Published at Jan 05 2019
·
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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.

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(sum)
local function from_a(x)
-- Given that:
-- (1) a + b + c = p
-- (2) a ^ 2 + b ^ 2 = c ^ 2
-- (2) c = sqrt(a ^ 2 + b ^ 2)
--
-- (2) -> (1) a + b + sqrt(a ^ 2 + b ^ 2) = p
--
-- Rearranging we get:
-- b = 0.5 * (p - (pa / (p - a)))
return (sum - sum * x / (sum - x)) / 2
end
local triplets = {}
for a=1, sum do
local b = from_a(a)
if a > b then
break
end
local frac
b, frac = math.modf(b)
if frac == 0.0 then
-- Mathematically from_a might yield non-natural numbers which are then
-- truncated by integer division, so here we filter only for integer
-- triplets.
table.insert(triplets, { a, b, sum - (a + b) })
end
end
return triplets
end
```

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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