Euler problems/101 to 110
(Removing category tags. See Talk:Euler_problems)
Revision as of 16:40, 30 November 2007
Investigate the optimum polynomial function to model the first k terms of a given sequence.
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For how many triangles in the text file does the interior contain the origin?
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Investigating sets with a special subset sum property.
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Finding Fibonacci numbers for which the first and last nine digits are pandigital.
Very nice problem. I didnt realize you could deal with the precision problem. Therefore I used this identity to speed up the fibonacci calculation: f_(2*n+k) = f_k*(f_(n+1))^2 + 2*f_(k-1)*f_(n+1)*f_n + f_(k-2)*(f_n)^2
import Data.List import Data.Char fibos = rec 0 1 where rec a b = a:rec b (a+b) fibo_2nk n k = let fk = fibo k fkm1 = fibo (k-1) fkm2 = fibo (k-2) fnp1sq = fnp1^2 fnp1 = fibo (n+1) fn = fibo n fnsq = fn^2 in fk*fnp1sq + 2*fkm1*fnp1*fn + fkm2*fnsq fibo x = let threshold = 30000 n = div x 3 k = n+mod x 3 in if x < threshold then fibos !! x else fibo_2nk n k findCandidates = rec 0 1 0 where m = 10^9 rec a b n = let continue = rec b (mod (a+b) m) (n+1) isBackPan a = (sort $ show a) == "123456789" in if isBackPan a then n:continue else continue search = let isFrontPan x = (sort $ take 9 $ show x) == "123456789" in map fst $ take 1 $ dropWhile (not.snd) $ zip findCandidates $ map (isFrontPan.fibo) findCandidates problem_104 = search
It took 8 sec on a 2.2Ghz machine.
Find the sum of the special sum sets in the file.
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Find the minimum number of comparisons needed to identify special sum sets.
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Determining the most efficient way to connect the network.
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Solving the Diophantine equation 1/x + 1/y = 1/n.
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How many distinct ways can a player checkout in the game of darts with a score of less than 100?
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10 Problem 110
Find an efficient algorithm to analyse the number of solutions of the equation 1/x + 1/y = 1/n.
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