12 Exercises.ipynb

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    "## Exercise 12.1\n",
    "\n",
    "Create a class to represent vectors of arbitrary length and which is initialised with a list of values, e.g.:\n",
    "```python\n",
    "x = MyVector([0, 2, 4])\n",
    "```\n",
    "\n",
    "Equip the class with methods that:\n",
    "\n",
    "1. Return the length of the vector (use name `size`)\n",
    "2. Compute the norm of the vector $\\sqrt{x \\cdot x}$ (use name `norm`)\n",
    "3. Compute the dot product of the vector with another vector (use name `dot`)\n",
    "\n",
    "Test your implementation using two vectors of length 3. To help you get started, a skeleton of the class is provided below. Don't forget to use `self` where necessary."
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    "class MyVector:\n",
    "    \"\"\"A vector object that can return its size and norm, and can compute the dot product \n",
    "    with another vector  \"\"\"\n",
    "    \n",
    "    def __init__(self, x):\n",
    "        self.x = x\n",
    "        \n",
    "    # Return length of vector\n",
    "    def size(self):\n",
    "        # Add your code here\n",
    "        pass  # This can be removed once the body is added\n",
    "    \n",
    "    # This allows access by index, e.g. y[2]\n",
    "    def __getitem__(self, index):\n",
    "        return self.x[index]\n",
    "\n",
    "    # Return norm of vector\n",
    "    def norm(self):\n",
    "        # Add your code here\n",
    "        pass  # This can be removed once the body is added\n",
    "    \n",
    "    # Return dot product of vector with another vector\n",
    "    def dot(self, other):\n",
    "        # Add your code here\n",
    "        pass  # This can be removed once the body is added"
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    "### Solution"
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    "import math  # Use this to get the sqrt\n",
    "\n",
    "class MyVector:\n",
    "    \"\"\"A vector object that can return its size and norm, and can compute the dot product \n",
    "    with another vector  \"\"\"\n",
    "\n",
    "    def __init__(self, x):\n",
    "        self.x = x\n",
    "\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
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    "# Create two vectors\n",
    "u = MyVector([1, 1, 2])\n",
    "v = MyVector([2, 1, 1])\n",
    "\n",
    "assert u.size() == 3\n",
    "assert round(u.norm() - 2.449489742783178) == 0.0\n",
    "assert round(u.dot(v) - 5.0, 10) == 0.0 "
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    "## Exercise 12.2\n",
    "\n",
    "1. Create a class for holding a student record entry. It should have the following attributes:\n",
    "   - Surname\n",
    "   - Forename\n",
    "   - Birth year\n",
    "   - Tripos year\n",
    "   - College\n",
    "   - CRSid (optional field)\n",
    "1. Equip your class with the method '`age`' that returns the age of the student in whole years\n",
    "1. Equip your class with the method '`__repr__`' such using `print` on a student record displays with the format\n",
    "\n",
    "       Surname: Bloggs, Forename: Andrea, College: Churchill\n",
    "\n",
    "1. Equip your class with the method `__lt__(self, other)` so that a list of record entries can be sorted by \n",
    "   (surname, forename) using the Python built-in sort function. \n",
    "   \n",
    "   Create a list of entries and test the sorting. Make sure you have two entries with the same\n",
    "   surname.\n",
    "\n",
    "> Recall that the methods starting with `__`, e.g. `__lt__` and `__repr__`, should **not** be called directly. \n",
    "> Python with map them to other operations, e.g. `__repr__` is called when using `print`, and `__lt__` is called \n",
    "> when using `<`. These functions must have a return value.\n",
    "\n",
    "*Hint:* To get the current year:"
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   "source": [
    "import datetime\n",
    "year = datetime.date.today().year\n",
    "print(year)"
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    "### Solution"
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    "import datetime \n",
    "class StudentEntry:\n",
    "    def __init__(self, surname, forename, birth_year, year, college, crsid=None):\n",
    "        self.surname = surname\n",
    "        self.forename = forename\n",
    "        self.birth_year = birth_year\n",
    "        self.year = year\n",
    "        self.college = college\n",
    "        self.crsid = crsid\n",
    "\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
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    "s0 = StudentEntry(\"Bloggs\", \"Andrea\", 1996, 1, \"Churchill\", \"ab1001\")       \n",
    "s1 = StudentEntry(\"Reali\", \"John\", 1997, 1, \"Corpus Christi\")       \n",
    "s2 = StudentEntry(\"Bacon\", \"Kevin\", 1996, 1, \"Newnham\")\n",
    "s3 = StudentEntry(\"Bacon\", \"Alexander\", 1996, 1, \"Queens\")\n",
    "\n",
    "assert s0 < s1\n",
    "assert s0 > s2\n",
    "assert s3 < s2\n",
    "assert s0.age() ==  datetime.date.today().year - 1996 \n",
    "assert s1.age() ==  datetime.date.today().year - 1997\n",
    "assert str(s1) == \"Surname: Reali, Forename: John, College: Corpus Christi\"\n",
    "\n",
    "# Test sorting\n",
    "s = [s0, s1, s2, s3]\n",
    "s.sort()\n",
    "for earlier, later in zip(s, s[1:]):\n",
    "    assert earlier.surname <= later.surname\n",
    "    if earlier.surname == later.surname:\n",
    "        assert earlier.forename <= later.forename"
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