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 * 3ef07e5: Refurbish the new new chapter 09 on maps
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Alexander Hess 2020-04-09 14:31:58 +02:00
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 9: Mappings & Sets"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Content Review"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The questions below assume that you have read [Chapter 9 <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/09_mappings_00_content.ipynb) in the book.\n",
"\n",
"Be concise in your answers! Most questions can be answered in *one* sentence."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Essay Questions "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1**: `dict` objects are well-suited **to model** discrete mathematical **functions** and to approximate continuous ones. What property of dictionaries is the basis for that claim, and how does it relate to functions in the mathematical sense?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2**: Explain why **hash tables** are a **trade-off** between **computational speed** and **memory** usage!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q3:** The `dict` type is an **iterable** that **contains** a **finite** number of key-value pairs. Despite that, why is it *not* considered a **sequence**?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q4**: Whereas *key* **look-ups** in a `dict` object run in so-called **[constant time <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_wiki.png\">](https://en.wikipedia.org/wiki/Time_complexity#Constant_time)** (i.e., *extremely* fast), that does not hold for *reverse* look-ups. Why is that?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q5**: Why is it conceptually correct that the Python core developers do not implement **slicing** with the `[]` operator for `dict` objects?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q6**: **Memoization** is an essential concept to know to solve problems in the real world. Together with the idea of **recursion**, it enables us to solve problems in a \"backwards\" fashion *effectively*.\n",
"\n",
"\n",
"Compare the **recursive** formulation of `fibonacci()` in [Chapter 8 <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/08_mappings_00_content.ipynb#\"Easy-at-third-Glance\"-Example:-Fibonacci-Numbers-%28revisited%29), the \"*Easy at second Glance*\" example, with the **iterative** version in [Chapter 4 <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/04_iteration_00_content.ipynb#\"Hard-at-first-Glance\"-Example:-Fibonacci-Numbers-%28revisited%29), the \"*Hard at first Glance*\" example!\n",
"\n",
"How are they similar and how do they differ?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q7**: How are the `set` and the `dict` type related? How could we use the latter to mimic the former?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### True / False Questions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Motivate your answer with *one short* sentence!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q8**: We may *not* put `dict` objects inside other `dict` objects because they are **mutable**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q9**: **Mutable** objects (e.g., `list`) may generally *not* be used as keys in a `dict` object. However, if we collect, for example, `list` objects in a `tuple` object, the composite object becomes **hashable**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q10**: **Mutability** of a `dict` object works until the underlying hash table becomes too crowded. Then, we cannot insert any items any more making the `dict` object effectively **immutable**. Luckily, that almost never happens in practice."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q11**: A `dict` object's [update() <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/stdtypes.html#dict.update) method only inserts key-value pairs whose key is *not* yet in the `dict` object. So, it does *not* overwrite anything."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q12**: The `set` type is both a mapping and a sequence."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.4"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": false,
"sideBar": true,
"skip_h1_title": true,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": false,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Important**: Click on \"*Kernel*\" > \"*Restart Kernel and Run All*\" *after* finishing the exercises in [JupyterLab <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_jp.png\">](https://jupyterlab.readthedocs.io/en/stable/) (e.g., in the cloud on [MyBinder <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_mb.png\">](https://mybinder.org/v2/gh/webartifex/intro-to-python/master?urlpath=lab/tree/09_mappings_02_exercises.ipynb)) to ensure that your solution runs top to bottom *without* any errors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 9: Mappings & Sets"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Coding Exercises"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The exercises below assume that you have read [Chapter 9 <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/09_mappings_00_content.ipynb) in the book.\n",
