Published at May 06 2019
·
0 comments

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
```

and such that,

```
a < b < c
```

For example,

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

Given an input integer N, find all Pythagorean triplets for which `a + b + c = N`

.

For example, with N = 1000, there is exactly one Pythagorean triplet for which `a + b + c = 1000`

: `{200, 375, 425}`

.

To run the tests, run the command `busted`

from within the exercise directory.

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

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.

```
local triplets_with_sum = require('pythagorean-triplet')
describe('pythagorean-triplet', function()
local function sort(triplets)
table.sort(triplets, function(a, b) return a[1] < b[1] end)
return triplets
end
describe('triplets_with_sum', function()
it('finds triplets whose sum is 12', function()
assert.same(
{ { 3, 4, 5 } },
sort(triplets_with_sum(12))
)
end)
it('finds triplets whose sum is 108', function()
assert.same(
{ { 27, 36, 45 } },
sort(triplets_with_sum(108))
)
end)
it('finds triplets whose sum is 1000', function()
assert.same(
{ { 200, 375, 425 } },
sort(triplets_with_sum(1000))
)
end)
it('finds no triplets whose sum is 1001', function()
assert.same({}, triplets_with_sum(1001))
end)
it('finds triplets whose sum is 90', function()
assert.same(
{
{ 9, 40, 41 },
{ 15, 36, 39 },
},
sort(triplets_with_sum(90))
)
end)
it('finds triplets whose sum is 840', function()
assert.same(
{
{ 40, 399, 401 },
{ 56, 390, 394 },
{ 105, 360, 375 },
{ 120, 350, 370 },
{ 140, 336, 364 },
{ 168, 315, 357 },
{ 210, 280, 350 },
{ 240, 252, 348 },
},
sort(triplets_with_sum(840))
)
end)
it('finds triplets whose sum is a large number (30000)', function()
assert.same(
{
{ 1200, 14375, 14425 },
{ 1875, 14000, 14125 },
{ 5000, 12000, 13000 },
{ 6000, 11250, 12750 },
{ 7500, 10000, 12500 },
},
sort(triplets_with_sum(30000))
)
end)
end)
end)
```

```
return function(n)
local a
local b
local c
local triplets = {}
for a = 1, n / 2 - 1 do -- VI
for b = a, n - a do -- II
c = n - a - b -- III
if a * a + b * b == c * c then
table.insert(triplets, {a, b, c})
end
end
end
return triplets
end
-- Reducing the size of the problem:
-- I a * a + b * b = c * c
-- II a + b + c = n
-- => III c = n - a - b
-- IV A triple where a == b is accepted, but
-- a + b is the same as b + a, so we can
-- => V skip all triplets where a < b.
-- Also, from I follows c > b + a, so we can use:
-- => VI a = 1 .. n / 2 - 1
-- Fun fact: using x * x the test takes 11s, with x^2 it takes 17s for me.
```

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?

Level up your programming skills with 3,385 exercises across 50 languages, and insightful discussion with our volunteer team of welcoming mentors.
Exercism is
**100% free forever**.

## Community comments