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moved problem3 to its own ps1_autotest assignment
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@trevorcampbell
trevorcampbell committed Aug 29, 2023
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399 changes: 399 additions & 0 deletions nbgrader/docs/source/user_guide/source/ps1_autotest/problem1.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "jupyter",
"locked": true,
"schema_version": 3,
"solution": false
}
},
"source": [
"For this problem set, we'll be using the Jupyter notebook:\n",
"\n",
"![](jupyter.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Part A (2 points)\n",
"\n",
"Write a function that returns a list of numbers, such that $x_i=i^2$, for $1\\leq i \\leq n$. Make sure it handles the case where $n<1$ by raising a `ValueError`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "squares",
"locked": false,
"schema_version": 3,
"solution": true
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"def squares(n):\n",
" \"\"\"Compute the squares of numbers from 1 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": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"squares(10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "correct_squares",
"locked": false,
"points": 1,
"schema_version": 3,
"solution": false
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"\"\"\"Check that squares returns the correct output for several inputs\"\"\"\n",
"### AUTOTEST squares(1); squares(2)\n",
"### HASHED AUTOTEST squares(3)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "squares_invalid_input",
"locked": false,
"points": 1,
"schema_version": 3,
"solution": false
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"\"\"\"Check that squares raises an error for invalid inputs\"\"\"\n",
"def test_func_throws(func, ErrorType):\n",
" try:\n",
" func()\n",
" except ErrorType:\n",
" return True\n",
" else:\n",
" print('Did not raise right type of error!')\n",
" return False\n",
" \n",
"### AUTOTEST test_func_throws(lambda : squares(0), ValueError)\n",
"### AUTOTEST test_func_throws(lambda : squares(-4), ValueError);\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"## Part B (1 point)\n",
"\n",
"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": {
"nbgrader": {
"grade": false,
"grade_id": "sum_of_squares",
"locked": false,
"schema_version": 3,
"solution": true
},
"vscode": {
"languageId": "python"
}
},
"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": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"sum_of_squares(10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "correct_sum_of_squares",
"locked": false,
"points": 0.5,
"schema_version": 3,
"solution": false
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"\"\"\"Check that sum_of_squares returns the correct answer for various inputs.\"\"\"\n",
"### AUTOTEST sum_of_squares(1)\n",
"### AUTOTEST sum_of_squares(2); sum_of_squares(10) \n",
"### AUTOTEST sum_of_squares(11) \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "sum_of_squares_uses_squares",
"locked": false,
"points": 0.5,
"schema_version": 3,
"solution": false
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"\"\"\"Check that sum_of_squares relies on squares.\"\"\"\n",
"\n",
"orig_squares = squares\n",
"del squares\n",
"\n",
"### AUTOTEST test_func_throws(lambda : sum_of_squares(1), NameError)\n",
"\n",
"squares = orig_squares\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Part C (1 point)\n",
"\n",
"Using LaTeX math notation, write out the equation that is implemented by your `sum_of_squares` function."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "sum_of_squares_equation",
"locked": false,
"points": 1,
"schema_version": 3,
"solution": true
}
},
"source": [
"$\\sum_{i=1}^n i^2$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Part D (2 points)\n",
"\n",
"Find a usecase for your `sum_of_squares` function and implement that usecase in the cell below."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "sum_of_squares_application",
"locked": false,
"points": 2,
"schema_version": 3,
"solution": true
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"def pyramidal_number(n):\n",
" \"\"\"Returns the n^th pyramidal number\"\"\"\n",
" return sum_of_squares(n)"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-938593c4a215c6cc",
"locked": true,
"points": 4,
"schema_version": 3,
"solution": false,
"task": true
}
},
"source": [
"---\n",
"## Part E (4 points)\n",
"\n",
"State the formulae for an arithmetic and geometric sum and verify them numerically for an example of your choice."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Part F (1 points)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-d3df8cd59fd0eb74",
"locked": false,
"schema_version": 3,
"solution": true,
"task": false
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"my_dictionary = {\n",
" 'one' : 1,\n",
" 'two' : 2,\n",
" 'three' : 3\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "cell-6e9ff83aa5dfaf17",
"locked": true,
"points": 0,
"schema_version": 3,
"solution": false,
"task": false
},
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"### AUTOTEST my_dictionary\n",
"### AUTOTEST my_dictionary[\"one\"]"
]
}
],
"metadata": {
"celltoolbar": "Create Assignment",
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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