 # JaeHyoLee's solution

## to Pythagorean Triplet in the Lua Track

Published at Jul 13 2018 · 1 comment
Instructions
Test suite
Solution

#### Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

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.

## Running the tests

To run the tests, run the command `busted` from within the exercise directory.

## Further information

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.

## Source

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

## Submitting Incomplete Solutions

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

### pythagorean-triplet_spec.lua

``````local pythagorean = require('pythagorean-triplet')

describe('pythagorean-triplet', function()
local function sort(triplets)
table.sort(triplets, function(a, b) return a < b end)
return triplets
end

describe('is_triplet', function()
it('should identify triplets', function()
assert.is_true(pythagorean.is_triplet(3, 4, 5))
assert.is_true(pythagorean.is_triplet(5, 12, 13))
end)

it('should identify non-triplets', function()
assert.is_false(pythagorean.is_triplet(3, 4, 6))
assert.is_false(pythagorean.is_triplet(5, 6, 17))
end)
end)

describe('triplets_with', function()
it('should generate all triplets with a specified maximum factor', function()
assert.same(
{ { 3, 4, 5 },  { 5, 12, 13 }, { 6, 8, 10 }, { 8, 15, 17}, { 9, 12, 15 } },
sort(pythagorean.triplets_with{ max_factor = 17 })
)
end)

it('should generate all triplets with a specified minimum and maximum factor', function()
assert.same(
{ { 6, 8, 10 }, { 9, 12, 15 } },
sort(pythagorean.triplets_with{ min_factor = 6, max_factor = 15 })
)
end)

it('should generate all triplets with a specified maximum factor and a specified sum', function()
assert.same(
{ { 18, 80, 82 }, { 30, 72, 78 }, { 45, 60, 75 } },
sort(pythagorean.triplets_with{ sum = 180, max_factor = 100 })
)
end)
end)
end)``````
``````local function is_triplet(a, b, c)
return a^2 + b^2 == c^2
end

local function is_natural_number(n)
return n==math.floor(n) and n > 0
end

local function triplets_with(constraints)
local min = constraints.min_factor or 3
local max = constraints.max_factor or assert(fail,"max_factor is mandatory")
local result = {}
for a = min, max do
for b = a + 1, max do
local c = math.sqrt(a^2 + b^2)
if (is_natural_number(c) and c <= max and (a+b+c) == (constraints.sum or a+b+c)) then table.insert(result, {a, b, c}) end
end
end
return result
end

return {
is_triplet = is_triplet,
triplets_with = triplets_with
}`````` 