Published at Jul 13 2018
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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.

You can run all the tests for an exercise by entering

```
$ gradle test
```

in your terminal.

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.

```
import static org.junit.Assert.assertEquals;
import java.util.Collections;
import java.util.List;
import java.util.Arrays;
import org.junit.Before;
import org.junit.Ignore;
import org.junit.Test;
public class BookStoreTest {
// This is sufficient accuracy since we're handling currency values, which should be equal to within 2 decimal places.
private static final double EQUALITY_TOLERANCE = 0.001;
private BookStore bookStore;
@Before
public void setUp() {
bookStore = new BookStore();
}
@Test
public void onlyASingleBook() {
List<Integer> books = Collections.singletonList(1);
assertEquals(8.00, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void twoOfSameBook() {
List<Integer> books = Arrays.asList(2, 2);
assertEquals(16.00, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void emptyBasket() {
List<Integer> books = Collections.emptyList();
assertEquals(0.00, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void twoDifferentBooks() {
List<Integer> books = Arrays.asList(1, 2);
assertEquals(15.20, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void threeDifferentBooks() {
List<Integer> books = Arrays.asList(1, 2, 3);
assertEquals(21.60, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void fourDifferentBooks() {
List<Integer> books = Arrays.asList(1, 2, 3, 4);
assertEquals(25.60, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void fiveDifferentBooks() {
List<Integer> books = Arrays.asList(1, 2, 3, 4, 5);
assertEquals(30.00, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void twoGroupsOfFourIsCheaperThanGroupOfFivePlusGroupOfThree() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 3, 4, 5);
assertEquals(51.20, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void groupOfFourPlusGroupOfTwoIsCheaperThanTwoGroupsOfThree() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 4);
assertEquals(40.80, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void twoEachOfFirst4BooksAnd1CopyEachOfRest() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 3, 4, 4, 5);
assertEquals(55.60, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void twoCopiesOfEachBook() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 3, 4, 4, 5, 5);
assertEquals(60.00, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void threeCopiesOfFirstBookAnd2EachOfRemaining() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1);
assertEquals(68.00, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void threeEachOFirst2BooksAnd2EachOfRemainingBooks() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 2);
assertEquals(75.20, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
@Ignore("Remove to run test")
@Test
public void fourGroupsOfFourAreCheaperThanTwoGroupsEachOfFiveAndThree() {
List<Integer> books = Arrays.asList(1, 1, 2, 2, 3, 3, 4, 5, 1, 1, 2, 2, 3, 3, 4, 5);
assertEquals(102.4, bookStore.calculateBasketCost(books), EQUALITY_TOLERANCE);
}
}
```

```
import java.util.*;
public class BookStore {
static int numTitles = 5;
static double singleCost = 8.00;
static double[] discountedRates = new double[] {
0.0, singleCost, 2*0.95*singleCost, 3*0.90*singleCost, 4*0.80*singleCost, 5*0.75*singleCost
};
double calculateBasketCost(List<Integer> basket) {
if (basket.isEmpty())
return 0.0;
// Calculate greedily the most dense grouping of stacks
List<LinkedList<Integer>> stacks = new LinkedList<>();
OUTER:
for (Integer bookID : basket) {
for (LinkedList<Integer> stack : stacks) {
if (!stack.contains(bookID)) {
stack.add(bookID);
continue OUTER;
}
}
// if above loop completes then a stack wasn't found (empty stacks or bookID in all existing stacks)
LinkedList<Integer> newStack = new LinkedList<>();
newStack.add(bookID);
stacks.add(newStack);
}
double greedyTotal = stacksCost(stacks);
double minimumTotal = greedyTotal;
Collections.sort(stacks, Comparator.comparingInt(List::size));
// try permutations by borrowing from larger groups to smaller groups
// moving from one place to one lower does nothing ex 5,4 borrow one from 5 results in 4,5 so must skip one place
//
// Borrow one, get cost, then revert. This doesn't explore all possibilities but the correct answer
// is approximated by the greedy solution, so this should be good enough.
int start = Math.max(3, stacks.get(0).size()+2);
for (int i=start; i<=numTitles; i++) {
List<LinkedList<Integer>> largeStacks = new LinkedList<>();
List<LinkedList<Integer>> smallStacks = new LinkedList<>();
for (LinkedList<Integer> stack : stacks) {
if (stack.size() == i)
largeStacks.add(stack);
else if (stack.size() == i-2)
smallStacks.add(stack);
if (largeStacks.isEmpty() || smallStacks.isEmpty())
continue;
List<Integer> difference = (LinkedList<Integer>)largeStacks.get(0).clone();
difference.removeAll(smallStacks.get(0));
largeStacks.get(0).remove(difference.get(0));
smallStacks.get(0).add(difference.get(0));
double total = stacksCost(stacks);
if (total < minimumTotal)
minimumTotal = total;
largeStacks.get(0).add(difference.get(0));
smallStacks.get(0).remove(difference.get(0));
}
}
return minimumTotal;
}
double stacksCost(List<LinkedList<Integer>> stacks) {
double total = 0.0;
for (List<Integer> stack : stacks)
total += discountedRates[(stack.size())];
return total;
}
}
```

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?

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