Published at May 25 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
```

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)
```

```
local sqrt = math.sqrt
local triplets_with_sum = {}
local mt = {__call = function(_, sum)
local half = sum // 2
local third = sum // 3
local candidates = {}
local triplets = {}
for i = 1, third-1 do
for j = i+1, half-1 do
local sum_ij = i+j
for k = j+1, half do
if sum_ij + k == sum then
candidates[#candidates + 1] = { i, j, k, }
end
end
end
end
for _,candidate in ipairs(candidates) do
if candidate[1]^2 + candidate[2]^2 == candidate[3]^2 then
triplets[#triplets + 1] = candidate
end
end
return triplets
end}
mt.__index = index
return setmetatable(triplets_with_sum, mt)
```

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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