import           Debug.Trace                            (trace)
import           Graphics.Rendering.Chart.Backend.Cairo
import           Graphics.Rendering.Chart.Easy
{-
Special Pythagorean Triplet
Problem 9

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 `abc`.
-}

main :: IO ()
main = do
  print answer
  print (product answer)

-- head $ [(a,b,c) | a <- [1..limit], b <- [a+1..limit], c <- [limit - a - b], a < b, b < c, a^2 + b^2 == c^2]
answer :: [Integer]
answer = head $
  [ [a, b, c] |
    a <- [1 .. limit],
    b <- [a + 1 .. limit],
    c <- [limit - a - b],
    b < c,
    a ^ 2 + b ^ 2 == c ^ 2]
  where limit = 1000

limit = 1000
version1 =   [ [a, b, c] |
    a <- [1 .. limit],
    b <- [a + 1 .. limit],
    c <- [limit - a - b],
    b < c,
    a ^ 2 + b ^ 2 == c ^ 2]

version2 =   [ [a, b, c] |
    a <- [1 .. limit],
    b <- [a + 1 .. limit],
    c <- [limit - a - b],
    b < c,
    a ^ 2 + b ^ 2 == c ^ 2]


solve :: Integer -> [(Integer, Integer, Integer)]
solve x = takeWhile (\(a,b,c) -> a + b + c == 1000) $ primitiveTriplesUnder x

euclid'sFormula :: Num c => (c, c) -> (c, c, c)
euclid'sFormula (m, n) = (a,b,c)
  where
    a = m^2 - n^2
    b = 2*m*n
    c = m^2 + n^2

listOfMNs :: Integer -> [(Integer, Integer)]
listOfMNs x =
  [ (m,n)
      | n <- [2,4..x]     -- one of them is even
      , m <- [n+1,n+3..x]
      , gcd m n == 1      -- coprime
  ]

listOfMNs' :: Integer -> [(Integer, Integer)]
listOfMNs' x =
  [ (m,n)
      | n <- [2,4..]     -- one of them is even
      , m <- [n+1,n+3..]
      , gcd m n == 1     -- coprime
      , a m n + b m n + c m n <= x
  ] where
      a m n = m^2 - n^2
      b m n = 2*m*n
      c m n = m^2 + n^2


primitiveTriplesUnder :: Integer -> [(Integer, Integer, Integer)]
primitiveTriplesUnder = map euclid'sFormula . listOfMNs


test :: [(Integer, Integer, Integer)]
test = [ (a,b,c)
          | a <- [3..],
            b <- take 10 [a+1..],
            c <- takeWhile (\c -> a^2 + b^2 <= c^2) [b+1..]
       ]

ls :: [(Integer, Integer)]
ls = filter (\(m,n) -> gcd m n == 1) $ zip [5,9..] [2,4..]

diags :: Integer -> [(Integer, Integer)]
diags n = [(x,y) | x<-[0..n], y<-[0..n]]


graph :: IO ()
graph = toFile def "test.png" $ do
    layout_title .= "Points"
    plot (line "points" [ [ (x,y) | (x,y) <- listOfMNs 30] ])


-- main'' = print ans'
ans' :: Integer -> [(Integer, Integer, Integer)]
ans' limit = [(a, b, c)
              | a <- [1 .. limit]
              , b <- [a + 1 .. limit]
              , c <- [limit - a - b]
              , b < c
             ]

{-
 - Solution to Project Euler problem 9
 - Copyright (c) Project Nayuki. All rights reserved.
 -
 - https://www.nayuki.io/page/project-euler-solutions
 - https://github.com/nayuki/Project-Euler-solutions
 -}


-- -- Computers are fast, so we can implement a brute-force search to directly solve the problem.
-- perim = 1000
-- main = putStrLn (show ans)
-- ans = head [a * b * (perim - a - b) | a <- [1..perim], b <- [a+1..perim], isIntegerRightTriangle a b]
-- isIntegerRightTriangle a b = a < b && b < c
-- 	&& a * a + b * b == c * c
-- 	where c = perim - a - b