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to Pythagorean Triplet in the Lua Track

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}.

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 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.

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