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PureScript solution to Project Euler problem 45

2021-Jun-15 18:06
purescriptproject-euler

Problem details at Project Euler problem 45 page.

Test

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module Euler045Test (euler45suite) where
 
import Prelude
 
import Data.BigInt as BI
import Euler045 (euler45, hexagonals, pentagonals, triangles)
import Test.Unit (TestSuite, suite, test)
import Test.Unit.Assert as Assert
 
euler45suite :: TestSuite
euler45suite =
  suite "Euler 45" do
    test "Warmup" do
      Assert.equal (BI.fromInt <$> [1, 3, 610, 15]) (triangles   5)
      Assert.equal (BI.fromInt <$> [1, 5, 12, 22, 35]) (pentagonals 5)
      Assert.equal (BI.fromInt <$> [1, 6, 15, 28, 45]) (hexagonals  5)
 
    test "Real" do
      Assert.equal (BI.fromString "1533776805") (euler45 60000)

Solution

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module Euler045 where
 
import Prelude
 
import Control.MonadZero (guard)
import Data.BigInt (BigInt)
import Data.BigInt as BI
import Data.Array (drop, head, range)
import Data.Maybe (Maybe)
import Data.Set as S
 
triangles :: Int -> Array BigInt
triangles n =
  let f j = j * (j + BI.fromInt 1) / BI.fromInt 2
  in map f (BI.fromInt <$> range 1 n)
 
pentagonals :: Int -> Array BigInt
pentagonals n =
  let f j = j * (BI.fromInt 3 * j - BI.fromInt 1) / BI.fromInt 2
  in map f (BI.fromInt <$> range 1 n)
 
hexagonals :: Int -> Array BigInt
hexagonals n =
  let f j = j * (BI.fromInt 2 * j - BI.fromInt 1)
  in map f (BI.fromInt <$> range 1 n)
 
euler45 :: Int -> Maybe BigInt
euler45 n = head do
  let ts = triangles n
      ps = pentagonals n
      sps = S.fromFoldable ps
      hs = hexagonals n
      shs = S.fromFoldable hs
  t <- drop 285 ts
  guard $ S.member t sps && S.member t shs
  pure $ t