Published at Jan 28 2019
·
2 comments

Instructions

Test suite

Solution

To try and encourage more sales of different books from a popular 5 book series, a bookshop has decided to offer discounts on multiple book purchases.

One copy of any of the five books costs $8.

If, however, you buy two different books, you get a 5% discount on those two books.

If you buy 3 different books, you get a 10% discount.

If you buy 4 different books, you get a 20% discount.

If you buy all 5, you get a 25% discount.

Note: that if you buy four books, of which 3 are different titles, you get a 10% discount on the 3 that form part of a set, but the fourth book still costs $8.

Your mission is to write a piece of code to calculate the price of any conceivable shopping basket (containing only books of the same series), giving as big a discount as possible.

For example, how much does this basket of books cost?

- 2 copies of the first book
- 2 copies of the second book
- 2 copies of the third book
- 1 copy of the fourth book
- 1 copy of the fifth book

One way of grouping these 8 books is:

- 1 group of 5 --> 25% discount (1st,2nd,3rd,4th,5th)
- +1 group of 3 --> 10% discount (1st,2nd,3rd)

This would give a total of:

- 5 books at a 25% discount
- +3 books at a 10% discount

Resulting in:

- 5 x (8 - 2.00) == 5 x 6.00 == $30.00
- +3 x (8 - 0.80) == 3 x 7.20 == $21.60

For a total of $51.60

However, a different way to group these 8 books is:

- 1 group of 4 books --> 20% discount (1st,2nd,3rd,4th)
- +1 group of 4 books --> 20% discount (1st,2nd,3rd,5th)

This would give a total of:

- 4 books at a 20% discount
- +4 books at a 20% discount

Resulting in:

- 4 x (8 - 1.60) == 4 x 6.40 == $25.60
- +4 x (8 - 1.60) == 4 x 6.40 == $25.60

For a total of $51.20

And $51.20 is the price with the biggest discount.

To run the tests, run the command `dotnet test`

from within the exercise directory.

Initially, only the first test will be enabled. This is to encourage you to solve the exercise one step at a time.
Once you get the first test passing, remove the `Skip`

property from the next test and work on getting that test passing.
Once none of the tests are skipped and they are all passing, you can submit your solution
using `exercism submit BookStore.cs`

For more detailed information about the C# track, including how to get help if you're having trouble, please visit the exercism.io C# language page.

Inspired by the harry potter kata from Cyber-Dojo. http://cyber-dojo.org

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
// This file was auto-generated based on version 1.4.0 of the canonical data.
using System;
using Xunit;
public class BookStoreTest
{
[Fact]
public void Only_a_single_book()
{
var basket = new[] { 1 };
Assert.Equal(8m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Two_of_the_same_book()
{
var basket = new[] { 2, 2 };
Assert.Equal(16m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Empty_basket()
{
var basket = Array.Empty<int>();
Assert.Equal(0m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Two_different_books()
{
var basket = new[] { 1, 2 };
Assert.Equal(15.2m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Three_different_books()
{
var basket = new[] { 1, 2, 3 };
Assert.Equal(21.6m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Four_different_books()
{
var basket = new[] { 1, 2, 3, 4 };
Assert.Equal(25.6m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Five_different_books()
{
var basket = new[] { 1, 2, 3, 4, 5 };
Assert.Equal(30m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Two_groups_of_four_is_cheaper_than_group_of_five_plus_group_of_three()
{
var basket = new[] { 1, 1, 2, 2, 3, 3, 4, 5 };
Assert.Equal(51.2m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Two_groups_of_four_is_cheaper_than_groups_of_five_and_three()
{
var basket = new[] { 1, 1, 2, 3, 4, 4, 5, 5 };
Assert.Equal(51.2m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Group_of_four_plus_group_of_two_is_cheaper_than_two_groups_of_three()
{
var basket = new[] { 1, 1, 2, 2, 3, 4 };
Assert.Equal(40.8m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Two_each_of_first_4_books_and_1_copy_each_of_rest()
{
var basket = new[] { 1, 1, 2, 2, 3, 3, 4, 4, 5 };
Assert.Equal(55.6m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Two_copies_of_each_book()
{
var basket = new[] { 1, 1, 2, 2, 3, 3, 4, 4, 5, 5 };
Assert.Equal(60m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Three_copies_of_first_book_and_2_each_of_remaining()
{
var basket = new[] { 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1 };
Assert.Equal(68m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Three_each_of_first_2_books_and_2_each_of_remaining_books()
{
var basket = new[] { 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 2 };
Assert.Equal(75.2m, BookStore.Total(basket));
}
[Fact(Skip = "Remove to run test")]
public void Four_groups_of_four_are_cheaper_than_two_groups_each_of_five_and_three()
{
var basket = new[] { 1, 1, 2, 2, 3, 3, 4, 5, 1, 1, 2, 2, 3, 3, 4, 5 };
Assert.Equal(102.4m, BookStore.Total(basket));
}
}
```

```
using System;
using System.Collections.Generic;
using System.Linq;
public static class BookStore
{
private static readonly decimal[] Discounts = new[] { 1m, 0.95m, 0.90m, 0.80m, 0.75m };
private static readonly decimal BasicPrice = 8;
private static decimal GroupPrice(int groupSize) => groupSize * BasicPrice * Discounts[groupSize - 1];
public static decimal Total(IEnumerable<int> books)
{
books = books.GroupBy(i => i).OrderByDescending(g => g.Count()).SelectMany(g => g);
return BasketTotal(books, 0);
}
private static decimal BasketTotal(IEnumerable<int> books, decimal cumulativePrice)
{
if (!books.Any())
return cumulativePrice;
var groups = books.Distinct();
var cheapestPrice = Decimal.MaxValue;
for (int i = 0; i < groups.Count(); i++)
{
var currentGroups = groups.Take(i + 1);
var currentBooks = new List<int>(books);
foreach (var book in currentGroups)
{
currentBooks.Remove(book);
}
var groupPrice = GroupPrice(i + 1);
var currentPrice = BasketTotal(currentBooks, cumulativePrice + groupPrice);
if (currentPrice < cheapestPrice)
cheapestPrice = currentPrice;
}
return cheapestPrice;
}
}
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

## Community comments

Wow, unbelievably good. Would love to see commentary on lines 14, 28.. mind melting.

Thanks!

Line 14: Book list is ordered by book counts. For example the list 1, 1, 2, 3, 4, 4, 5, 5 is ordered to 1, 1, 4, 4, 5, 5, 2, 3

Line 28: Goes through all available group sizes. The list from line 14 is originally 1, 1, 4, 4, 5, 5, 2, 3. First iteration of line 28 reduces this list to 1, 4, 4, 5, 5, 2, 3 which is then later passed on recursively. Second iteration reduces the list to 1, 4, 5, 5, 2, 3. Third iteration reduces it to 1, 4, 5, 2, 3 and so on. The sorting on line 14 is done so this trick would work. If the list is not sorted by counts then we won't get the correct results. As per the example the cheapest way to group the basket 1, 1, 2, 3, 4, 4, 5, 5 is 2 groups of 4. But if the list is not sorted we would get this: