From 1b689521c1eaaa2a18cb11c29281630ed7aee8dc Mon Sep 17 00:00:00 2001
From: Bill Ewanick <bill@ewanick.com>
Date: Thu, 14 Sep 2023 15:06:12 -0400
Subject: [PATCH] Finish up Euler 9

---
 src/projectEuler/question9.hs | 71 +++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)

diff --git a/src/projectEuler/question9.hs b/src/projectEuler/question9.hs
index 1b0f549..68e02e1 100644
--- a/src/projectEuler/question9.hs
+++ b/src/projectEuler/question9.hs
@@ -1,3 +1,4 @@
+import           Debug.Trace                            (trace)
 import           Graphics.Rendering.Chart.Backend.Cairo
 import           Graphics.Rendering.Chart.Easy
 {-
@@ -22,13 +23,83 @@ answer :: String
 answer = "I dunno"
 
 
+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
\ No newline at end of file