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Published at Jul 13 2018
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Instructions

Test suite

Solution

A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,

```
a**2 + b**2 = c**2
```

For example,

```
3**2 + 4**2 = 9 + 16 = 25 = 5**2.
```

There exists exactly one Pythagorean triplet for which a + b + c = 1000.

Find the product a * b * c.

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 pythagorean_triplet_test.py`

- Python 3.4+:
`pytest pythagorean_triplet_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 pythagorean_triplet_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/pythagorean-triplet`

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.

Problem 9 at Project Euler http://projecteuler.net/problem=9

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

```
import unittest
from pythagorean_triplet import triplets_with_sum
# Tests adapted from `problem-specifications//canonical-data.json` @ v1.0.0
class PythagoreanTripletTest(unittest.TestCase):
def test_triplets_sum_12(self):
expected = set([(3, 4, 5)])
self.assertEqual(triplets_with_sum(12), expected)
def test_triplets_sum_108(self):
expected = set([(27, 36, 45)])
self.assertEqual(triplets_with_sum(108), expected)
def test_triplets_sum_1000(self):
expected = set([(200, 375, 425)])
self.assertEqual(triplets_with_sum(1000), expected)
def test_no_triplet_exists(self):
expected = set([])
self.assertEqual(triplets_with_sum(1001), expected)
def test_two_matching_triplets(self):
expected = set([(9, 40, 41), (15, 36, 39)])
self.assertEqual(triplets_with_sum(90), expected)
def test_several_matching_triplets(self):
expected = set([(40, 399, 401),
(56, 390, 394),
(105, 360, 375),
(120, 350, 370),
(140, 336, 364),
(168, 315, 357),
(210, 280, 350),
(240, 252, 348)])
self.assertEqual(triplets_with_sum(840), expected)
def test_triplets_for_large_numbers(self):
expected = set([(1200, 14375, 14425),
(1875, 14000, 14125),
(5000, 12000, 13000),
(6000, 11250, 12750),
(7500, 10000, 12500)])
self.assertEqual(triplets_with_sum(30000), expected)
if __name__ == '__main__':
unittest.main()
```

```
from math import ceil, gcd, sqrt
def triplets_in_range(range_start, range_end):
for limit in range(range_start, range_end, 4):
for x, y, z in primitive_triplets(limit):
a, b, c = (x, y, z)
# yield multiples of primitive triplet
while a < range_start:
a, b, c = (a + x, b + y, c + z)
while c < range_end:
yield (a, b, c)
a, b, c = (a + x, b + y, c + z)
def euclidian_coprimes(limit):
"""See Euclidean algorithm
https://en.wikipedia.org/wiki/Euclidean_algorithm#Description
"""
mn = limit // 2
for n in range(1, int(ceil(sqrt(mn)))):
if mn % n == 0:
m = mn // n
if (m - n) % 2 == 1 and gcd(m, n) == 1:
yield m, n
def primitive_triplets(limit):
"""See Euclid's formula
https://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple
"""
for m, n in euclidian_coprimes(limit):
a = m ** 2 - n ** 2
b = 2 * m * n
c = m ** 2 + n ** 2
yield sorted([a, b, c])
def triplets_with_sum(triplet_sum):
return {
triplet
for triplet in triplets_in_range(1, triplet_sum // 2)
if sum(triplet) == triplet_sum
}
```

A huge amount can be learned from reading other peopleโs 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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