new: Solved problems 31 to 41

Problems 21-28/problem_23.hs

@@ -1,5 +1,5 @@
-import Data.List
-import System.Random
+import Data.List (nub)
+import System.Random (getStdGen, randomRs)
 
 rndSelect :: [a] -> Int -> IO [a]
 rndSelect ls n = do

Problems 21-28/problem_24.hs

@@ -1,5 +1,5 @@
-import Data.List
-import System.Random
+import Data.List (nub)
+import System.Random (getStdGen, randomRs)
 
 diffSelect :: Int -> Int -> IO [Int]
 diffSelect n m = do

Problems 21-28/problem_25.hs

@@ -1,5 +1,5 @@
-import Data.List
-import System.Random
+import Data.List (nub)
+import System.Random (getStdGen, randomRs)
 
 rndPermu :: [a] -> IO [a]
 rndPermu ls = do

Problems 21-28/problem_27.hs

@@ -1,4 +1,4 @@
-import Data.List
+import Data.List (groupBy, nub, permutations, sortBy)
 
 group' :: [Int] -> [a] -> [[[a]]]
 group' ln ls = map ((([([fst] <*>)] <*>) . groupBy grouper . sortBy sorter) . zip ls) (nub (permutations placers))

Problems 21-28/problem_28.hs

@@ -1,4 +1,4 @@
-import Data.List
+import Data.List (sortBy)
 
 lsort :: [[a]] -> [[a]]
 lsort = sortBy (\x y -> length x `compare` length y)

Problems 31-41/problem_31.hs

@@ -0,0 +1,5 @@
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+isPrime :: (Integral n) => n -> Bool
+isPrime n = (n >= 2) && all ((/= 0) . (n `mod`)) [2 .. isqrt n]

Problems 31-41/problem_32.hs

@@ -0,0 +1,7 @@
+myGCD :: (Integral n) => n -> n -> n
+myGCD m n =
+  if remainder == 0
+    then abs n
+    else myGCD n remainder
+  where
+    remainder = m `mod` n

Problems 31-41/problem_33.hs

@@ -0,0 +1,10 @@
+myGCD :: (Integral n) => n -> n -> n
+myGCD m n =
+  if remainder == 0
+    then abs n
+    else myGCD n remainder
+  where
+    remainder = m `mod` n
+
+coprime :: (Integral n) => n -> n -> Bool
+coprime m n = myGCD m n == 1

Problems 31-41/problem_34.hs

@@ -0,0 +1,13 @@
+myGCD :: (Integral n) => n -> n -> n
+myGCD m n =
+  if remainder == 0
+    then abs n
+    else myGCD n remainder
+  where
+    remainder = m `mod` n
+
+coprime :: (Integral n) => n -> n -> Bool
+coprime m n = myGCD m n == 1
+
+totient :: (Integral n) => n -> n
+totient m = fromIntegral $ length $ filter (coprime m) [1 .. m - 1]

Problems 31-41/problem_35.hs

@@ -0,0 +1,10 @@
+import Data.List (find)
+
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+primeFactors :: (Integral n) => n -> [n]
+primeFactors n =
+  case find ((== 0) . (n `mod`)) [2 .. isqrt n] of
+    Nothing -> [n]
+    Just m -> m : primeFactors (n `div` m)

Problems 31-41/problem_36.hs

@@ -0,0 +1,13 @@
+import Data.List (find, group)
+
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+primeFactors :: (Integral n) => n -> [n]
+primeFactors n =
+  case find ((== 0) . (n `mod`)) [2 .. isqrt n] of
+    Nothing -> [n]
+    Just m -> m : primeFactors (n `div` m)
+
+primeFactorsMult :: (Integral n) => n -> [(n, n)]
+primeFactorsMult = map (\g -> (head g, fromIntegral $ length g)) . group . primeFactors

Problems 31-41/problem_37.hs

@@ -0,0 +1,16 @@
+import Data.List (find, group)
+
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+primeFactors :: (Integral n) => n -> [n]
+primeFactors n =
+  case find ((== 0) . (n `mod`)) [2 .. isqrt n] of
+    Nothing -> [n]
+    Just m -> m : primeFactors (n `div` m)
+
+primeFactorsMult :: (Integral n) => n -> [(n, n)]
+primeFactorsMult = map (\g -> (head g, fromIntegral $ length g)) . group . primeFactors
+
+phi :: (Integral n) => n -> n
+phi = product . map (\(p, r) -> (p - 1) * p ^ (r - 1)) . primeFactorsMult

Problems 31-41/problem_39.hs

@@ -0,0 +1,8 @@
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+isPrime :: (Integral n) => n -> Bool
+isPrime n = (n >= 2) && all ((/= 0) . (n `mod`)) [2 .. isqrt n]
+
+primesR :: (Integral n) => n -> n -> [n]
+primesR m n = filter isPrime [m .. n]

Problems 31-41/problem_40.hs

@@ -0,0 +1,16 @@
+import Data.List (find)
+
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+isPrime :: (Integral n) => n -> Bool
+isPrime n = (n >= 2) && all ((/= 0) . (n `mod`)) [2 .. isqrt n]
+
+goldbach :: (Integral n) => n -> (n, n)
+goldbach n =
+  if odd n
+    then error "Odd number was given"
+    else (p, n - p)
+  where
+    Just p = find (\p -> (n - p) `elem` primes) primes
+    primes = filter isPrime [2 .. n - 1]

Problems 31-41/problem_41.hs

@@ -0,0 +1,22 @@
+import Data.List (find)
+
+isqrt :: (Integral n) => n -> n
+isqrt = floor . sqrt . fromIntegral
+
+isPrime :: (Integral n) => n -> Bool
+isPrime n = (n >= 2) && all ((/= 0) . (n `mod`)) [2 .. isqrt n]
+
+goldbach :: (Integral n) => n -> (n, n)
+goldbach n =
+  if odd n
+    then error "Odd number was given"
+    else (p, n - p)
+  where
+    Just p = find (\p -> (n - p) `elem` primes) primes
+    primes = filter isPrime [2 .. n - 1]
+
+goldbachList' :: (Integral n) => n -> n -> n -> [(n, n)]
+goldbachList' m n d = filter (\(p, q) -> p > d && q > d) $ map goldbach $ filter even [m .. n]
+
+goldbachList :: (Integral n) => n -> n -> [(n, n)]
+goldbachList m n = goldbachList' m n 1