Published at Apr 23 2019
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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.

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
`raise Exception`

, you should write:

```
raise Exception("Meaningful message indicating the source of the error")
```

To run the tests, run the appropriate command below (why they are different):

- Python 2.7:
`py.test book_store_test.py`

- Python 3.4+:
`pytest book_store_test.py`

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
`python -m pytest book_store_test.py`

`pytest`

options-
`-v`

: enable verbose output -
`-x`

: stop running tests on first failure -
`--ff`

: run failures from previous test before running other test cases

For other options, see `python -m pytest -h`

Note that, when trying to submit an exercise, make sure the solution is in the `$EXERCISM_WORKSPACE/python/book-store`

directory.

You can find your Exercism workspace by running `exercism debug`

and looking for the line that starts with `Workspace`

.

For more detailed information about running tests, code style and linting, please see Running the Tests.

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 unittest
from book_store import calculate_total
# Tests adapted from `problem-specifications//canonical-data.json` @ v1.4.0
class BookStoreTest(unittest.TestCase):
def test_only_a_single_book(self):
self.assertEqual(calculate_total([1]), 800)
def test_two_of_the_same_book(self):
self.assertEqual(calculate_total([2, 2]), 1600)
def test_empty_basket(self):
self.assertEqual(calculate_total([]), 0)
def test_two_different_books(self):
self.assertEqual(calculate_total([1, 2]), 1520)
def test_three_different_books(self):
self.assertEqual(calculate_total([1, 2, 3]), 2160)
def test_four_different_books(self):
self.assertEqual(calculate_total([1, 2, 3, 4]), 2560)
def test_five_different_books(self):
self.assertEqual(calculate_total([1, 2, 3, 4, 5]), 3000)
def test_two_groups_of_4_is_cheaper_than_group_of_5_plus_group_of_3(self):
self.assertEqual(calculate_total([1, 1, 2, 2, 3, 3, 4, 5]), 5120)
def test_two_groups_of_4_is_cheaper_than_groups_of_5_and_3(self):
self.assertEqual(calculate_total([1, 1, 2, 3, 4, 4, 5, 5]), 5120)
def test_group_of_4_plus_group_of_2_is_cheaper_than_2_groups_of_3(self):
self.assertEqual(calculate_total([1, 1, 2, 2, 3, 4]), 4080)
def test_two_each_of_first_4_books_and_1_copy_each_of_rest(self):
self.assertEqual(calculate_total([1, 1, 2, 2, 3, 3, 4, 4, 5]), 5560)
def test_two_copies_of_each_book(self):
self.assertEqual(calculate_total([1, 1, 2, 2, 3, 3, 4, 4, 5, 5]), 6000)
def test_three_copies_of_first_book_and_2_each_of_remaining(self):
self.assertEqual(
calculate_total([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1]), 6800)
def test_three_each_of_first_2_books_and_2_each_of_remaining_books(self):
self.assertEqual(
calculate_total([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 2]), 7520)
def test_four_groups_of_4_are_cheaper_than_2_groups_each_of_5_and_3(self):
self.assertEqual(
calculate_total([1, 1, 2, 2, 3, 3, 4, 5, 1, 1, 2, 2, 3, 3, 4, 5]),
10240)
if __name__ == '__main__':
unittest.main()
```

```
from collections import Counter
DISCOUNTS = {2: 5, 3: 10, 4: 20, 5: 25}
SET_PRICES = { n : 8 * n * (100 - DISCOUNTS.get(n, 0)) for n in range(1, 5 + 1) }
def calculate_total(books):
return CachedTotalCalculator(books).total
class CachedTotalCalculator:
def __init__(self, books):
self._cache = {}
self.total = self._calculate(Counter(books))
def _calculate(self, counts):
cache_key = ':'.join(str(count) for count in sorted(counts.values()))
if cache_key in self._cache:
return self._cache[cache_key]
else:
return self._cache.setdefault(cache_key, self._uncached(counts))
def _uncached(self, counts):
if not counts:
return 0
if len(counts) == 1:
return SET_PRICES[1] * sum(counts.values())
def possible_first_groups():
for size in range(len(counts), 0, -1):
yield [book for book, _ in counts.most_common(size)]
min_total = None
for group in possible_first_groups():
left = counts - Counter(group)
total = SET_PRICES[len(group)] + self._calculate(left)
if min_total is None or total < min_total:
min_total = total
return min_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?

## Community comments