
    "\n",
    "    global alpha, beta\n",
    "    \n",
    "    X = [v - alpha * u for (u,v) in zip(x,y)]\n",
    "    Y = [w - beta * u for (u,w) in zip(x,z)]\n",
    "    ax.plot(X,Y,**kwargs)     \n",
    "\n",
    "def afficheSolution(s):\n",
    "    \n",
    "    global alpha, beta\n",
    "\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111,aspect = 'equal')\n",
    "    plt.axis('equal')\n",
    "    plt.axis('off')\n",
    "    \n",
    "    plot3d(ax,[2,2.5],[0,0],[0,0], color = '0.8', linewidth = 0.5)\n",
    "    plot3d(ax,[0,0],[2,2.5],[0,0], color = '0.8', linewidth = 0.5)\n",
    "    plot3d(ax,[0,0],[0,0],[2,2.5], color = '0.8', linewidth = 0.5)\n",
    "    \n",
    "    ax.annotate(r\"$x$\",xy = (-alpha * 2.5,-beta*2.5),fontsize = 18,\n",
    "            horizontalalignment='right', verticalalignment='top')\n",
    "    ax.annotate(r\"$y$\",xy = (2.5,0),fontsize = 18)\n",
    "    ax.annotate(r\"$z$\",xy = (0,2.5),fontsize = 18,\n",
    "                horizontalalignment='center', verticalalignment='bottom') \n",
    "    for a in range(3):\n",
    "        for b in range(3):\n",
    "            plot3d(ax,[a,a],[b,b],[0,2], color = '0', linewidth = 0.5)\n",
    "            plot3d(ax,[a,a],[0,2],[b,b], color = '0', linewidth = 0.5)\n",
    "            plot3d(ax,[0,2],[a,a],[b,b], color = '0', linewidth = 0.5)\n",
    "        \n",
    "    xc,yc,zc = int(s[0]),int(s[1]),int(s[2])\n",
    "    x,y,z = [xc], [yc], [zc]\n",
    "        \n",
    "    for c in s[3:]:\n",
    "        if c == 'X':\n",
    "            xc += 1\n",
    "        elif c == 'x':\n",
    "            xc -= 1\n",
    "        elif c == 'Y':\n",
    "            yc += 1\n",
    "        elif c == 'y':\n",
    "            yc -= 1\n",
    "        elif c == 'Z':\n",
    "            zc += 1\n",
    "        else:\n",
    "            zc -= 1\n",
    "        x.append(xc)\n",
    "        y.append(yc)\n",
    "        z.append(zc)\n",
    "        \n",
    "    plot3d(ax,x,y,z,color = 'blue', linewidth = 3, marker = 'o')\n",
    "    plot3d(ax,[int(s[0])],[int(s[1])],[int(s[2])],color = 'green', marker = 'o')  \n",
    "    plot3d(ax,[xc],[yc],[zc],color = 'red', marker = 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "whJ8tpIhBPSf",
   "metadata": {
    "id": "whJ8tpIhBPSf"
   },
   "source": [
    "### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "jge3H-cSDEzf",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "executionInfo": {
     "elapsed": 290,
     "status": "ok",
     "timestamp": 1670626090552,
     "user": {
      "displayName": "Yves Lemaire",
      "userId": "04690556979859113270"
     },
     "user_tz": -60
    },
    "id": "jge3H-cSDEzf",
    "outputId": "8f1ca00a-5b8f-4aa4-9770-730347ee6d37"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "afficheSolution('000XXYYxxZZXzXyyxxZYzzXZZyXYY')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.5"
  },
  "vscode": {
   "interpreter": {
    "hash": "369f2c481f4da34e4445cda3fffd2e751bd1c4d706f27375911949ba6bb62e1c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}