"\n",
"The `...`'s in the code cells indicate where you need to fill in code snippets. The number of `...`'s within a code cell give you a rough idea of how many lines of code are needed to solve the task. You should not need to create any additional code cells for your final solution. However, you may want to use temporary code cells to try out some ideas."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Working with Nested Data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's write some code to analyze the historic soccer game [Brazil vs. Germany <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_wiki.png\">](https://en.wikipedia.org/wiki/Brazil_v_Germany_%282014_FIFA_World_Cup%29) during the 2014 World Cup.\n",
"\n",
"Below, `players` consists of two nested `dict` objects, one for each team, that hold `tuple` objects (i.e., records) with information on the players. Besides the jersey number, name, and position, each `tuple` objects contains a `list` object with the times when the player scored."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"players = {\n",
" \"Brazil\": [\n",
" (12, \"Júlio César\", \"Goalkeeper\", []),\n",
" (4, \"David Luiz\", \"Defender\", []),\n",
" (6, \"Marcelo\", \"Defender\", []),\n",
" (13, \"Dante\", \"Defender\", []),\n",
" (23, \"Maicon\", \"Defender\", []),\n",
" (5, \"Fernandinho\", \"Midfielder\", []),\n",
" (7, \"Hulk\", \"Midfielder\", []),\n",
" (8, \"Paulinho\", \"Midfielder\", []),\n",
" (11, \"Oscar\", \"Midfielder\", [90]),\n",
" (16, \"Ramires\", \"Midfielder\", []),\n",
" (17, \"Luiz Gustavo\", \"Midfielder\", []),\n",
" (19, \"Willian\", \"Midfielder\", []),\n",
" (9, \"Fred\", \"Striker\", []),\n",
" ],\n",
" \"Germany\": [\n",
" (1, \"Manuel Neuer\", \"Goalkeeper\", []),\n",
" (4, \"Benedikt Höwedes\", \"Defender\", []),\n",
" (5, \"Mats Hummels\", \"Defender\", []),\n",
" (16, \"Philipp Lahm\", \"Defender\", []),\n",
" (17, \"Per Mertesacker\", \"Defender\", []),\n",
" (20, \"Jérôme Boateng\", \"Defender\", []),\n",
" (6, \"Sami Khedira\", \"Midfielder\", [29]),\n",
" (7, \"Bastian Schweinsteiger\", \"Midfielder\", []),\n",
" (8, \"Mesut Özil\", \"Midfielder\", []),\n",
" (13, \"Thomas Müller\", \"Midfielder\", [11]),\n",
" (14, \"Julian Draxler\", \"Midfielder\", []),\n",
" (18, \"Toni Kroos\", \"Midfielder\", [24, 26]),\n",
" (9, \"André Schürrle\", \"Striker\", [69, 79]),\n",
" (11, \"Miroslav Klose\", \"Striker\", [23]),\n",
" ],\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.1**: Write a dictionary comprehension to derive a new `dict` object, called `brazilian_players`, that maps a Brazilian player's name to his position!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"brazilian_players = {...: ...}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"brazilian_players"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.2**: Generalize the code fragment into a `get_players()` function: Passed a `team` name, it returns a `dict` object like `brazilian_players`. Verify that the function works for the German team as well!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def get_players(team):\n",
" \"\"\"Creates a dictionary mapping the players' names to their position.\"\"\"\n",
" return {...: ...}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"get_players(\"Germany\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Often, we are given a `dict` object like the one returned from `get_players()`: Its main characteristic is that it maps a large set of unique keys (i.e., the players' names) onto a smaller set of non-unique values (i.e., the positions).\n",
"\n",
"**Q1.3**: Create a generic `invert()` function that swaps the keys and values of a `mapping` argument passed to it and returns them in a *new* `dict` object! Ensure that *no* key gets lost! Verify your implementation with the `brazilian_players` dictionary!\n",
"\n",
"Hints: Think of this as a grouping operation. The *new* values are `list` or `tuple` objects that hold the original keys. You may want to use either the [defaultdict <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/collections.html#collections.defaultdict) type from the [collections <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/collections.html) module in the [standard library <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/index.html) or the [setdefault() <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/stdtypes.html#dict.setdefault) method on the ordinary `dict` type."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def invert(mapping):\n",
" \"\"\"Invert the keys and values of a mapping argument.\"\"\"\n",
" ...\n",
" ...\n",
" ...\n",
" return ..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"invert(brazilian_players)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.4**: Write a `score_at_minute()` function: It takes two arguments, `team` and `minute`, and returns the number of goals the `team` has scored up until this time in the game.\n",
