2. Graph Theory (n-Cubes).ipynb

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   "source": [
    "from graphviz import Graph\n",
    "from operator import eq\n",
    "from itertools import combinations_with_replacement, combinations, permutations, product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getBinStrings(n):\n",
    "    return list(product(range(2), repeat=n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getNCubeEdges(n):\n",
    "    return [pair for pair in combinations(getBinStrings(n), 2)\n",
    "                          if sum(eq(*x) for x in (zip(*pair))) == n-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tupToStr(tup):\n",
    "    return \"\".join(str(x) for x in tup)\n",
    "def tupToStrLst(tupList):\n",
    "    return [tupToStr(x) for x in tupList]"
   ]
  },
  {
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   "execution_count": 5,
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   "source": [
    "def getNCubeGraph(n):\n",
    "    nodes = tupToStrLst(getBinStrings(n))\n",
    "    edges = [tupToStrLst(x) for x in getNCubeEdges(n)]\n",
    "    \n",
    "    cube = Graph()\n",
    "    for x in nodes:\n",
    "        cube.node(x, x)\n",
    "        \n",
    "    for x in edges:\n",
    "        cube.edge(*x)\n",
    "        \n",
    "    return cube"
   ]
  },
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