From 8f5004d6ff65bd78ee745cd70fe52cb9ec50cf65 Mon Sep 17 00:00:00 2001
From: Bill Ewanick <bill@ewanick.com>
Date: Fri, 15 Sep 2023 02:47:36 -0400
Subject: [PATCH] Performance improvements with math

---
 src/projectEuler/question12.hs | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 src/projectEuler/question12.hs

diff --git a/src/projectEuler/question12.hs b/src/projectEuler/question12.hs
new file mode 100644
index 0000000..afe1a00
--- /dev/null
+++ b/src/projectEuler/question12.hs
@@ -0,0 +1,32 @@
+-- module Main where
+import           Data.IntSet                           (size)
+import           Data.List                             (unfoldr)
+import           Math.NumberTheory.ArithmeticFunctions (divisorsSmall)
+
+main :: IO ()
+main = print ans
+
+-- triangleNumber :: Integer -> [Integer]
+-- triangleNumber 1 = [1]
+-- triangleNumber n = sum [1..n] : triangleNumber (n-1)
+triangleNumber i = (i * (i + 1)) `div` 2
+triangleNumbers = map triangleNumber [1..]
+-- triangleNumbers :: [Int]
+-- triangleNumbers = unfoldr (\b-> Just (sum [1..b],b+1)) 1
+
+-- isDivisible a b = a `rem` b == 0
+-- divisors n = filter (isDivisible n) [1..(floor . sqrt) n ]
+
+-- Triangle Numbers With More than N divisors
+tnwmtNd :: Int -> [Int]
+tnwmtNd n = filter ((>= n) . size . divisorsSmall) triangleNumbers
+
+ans :: Int
+ans = head $ tnwmtNd 500
+{-
+λ> main
+76576500
+(0.00 secs, 114,944 bytes)
+
+First triangle number to have over 500 divisors is 76576500
+-}