From f1fbe33d234e49b1244f1fbe5f0e93d7a24dbbc6 Mon Sep 17 00:00:00 2001 From: "Yann Esposito (Yogsototh)" Date: Thu, 24 Nov 2011 17:03:53 +0100 Subject: [PATCH] 060 done but cheated a bit --- .gitignore | 3 ++ 014-scanned.hs | 41 +++++++++++++++++++++ 058.rb | 2 ++ 060 | Bin 824624 -> 0 bytes 060-cheat.hs | 44 +++++++++++++++++++++++ 060.hi | Bin 992 -> 0 bytes 060.hs | 96 +++++++++++++++++++++++++++++-------------------- 060.o | Bin 13524 -> 0 bytes 060.rb | 32 +++++++++++++++++ Prime.hi | Bin 790 -> 0 bytes Prime.hs | 4 +-- Prime.o | Bin 19944 -> 0 bytes 12 files changed, 182 insertions(+), 40 deletions(-) create mode 100644 .gitignore create mode 100644 014-scanned.hs delete mode 100755 060 create mode 100644 060-cheat.hs delete mode 100644 060.hi delete mode 100644 060.o create mode 100644 060.rb delete mode 100644 Prime.hi delete mode 100644 Prime.o diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..7806da8 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +*.hi +*.o +*.prof diff --git a/014-scanned.hs b/014-scanned.hs new file mode 100644 index 0000000..401090d --- /dev/null +++ b/014-scanned.hs @@ -0,0 +1,41 @@ +import Data.List +type YInt = Int + +collatz :: YInt -> YInt +collatz n + | n < 0 = 1 + | even n = n `quot` 2 + | otherwise = 3 * n + 1 + +-- The l `seq` is necessary to not be lazy (non-strict) +-- And not to fill the stack +lencollatz' :: YInt -> YInt -> YInt +lencollatz' l 1 = l +lencollatz' l n = l `seq` lencollatz' (l + 1) (collatz n) + +lencollatz = lencollatz' 0 + +-- The j `seq` is necessary to not be lazy (non-strict) +-- And not to fill the stack +maximalIndex :: (YInt, YInt) -> YInt -> [YInt] -> (YInt, YInt) +maximalIndex (m, i) j [] = (m, i) +maximalIndex (m, i) j (x : xs) = j `seq` maximalIndex res (j + 1) xs + where res = if x > m then (x, j) else (m, i) + +showCollatz :: YInt -> String +showCollatz 1 = "1" +showCollatz n = show n ++ " → " ++ showCollatz ( collatz n ) + +pure (Just x) = x + +main = do + putStrLn $ "max len: " ++ show m + putStrLn $ "max value: " ++ show i + -- print mrec + -- print irec + -- putStrLn $ showCollatz $ toInteger i + where + array = map lencollatz [1 .. 1000000] + m = maximum array + i = 1 + pure (elemIndex m array) + (mrec, irec) = maximalIndex (0, 0) 1 array diff --git a/058.rb b/058.rb index 1300186..a689a5b 100644 --- a/058.rb +++ b/058.rb @@ -1,3 +1,5 @@ +#!/usr/bin/env ruby +# -*- encoding: utf-8 -*- problem=%{ -- Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. -- diff --git a/060 b/060 deleted file mode 100755 index 02eb23929363bef22ce7a2d04acf3356776752f4..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 824624 zcmc${4}4U`xi@|iHn70j4H`Aps1YNL6%_;(3TOmEP*J0z(nhUNTaS|cn%yITXnskk1^49csiR=zdb zDzwhE&bCJ43ExevM;ZLfM+N@N!m|MWjljQ!fEPXz2=d=)fccN_@L2xgVp*umf4jaj z%HluPx3bmy6M#=#8Vd5?(t9lH_*P5k@_i{$qW%@3N{D_gq$0c1hKW zRkd}Ou3dfU8^>gbfj!=rb6`^@#v|K*gU 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By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. +-- +-- Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. +-- + +import Prime + + +numOfDigits x + | x < 10 = 1 + | x < 100 = 2 + | x < 1000 = 3 + | x < 10000 = 4 + | x < 100000 = 5 + | x < 1000000 = 6 + | x < 10000000 = 7 +-- | otherwise = truncate (logBase 10 x) + +-- equivalent but faster than "read (show x ++ show y)" +concatNumbers :: Int -> Int -> Int +concatNumbers x y = (10^numOfDigits y)*x + y + +solve = do + a <- primesTo10000 + let m = f a $ dropWhile (<= a) primesTo10000 + b <- m + let n = f b $ dropWhile (<= b) m + c <- n + let o = f c $ dropWhile (<= c) n + d <- o + let p = f d $ dropWhile (<= d) o + e <- p + return [a,b,c,d,e] + where + f x = filter (\y -> all is_prime [concatNumbers x y, concatNumbers y x]) + primesTo10000 = takeWhile (<= 10000) primes + + +main = do + print $ head $ solve + print $ sum $ head $ solve diff --git a/060.hi b/060.hi deleted file mode 100644 index 222692344f81e8a8b72f31aa091aed47d34978a8..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 992 zcmZQz{B@222v~sF42TVZ*a(P?ftV>1h(mx35MX3@cys^s16tP)KbMPrmfCUW?-J9{ z`8*ACoR^!w^w@QI z!><}Q|D~VZO~1n=_|{3K>ifCvyW%mwPpHOwxgJb{|KEv(i#&f{SNu4bG)26$=O9c% zpx(l6$#wIOoX!WO7PZDs-UgEpbO|%&y1Kx2deb4F=zWUfS|ABlAQsx7?fiZwUscDP zWowh(b3R)R4$SpzTf)D|o>P$Kz5C4Ib5tRt@aOh3OtP|O1!fG^{D1fqm_Yi4msv)A zSHlD8;Aeg7h&6fe1z}5D8S}z>sM->xZxHpW|{V zd<@Zd;=rK-k^%yd6`-gW1;xD>5QBg?gkoUHP0Y-Lv3(J2)_|hS+*FuEQerWT&5@pw ztXlw-gvxPe=9Q$Trxxj^=N3SPxLguT67@n#3v%F^+&!H2oDha^g7|JZ`H3Y^E$kox zzfzc?oM01tGK*pI+%Bm}rRjPhMTyBUGr2)poO2S3i&KlCrf`6SkaU6h!5R7GFk1qO zQgcdEU?y+|R~DC~=IVL+L*+R`QY%XIf>IMxpaKFQ13e)g)C;LBfa&DOERF|-0gTTE R=D?f*_8mwyOn}ML9{?$u;)nnM diff --git a/060.hs b/060.hs index 7a7c252..40f8434 100644 --- a/060.hs +++ b/060.hs @@ -1,50 +1,70 @@ --- --- The primes 3, 7, 109, and 673, are quite remarkable. --- By taking any two primes and concatenating them in any order the result will always be prime. --- For example, taking 7 and 109, both 7109 and 1097 are prime. --- The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. +-- Problem 60 +-- 02 January 2004 +-- +-- The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. -- -- Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. -- --- Should use the following property --- [x,y,z,t] special <=> [x,y,z] & [x,y,t] & [x,z,t] & [y,z,t] special - - -import Debug.Trace -import Data.List import Prime -is_couple_prime x y = ( is_prime $ read $ strx ++ stry ) && (is_prime $ read $ stry ++ strx) - where - strx = show x - stry = show y +numOfDigits x + | x < 10 = 1 + | x < 100 = 2 + | x < 1000 = 3 + | x < 10000 = 4 + | x < 100000 = 5 + | x < 1000000 = 6 + | x < 10000000 = 7 +-- | otherwise = truncate (logBase 10 x) -first_concat_prime_with_list x [] = True -first_concat_prime_with_list x (y:ys) = is_couple_prime x y && first_concat_prime_with_list x ys +-- equivalent but faster than "read (show x ++ show y)" +concatNumbers :: Int -> Int -> Int +concatNumbers x y = (10^numOfDigits y)*x + y --- are_concat_primes [3,7,109,673] return true if number are primes --- even with concat -are_concat_primes [] = True -are_concat_primes (x:xs) = (are_concat_primes xs) && first_concat_prime_with_list x xs +areConcatPrime :: [Int] -> Bool +areConcatPrime [] = True +areConcatPrime (x:xs) = + -- (areConcatPrime xs) && (and $ map concatPrime_x xs) + all concatPrime_x xs + where + concatPrime_x :: Int -> Bool + concatPrime_x y = all is_prime [concatNumbers x y, concatNumbers y x] -special_numbers 1 = take 300 primes --- special_numbers n = nub $ flatten $ filter (\x -> traceShow x are_concat_primes x) $ subsets n (special_numbers (n-1)) -special_numbers n = nub $ flatten $ filter are_concat_primes $ subsets n (special_numbers (n-1)) - where - flatten [] = [] - flatten ([]:ys) = flatten ys - flatten ((x:xs):ys) = x:flatten (xs:ys) -subsets :: Integer -> [a] -> [[a]] -subsets 0 _ = [[]] -subsets n [] = [] -subsets n (x:xs) = [x:ys | ys <- subsets (n-1) xs ] ++ subsets n xs +-- for 1 should return a list of one element list containing a unique prime +-- +cprimes :: Int -> [[Int]] +cprimes n = concatMap (memoizedConcatPrimes n) [(n-1)..] + +-- concatPrimes' :: Int -> Int -> [[Int]] +-- concatPrimes' 0 _ = [[]] +-- concatPrimes' _ (-1) = error "concatPrimes' ERROR" +-- concatPrimes' _ 0 = [] +-- concatPrimes' 1 max = [[ primes !! fromInt max ]] +-- concatPrimes' n max = filter areConcatPrime [ p:cprimes | cprimes <- subsets ] +-- where p = primes !! fromInt max +-- -- subsets = memoized !! fromInt (n-1) +-- subsets = concatMap (concatPrimes' (n-1)) [0..(max-1)] + +memoizedConcatPrimes n max = + let p = primes !! max + subsets = concatMap (memoizedConcatPrimes (n-1)) [0..(max-1)] + concatPrimes 0 _ = [[]] + concatPrimes _ 0 = [] + concatPrimes 1 max = [[ primes !! max ]] + concatPrimes n max = filter areConcatPrime [p:cprimes | cprimes <- subsets ] + in map (map concatPrimes [0..] !! n) [0..] !! max main = do - putStrLn $ show $ are_concat_primes [3,7,109,673] - putStrLn $ show $ numbers - putStrLn $ show $ result - where - numbers = take 5 $ special_numbers 5 - result = sum numbers + print $ take 20 $ cprimes 2 + print $ cprimes 3 !! 0 + print $ cprimes 3 !! 1 + print $ cprimes 3 !! 2 + print $ take 20 $ cprimes 3 + print $ cprimes 4 !! 0 + print $ cprimes 4 !! 1 + print $ cprimes 4 !! 2 + let res = take 3 $ cprimes 5 + print res + print (map sum res) diff --git a/060.o b/060.o deleted file mode 100644 index b7926fd069cafd0163f04ab27079f938828e8c12..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 13524 zcmcIq4Rln;b)IEqg!w7LCKx9qrpCt9A%wr!1pEVtd+)^NNUHfL*kQ$#7;^vJpn)3!?9`0iSao~OH)oP4vMWLN}^+n((jwO zv+waFI7GGIIofZ&JNMqXGjnI&yn)9e<%>h1kg`umg_XyYdSaZZnXO@p8li@%p39dn zla7OCKGHLd%t0s1%6K9SXUK9Dvhz|jD0%+W1; zc;i(50r}_L_7A_VeeDP2pKb>7pDOtO0Oon%M%sr!elz~^kuK)xosxsO*1opIBXf}+ zH_}bZw#CD8k*>^%E}e|X!ok|@g)?Kzwb9KsCk5Nojdkk;&7A1AE!MSrwl`bbNX9MU zy1K{n;W|B2!X{!zccNH($~!%#J9`j;b&FM10*d~4zCU(t-?i8B4PV#vJ#e2fv^{#X 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