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    "# Homework: Caesar Cipher"
   ]
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   "source": [
    "**Q1**. Ciphers and Statistics\n",
    "\n",
    "A Caesar cipher is a very simple method of encoding and decoding data. The cipher simply replaces characters with the character offset by $k$ places. For example, if the offset is 3, we replace `a` with `d`, `b` with `e` etc. The cipher wraps around so we replace `y` with `b`, `z` with `c` and so on. Punctuation, spaces and numbers are left unchanged."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (25 points) Write a function `encode` that takes as arguments a string and an integer offset and returns the encoded cipher."
   ]
  },
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   "source": [
    "- (5 points) Write a function `decode` that takes as arguments a cipher and an integer offset and returns the decoded string. "
   ]
  },
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   "execution_count": null,
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   "source": [
    "- (50 points) Write a function `auto_decode` that takes as argument a cipher and uses a statistical method to guess the optimal offset to decode the cipher, assuming the original string is in English which has the following letter frequency:\n",
    "\n",
    "```python\n",
    "freq = {\n",
    " 'a': 0.08167,\n",
    " 'b': 0.01492,\n",
    " 'c': 0.02782,\n",
    " 'd': 0.04253,\n",
    " 'e': 0.12702,\n",
    " 'f': 0.02228,\n",
    " 'g': 0.02015,\n",
    " 'h': 0.06094,\n",
    " 'i': 0.06966,\n",
    " 'j': 0.00153,\n",
    " 'k': 0.00772,\n",
    " 'l': 0.04025,\n",
    " 'm': 0.02406,\n",
    " 'n': 0.06749,\n",
    " 'o': 0.07507,\n",
    " 'p': 0.01929,\n",
    " 'q': 0.00095,\n",
    " 'r': 0.05987,\n",
    " 's': 0.06327,\n",
    " 't': 0.09056,\n",
    " 'u': 0.02758,\n",
    " 'v': 0.00978,\n",
    " 'w': 0.0236,\n",
    " 'x': 0.0015,\n",
    " 'y': 0.01974,\n",
    " 'z': 0.00074\n",
    "}\n",
    "```"
   ]
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   "source": [
    "- (20 points) Encode the following nursery rhyme using a random offset from 10 to 20, then recover the original using `auto_decode`:\n",
    "\n",
    "```text\n",
    "Baa, baa, black sheep,\n",
    "Have you any wool?\n",
    "Yes, sir, yes, sir,\n",
    "Three bags full;\n",
    "One for the master,\n",
    "And one for the dame,\n",
    "And one for the little boy\n",
    "Who lives down the lane.\n",
    "```"
   ]
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   "cell_type": "code",
   "execution_count": 62,
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