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   "source": [
    "# Like the naive algorithm but we break out of the inner loop as soon as our\n",
    "# mismatch budget exceeds the maximum allowed Hamming distance.\n",
    "def naive_approx_hamming(p, t, maxHammingDistance=1):\n",
    "    occurrences = []\n",
    "    for i in range(0, len(t) - len(p) + 1): # for all alignments\n",
    "        nmm = 0\n",
    "        for j in range(0, len(p)):          # for all characters\n",
    "            if t[i+j] != p[j]:               # does it match?\n",
    "                nmm += 1                     # mismatch\n",
    "                if nmm > maxHammingDistance:\n",
    "                    break                    # exceeded maximum distance\n",
    "        if nmm <= maxHammingDistance:\n",
    "            # approximate match; return pair where first element is the\n",
    "            # offset of the match and second is the Hamming distance\n",
    "            occurrences.append((i, nmm))\n",
    "    return occurrences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (7, 2)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_approx_hamming('needle', 'needle noodle nargle', maxHammingDistance=2)"
   ]
  }
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