Letter Table Code

letter-table.ipynb

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   "source": [
    "indata = [(\"E\", 21912),\n",
    "(\"T\", 16587),\n",
    "(\"A\", 14810),\n",
    "(\"O\", 14003),\n",
    "(\"I\", 13318),\n",
    "(\"N\", 12666),\n",
    "(\"S\", 11450),\n",
    "(\"R\", 10977),\n",
    "(\"H\", 10795),\n",
    "(\"D\", 7874),\n",
    "(\"L\", 7253),\n",
    "(\"U\", 5246),\n",
    "(\"C\", 4943),\n",
    "(\"M\", 4761),\n",
    "(\"F\", 4200),\n",
    "(\"Y\", 3853),\n",
    "(\"W\", 3819),\n",
    "(\"G\", 3693),\n",
    "(\"P\", 3316),\n",
    "(\"B\", 2715),\n",
    "(\"V\", 2019),\n",
    "(\"K\", 1257),\n",
    "(\"X\", 315),\n",
    "(\"Q\", 205),\n",
    "(\"J\", 188),\n",
    "(\"Z\", 128)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ETAOINSRHDLUCMFYWGPBVKXQJZ'"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\".join(x[0] for x in indata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.08123837786542185,\n",
       " 'B': 0.014892788379785303,\n",
       " 'C': 0.027114199985738028,\n",
       " 'D': 0.043191828988003486,\n",
       " 'E': 0.12019549870270922,\n",
       " 'F': 0.02303856765933638,\n",
       " 'G': 0.020257483420459344,\n",
       " 'H': 0.05921460425774672,\n",
       " 'I': 0.07305420097310522,\n",
       " 'J': 0.0010312501714179142,\n",
       " 'K': 0.006895114178044245,\n",
       " 'L': 0.03978541219837304,\n",
       " 'M': 0.02611586205383345,\n",
       " 'N': 0.06947773761265585,\n",
       " 'O': 0.07681168165087793,\n",
       " 'P': 0.018189497704371293,\n",
       " 'Q': 0.0011245015167057042,\n",
       " 'R': 0.06021294218965129,\n",
       " 'S': 0.06280752373795274,\n",
       " 'T': 0.09098588613462202,\n",
       " 'U': 0.02877626808116158,\n",
       " 'V': 0.011074968596238131,\n",
       " 'W': 0.020948640450239437,\n",
       " 'X': 0.0017278925744502285,\n",
       " 'Y': 0.021135143140815018,\n",
       " 'Z': 0.0007021277762845373}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = sum(x[1] for x in indata)\n",
    "freq = {k: v/total for k,v in indata}\n",
    "freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sort = list(sorted(freq.keys(), key=lambda x: -freq[x]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_expectation(buckets):\n",
    "    expected = 0\n",
    "    for bi, bucket in enumerate(buckets):\n",
    "        for li, l in enumerate(bucket):\n",
    "            expected += freq[l] * (bi + 1 + li + 1)\n",
    "    return expected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.920983198301728"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "buckets = [\n",
    "    'ABCDEFG',\n",
    "    'HIJKLMN',\n",
    "    'OPQRST',\n",
    "    'UVWXYZ'\n",
    "]\n",
    "get_expectation(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.844884615173639"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "buckets = [\n",
    "    'EACDGBF',\n",
    "    'INLMHKJ',\n",
    "    'ROTSPQ',\n",
    "    'UYWVXZ',\n",
    "]\n",
    "get_expectation(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.788813129789416"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "buckets = [\n",
    "    'EOLPBKJ',\n",
    "    'ATCMFVQ',\n",
    "    'RNUHYX',\n",
    "    'ISDGWZ'\n",
    "]\n",
    "get_expectation(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.467891367668112"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "buckets = [\n",
    "    'ETOSLYK',\n",
    "    'AIRUWX',\n",
    "    'NHCGQ',\n",
    "    'DMPJ',\n",
    "    'FBZ',\n",
    "    'V',\n",
    "]\n",
    "'ETA OIN SRHD LUCMF YWGPBV KXQJZ'\n",
    "get_expectation(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.479668464040635"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "buckets = [\n",
    "    'ETOSLYK',\n",
    "    'AIRUWX',\n",
    "    'NHCGQ',\n",
    "    'DMPJ',\n",
    "    'FBVZ',\n",
    "]\n",
    "get_expectation(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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