"\n",
"Hints: The function may reference the global `players` for simplicity. Earn bonus points if you can write this in a one-line expression using some *reduction* function and a *generator expression*."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def score_at_minute(team, minute):\n",
" \"\"\"Determine the number of goals scored by a team until a given minute.\"\"\"\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" return ..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The score at half time was:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"score_at_minute(\"Brazil\", 45)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"score_at_minute(\"Germany\", 45)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The final score was:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"score_at_minute(\"Brazil\", 90)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"score_at_minute(\"Germany\", 90)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.5**: Write a `goals_by_player()` function that takes an argument like the global `players`, and returns a `dict` object mapping the players to the number of goals they scored!\n",
"\n",
"Hints: Do *not* \"hard code\" the names of the teams! Earn bonus points if you can solve it in a one-line dictionary comprehension."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def goals_by_player(players):\n",
" \"\"\"Create a dictionary mapping the players' names to the number of goals.\"\"\"\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" return ..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"goals_by_player(players)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.6**: Write a *dictionary comprehension* to filter out the players who did *not* score from the preceding result. Then, write a *set comprehension* that does the same but discards the number of goals scored.\n",
"\n",
"Hints: Reference the `goals_by_player()` function from before."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"{...: ...}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"{...}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.7**: Write a `all_goals()` function that takes one argument like the global `players` and returns a `list` object containing $2$-element `tuple` objects where the first element is the minute a player scored and the second his name! The list should be sorted by the time.\n",
"\n",
"Hints: You may want to use either the built-in [sorted() <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/functions.html#sorted) function or the `list` type's [sort() <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_py.png\">](https://docs.python.org/3/library/stdtypes.html#list.sort) method. Earn bonus points if you can write a one-line expression with a *generator expression*."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def all_goals(players):\n",
" \"\"\"Create a time table of the individual goals.\"\"\"\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" return ..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"all_goals(players)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1.8**: Lastly, write a `summary()` function that takes one argument like the global `players` and prints out a concise report of the goals, the score at the half, and the final result.\n",
"\n",
"Hints: Use the `all_goals()` and `score_at_minute()` functions from before.\n",
"\n",
"The output should look similar to this:\n",
"```\n",
"12' Gerd Müller scores\n",
"...\n",
"HALFTIME: TeamA 1 TeamB 2\n",
"77' Ronaldo scores\n",
"...\n",
"FINAL: TeamA 1 TeamB 3\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def summary(players):\n",
" \"\"\"Create a written summary of the game.\"\"\"\n",
" # Create two lists with the goals of either half.\n",
" ...\n",
" ...\n",
" ...\n",
"\n",
" # Print the goals of the first half.\n",
" ...\n",
" ...\n",
"\n",
" # Print the half time score.\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
"\n",
" # Print the goals of the second half.\n",
" ...\n",
" ...\n",
"\n",
" # Print the final score.\n",
" ...\n",
" ...\n",
" ...\n",
" ...\n",
" ..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"summary(players)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Memoization without Side Effects"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"It is considered *bad practice* to make a function and thereby its correctness dependent on a program's *global state*: For example, in the \"*Easy at second Glance: Fibonacci Numbers*\" section in [Chapter 9 <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/09_mappings_00_content.ipynb#\"Easy-at-second-Glance\"-Example:-Fibonacci-Numbers--%28revisited%29), we use a global `memo` to store the Fibonacci numbers that have already been calculated.\n",
"\n",
