From aad8467fb9da1ed56e393376ee693dc09d83f6ad Mon Sep 17 00:00:00 2001
From: Daniele Fucini <dfucini@gmail.com>
Date: Fri, 29 Mar 2024 11:50:11 +0100
Subject: [PATCH] Add Haskell solutions for Problems 1, 2, 3

---
 Haskell/p001.hs | 12 ++++++++++++
 Haskell/p002.hs | 18 ++++++++++++++++++
 Haskell/p003.hs | 23 +++++++++++++++++++++++
 3 files changed, 53 insertions(+)
 create mode 100644 Haskell/p001.hs
 create mode 100644 Haskell/p002.hs
 create mode 100644 Haskell/p003.hs

diff --git a/Haskell/p001.hs b/Haskell/p001.hs
new file mode 100644
index 0000000..ecad635
--- /dev/null
+++ b/Haskell/p001.hs
@@ -0,0 +1,12 @@
+-- If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
+--
+-- Find the sum of all the multiples of 3 or 5 below 1000.
+sumMultiples :: (Integral n) => n
+sumMultiples = sum(filter p [ n | n <- [1..999] ])
+                where p n = n `mod` 3 == 0 || n `mod` 5 == 0
+
+main :: IO ()
+main =  do
+    let result = sumMultiples
+    putStrLn $ "Project Euler, Problem 1\n"
+        ++ "Answer: " ++ (show result)
diff --git a/Haskell/p002.hs b/Haskell/p002.hs
new file mode 100644
index 0000000..4c48568
--- /dev/null
+++ b/Haskell/p002.hs
@@ -0,0 +1,18 @@
+-- Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
+--
+-- 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
+--
+-- By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
+fib :: (Integral n) => n -> n
+fib 0 = 0
+fib 1 = 1
+fib n = fib (n-1) + fib(n-2)
+
+sumEvenFib :: (Integral n) => n
+sumEvenFib = sum $ filter even $ takeWhile (<=4000000) (map fib [0..])
+
+main :: IO ()
+main =  do
+    let result = sumEvenFib
+    putStrLn $ "Project Euler, Problem 2\n"
+        ++ "Answer: " ++ (show result)
diff --git a/Haskell/p003.hs b/Haskell/p003.hs
new file mode 100644
index 0000000..1abb4e6
--- /dev/null
+++ b/Haskell/p003.hs
@@ -0,0 +1,23 @@
+-- The prime factors of 13195 are 5, 7, 13 and 29.  --
+-- What is the largest prime factor of the number 600851475143?
+
+isPrime :: (Integral n) => n -> Bool
+isPrime 1 = False
+isPrime 2 = True
+isPrime 3 = True
+isPrime n =
+    n `mod` 2 /= 0 && n `mod` 3 /= 0 && null [ x | x <- candidates, n `mod` x == 0 || n `mod` (x+2) == 0 ]
+    where candidates = [5,11..limit]
+          limit = floor(sqrt(fromIntegral n)) + 1
+
+maxPrimeFactor :: (Integral n) => n -> n
+maxPrimeFactor n
+    | isPrime n         = n         
+    | n `mod` 2 == 0    = maxPrimeFactor $ fromIntegral n `div` 2
+    | otherwise         = maxPrimeFactor $ fromIntegral n `div` head [i | i <- [3,5..], n `mod` i == 0 && isPrime i]
+
+main :: IO ()
+main = do
+    let result = maxPrimeFactor 600851475143
+    putStrLn $ "Project Euler, Problem 3\n"
+        ++ "Answer: " ++ (show result)