example_exercise.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an example exercise notebook.  First, a code cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "from py2neo import neo4j, node, rel\n",
    "\n",
    "# create connection to database using defaults\n",
    "graph_db = neo4j.GraphDatabaseService()\n",
    "\n",
    "# create connection to database using explicit URL of REST API endpoint.\n",
    "graph_db = neo4j.GraphDatabaseService( \"http://localhost:7474/db/data/\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does it make you feel that we placed non-working and totally unrelated code at the top of this exercise?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "how_does_that_make_you_feel",
     "locked": false,
     "points": 1,
     "solution": true
    }
   },
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part A (2 points) - squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function that returns a list of numbers, such that xi=i2, for 1≤i≤n. Make sure it handles the case where n<1 by raising a ValueError."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "squares",
     "locked": false,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def squares( n ):\n",
    "    \"\"\"\n",
    "    Compute the squares of the numbers one to n, such that the\n",
    "    ith element of the returned list equals i^2.\n",
    "    \"\"\"\n",
    "    \n",
    "    ### BEGIN SOLUTION\n",
    "    if n < 1:\n",
    "        raise ValueError( \"n must be greater than or equal to 1\" )\n",
    "    return [ i ** 2 for i in range( 1, n + 1 ) ]\n",
    "    ### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your function should print [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] for n=10. Check that it does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "squares( 10 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "correct_squares",
     "locked": true,
     "points": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"Check that squares returns the correct output for several inputs\"\"\"\n",
    "from nose.tools import assert_equal\n",
    "assert_equal( squares( 1 ), [ 1 ] )\n",
    "assert_equal( squares( 2 ), [ 1, 4 ] )\n",
    "assert_equal( squares( 10 ), [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ] )\n",
    "assert_equal( squares( 11 ), [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 ] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "squares_invalid_input",
     "locked": true,
     "points": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"Check that squares raises an erorr for invalid inputs\"\"\"\n",
    "from nose.tools import assert_raises\n",
    "assert_raises( ValueError, squares, 0 )\n",
    "assert_raises( ValueError, squares, -1 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part B (1 point) - sum of squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using your squares function, write a function that computes the sum of the squares of the numbers from 1 to n. Your function should call the squares function -- it should NOT reimplement its functionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": false,
     "grade_id": "sum_of_squares",
     "locked": false,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def sum_of_squares(n):\n",
    "    \"\"\"Compute the sum of the squares of numbers from 1 to n.\"\"\"\n",
    "    ### BEGIN SOLUTION\n",
    "    return sum(squares(n))\n",
    "    ### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sum of squares from 1 to 10 should be 385. Verify that this is the answer you get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sum_of_squares( 10 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "correct_sum_of_squares",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"Check that sum_of_squares returns the correct answer for various inputs.\"\"\"\n",
    "assert_equal(sum_of_squares(1), 1)\n",
    "assert_equal(sum_of_squares(2), 5)\n",
    "assert_equal(sum_of_squares(10), 385)\n",
    "assert_equal(sum_of_squares(11), 506)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "sum_of_squares_uses_squares",
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"Check that sum_of_squares relies on squares.\"\"\"\n",
    "orig_squares = squares\n",
    "del squares\n",
    "try:\n",
    "    assert_raises(NameError, sum_of_squares, 1)\n",
    "except AssertionError:\n",
    "    raise AssertionError(\"sum_of_squares does not use squares\")\n",
    "finally:\n",
    "    squares = orig_squares"
   ]
  }
 ],
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