"That `memo` dictionary could be \"manipulated.\" More often than not, such things happen by accident: Imagine we wrote two independent recursive functions that both rely on memoization to solve different problems, and, unintentionally, we made both work with the *same* global `memo`. As a result, we would observe \"random\" bugs depending on the order in which we executed these functions. Such bugs are hard to track down in practice.\n",
"\n",
"A common remedy is to avoid global state and pass intermediate results \"down\" the recursion tree in a \"hidden\" argument. By convention, we prefix parameter names with a single leading underscore `_`, such as with `_memo` below, to indicate that the caller of our `fibonacci()` function *must not* use it. Also, we make `_memo` a *keyword-only* argument to force ourselves to always explicitly name it in a function call. Because it is an **implementation detail**, the `_memo` parameter is *not* mentioned in the docstring.\n",
"\n",
"Your task is to complete this version of `fibonacci()` so that the function works *without* any **side effects** in the global scope."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"#### \"Easy at third Glance\" Example: [Fibonacci Numbers <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_wiki.png\">](https://en.wikipedia.org/wiki/Fibonacci_number)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"code_folding": [],
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def fibonacci(i, *, debug=False, _memo=None):\n",
" \"\"\"Calculate the ith Fibonacci number.\n",
"\n",
" Args:\n",
" i (int): index of the Fibonacci number to calculate\n",
" debug (bool): show non-cached calls; defaults to False\n",
"\n",
" Returns:\n",
" ith_fibonacci (int)\n",
" \"\"\"\n",
" # answer to Q2.1\n",
" if ...:\n",
" ... = {\n",
" 0: 0,\n",
" 1: 1,\n",
" }\n",
"\n",
" # answer to Q2.2\n",
" if ...:\n",
" return ...\n",
"\n",
" if debug: # added for didactical purposes\n",
" print(f\"fibonacci({i}) is calculated\")\n",
"\n",
" # answer to Q2.3\n",
" recurse = (\n",
" fibonacci(...)\n",
" + fibonacci(...)\n",
" )\n",
" # answer to Q2.4\n",
" ... = ...\n",
" return ..."
]
},
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"cell_type": "markdown",
"metadata": {
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"slide_type": "skip"
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"source": [
"**Q2.1**: When `fibonacci()` is initially called, `_memo` is set to `None`. So, there is *no* `dict` object yet. Implement the *two* base cases in the first `if` statement!\n",
"\n",
"Hints: All you need to do is create a *new* `dict` object with the results for `i=0` and `i=1`. This object is then passed on in the recursive function calls. Use the `is` operator in the `if` statement."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2.2**: When `fibonacci()` is called for non-base cases (i.e., `i > 1`), it first checks if the result is already in the `_memo`. Implement that step in the second `if` statement!\n",
"\n",
"Hint: Use the early exit pattern."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2.3**: If `fibonacci()` is called for an `i` argument whose result is not yet in the `_memo`, it must calculate it with the usual recursive function calls. Fill in the arguments to the two recursive `fibonacci()` calls!\n",
"\n",
"Hint: You must pass on the hidden `_memo`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2.4**: Lastly, after the two recursive calls have returned, `fibonacci()` must store the `recurse` result for the given `i` in the `_memo` *before* returning it. Implement that logic!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2.5**: What happens to the hidden `_memo` after the initial call to `fibonacci()` returned? How many hidden `_memo` objects exist in memory during the entire computation?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"Because `fibonacci()` is now independent of the *global state*, the same eleven recursive function calls are made each time! So, this `fibonacci()` is a **pure** function, meaning it has *no* side effects.\n",
"\n",
"**Q2.6**: Execute the following code cell a couple of times to observe that!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "skip"
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"outputs": [],
"source": [
"fibonacci(12, debug=True) # = 13th Fibonacci number -> 11 recursive calls necessary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The runtime of `fibonacci()` is now stable: Ther is no message that \"an intermediate result is being cached\" as in [Chapter 9 <img height=\"12\" style=\"display: inline-block\" src=\"static/link_to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/09_mappings_00_content.ipynb#\"Easy-at-second-Glance\"-Example:-Fibonacci-Numbers--%28revisited%29).\n",
"\n",
"**Q2.7**: Execute the following code cells a couple of times to observe that!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%%timeit -n 1\n",
"fibonacci(99)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%%timeit -n 1\n",
"fibonacci(999)"
]
}
],
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"display_name": "Python 3",
"language": "python",
"name": "python3"
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