From de4106efe7cebe84b804aeebd2f9dc6b201f9b5d Mon Sep 17 00:00:00 2001
From: Daniele Fucini <dfucini@gmail.com>
Date: Sat, 23 Nov 2024 17:46:34 +0100
Subject: [PATCH] Improve Haskell solution for Problem 10 using prime sieve

---
 Haskell/ProjectEuler.hs | 5 +++++
 Haskell/p010.hs         | 7 ++-----
 2 files changed, 7 insertions(+), 5 deletions(-)

diff --git a/Haskell/ProjectEuler.hs b/Haskell/ProjectEuler.hs
index b4b6b39..e0da29d 100644
--- a/Haskell/ProjectEuler.hs
+++ b/Haskell/ProjectEuler.hs
@@ -1,5 +1,6 @@
 module ProjectEuler
 ( isPrime
+, primeSieve
 , lcmm
 , digitSum
 , sumProperDivisors
@@ -9,6 +10,7 @@ module ProjectEuler
 
 import Data.Char (digitToInt)
 import Data.List (nub)
+import Data.List.Ordered (minus, unionAll)
 
 isPrime :: (Integral n) => n -> Bool
 isPrime 1 = False
@@ -19,6 +21,9 @@ isPrime n =
     where candidates = [5,11..limit]
           limit = floor(sqrt(fromIntegral n)) + 1
 
+primeSieve :: (Integral n) => [n]
+primeSieve = 2:3:[5,7..] `minus` unionAll [[p*p, p*p+2*p..] | p <- tail primeSieve]
+
 lcmm :: (Integral n) => [n] -> n
 lcmm values
     | length values == 2    = lcm (head values) (last values)
diff --git a/Haskell/p010.hs b/Haskell/p010.hs
index d8bc5fd..e4d02c2 100644
--- a/Haskell/p010.hs
+++ b/Haskell/p010.hs
@@ -2,12 +2,9 @@
 --
 -- Find the sum of all the primes below two million.
 
-import ProjectEuler (isPrime)
-
-sumPrimes :: Int -> Int
-sumPrimes n = sum [ x | x <- [1..n], isPrime x ]
+import ProjectEuler (primeSieve)
 
 main = do
-    let result = sumPrimes 2000000
+    let result = sum $ takeWhile (<2000000) primeSieve
     putStrLn $ "Project Euler, Problem 10\n"
         ++ "Answer: " ++ show result