412 lines
11 KiB
Text
412 lines
11 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"# Chapter 5: Bits & Numbers"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Coding Exercises"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Read [Chapter 5](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/05_numbers_00_lecture.ipynb) of the book. Then, work through the exercises below. The `...` indicate where you need to fill in your answers. You should not need to create any additional code cells."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Discounting Customer Orders (revisited)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The \"*Volume of a Sphere*\" problem in [Chapter 2's Exercises](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/02_functions_02_exercises.ipynb#Volume-of-a-Sphere) section revealed that we must consider the effects of the `float` type's imprecision.\n",
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"\n",
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"This becomes even more important when we deal with numeric data modeling accounting or finance data (cf., [this comment](https://stackoverflow.com/a/24976426) on \"falsehoods programmers believe about money\").\n",
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"\n",
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"In addition to the *inherent imprecision* of numbers in general, the topic of **[rounding numbers](https://en.wikipedia.org/wiki/Rounding)** is also not as trivial as we might expect! [This article](https://realpython.com/python-rounding/) summarizes everything the data science practitioner needs to know.\n",
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"\n",
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"In this exercise, we revisit the \"*Discounting Customer Orders*\" problem from [Chapter 3's Exercises](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/03_conditionals_02_exercises.ipynb#Discounting-Customer-Orders) section and make the `discounted_price()` function work *correctly* for real-life sales data."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q1**: Execute the code cells below! What results would you have *expected*, and why?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"round(1.5)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"round(2.5)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"round(2.675, 2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q2**: The built-in [round()](https://docs.python.org/3/library/functions.html#round) function implements the \"**[round half to even](https://en.wikipedia.org/wiki/Rounding#Round_half_to_even)**\" strategy. Describe in one or two sentences what that means!"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q3**: For the revised `discounted_price()` function, we have to tackle *two* issues: First, we have to replace the built-in `float` type with a data type that allows us to control the precision. Second, the discounted price should be rounded according to a more human-friendly rounding strategy, namely \"**[round half away from zero](https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero)**.\"\n",
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"\n",
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"Describe in one or two sentences how \"**[round half away from zero](https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero)**\" is more in line with how humans think of rounding!"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q4**: We use the `Decimal` type from the [decimal](https://docs.python.org/3/library/decimal.html) module in the [standard library](https://docs.python.org/3/library/index.html) to tackle *both* issues simultaneously.\n",
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"\n",
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"Assign `euro` a numeric object such that both `Decimal(\"1.5\")` and `Decimal(\"2.5\")` are rounded to `Decimal(\"2\")` (i.e., no decimal) with the [quantize()](https://docs.python.org/3/library/decimal.html#decimal.Decimal.quantize) method!"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from decimal import Decimal"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"euro = ..."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"Decimal(\"1.5\").quantize(...)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"Decimal(\"2.5\").quantize(...)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q5**: Obviously, the two preceding code cells still [round half to even](https://en.wikipedia.org/wiki/Rounding#Round_half_to_even).\n",
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"\n",
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"The [decimal](https://docs.python.org/3/library/decimal.html) module defines a `ROUND_HALF_UP` flag that we can pass as the second argument to the [quantize()](https://docs.python.org/3/library/decimal.html#decimal.Decimal.quantize) method. Then, it [rounds half away from zero](https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero).\n",
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"\n",
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"Add `ROUND_HALF_UP` to the code cells! `Decimal(\"2.5\")` should now be rounded to `Decimal(\"3\")`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from decimal import ROUND_HALF_UP"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"Decimal(\"1.5\").quantize(...)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"Decimal(\"2.5\").quantize(...)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q6**: Instead of `euro`, define `cents` such that rounding occurs to *two* decimals! `Decimal(\"2.675\")` should now be rounded to `Decimal(\"2.68\")`. Do *not* forget to include the `ROUND_HALF_UP` flag!"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"cents = ..."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"Decimal(\"2.675\").quantize(...)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q7**: Rewrite the function `discounted_price()` from [Chapter 3's Exercises](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/03_conditionals_02_exercises.ipynb#Discounting-Customer-Orders) section!\n",
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"\n",
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"It takes the *positional* arguments `unit_price` and `quantity` and implements a discount scheme for a line item in a customer order as follows:\n",
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"\n",
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"- if the unit price is over 100 dollars, grant 10% relative discount\n",
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"- if a customer orders more than 10 items, one in every five items is for free\n",
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"\n",
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"Only one of the two discounts is granted, whichever is better for the customer.\n",
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"\n",
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"The function then returns the overall price for the line item as a `Decimal` number with a precision of *two* decimals.\n",
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"\n",
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"Enable **duck typing** by allowing the function to be called with various numeric types as the arguments, in particular, `quantity` may be a non-integer as well: Use an appropriate **abstract base class** from the [numbers](https://docs.python.org/3/library/numbers.html) module in the [standard library](https://docs.python.org/3/library/index.html) to verify the arguments' types and also that they are both positive!\n",
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"\n",
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"It is considered a *best practice* to only round towards the *end* of the calculations."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numbers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def discounted_price(...):\n",
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" ..."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q8**: Execute the code cells below and verify the final price for the following four test cases:\n",
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"\n",
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"- $7$ smartphones @ $99.00$ USD\n",
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"- $3$ workstations @ $999.00$ USD\n",
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"- $19$ GPUs @ $879.95$ USD\n",
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"- $14$ Raspberry Pis @ $35.00$ USD\n",
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"\n",
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"The output should now *always* be a `Decimal` number with *two* decimals!"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(99, 7)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(999, 3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(879.95, 19)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(35, 14)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This also works if `quantity` is passed in as a `float` type."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(99, 7.0)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Decimals beyond the first two are gracefully discarded (i.e., *without* rounding errors accumulating)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(99.0001, 7)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The basic input validation ensures that the user of `discounted_price()` does not pass in invalid data. Here, the `\"abc\"` creates a `TypeError`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(\"abc\", 7)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"A `-1` passed in as `unit_price` results in a `ValueError`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"discounted_price(-1, 7)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.4"
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},
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"toc": {
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"base_numbering": 1,
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"nav_menu": {},
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"number_sections": false,
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"sideBar": true,
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"skip_h1_title": true,
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"title_cell": "Table of Contents",
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"title_sidebar": "Contents",
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"toc_cell": false,
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"toc_position": {},
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"toc_section_display": false,
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"toc_window_display": false
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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