Difference between revisions of "Euler problems/21 to 30"
Jim Burton (talk | contribs) (Added soplution for p28) |
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Solution: |
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<haskell> |
<haskell> |
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+ | corners :: Int -> (Int, Int, Int, Int) |
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⚫ | |||
+ | corners i = (n*n, 1+(n*(2*m)), 2+(n*(2*m-1)), 3+(n*(2*m-2))) |
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+ | where m = (i-1) `div` 2 |
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+ | n = 2*m+1 |
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+ | |||
+ | sumcorners :: Int -> Int |
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+ | sumcorners i = a+b+c+d where (a, b, c, d) = corners i |
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+ | |||
+ | sumdiags :: Int -> Int |
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+ | sumdiags i | even i = error "not a spiral" |
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+ | | i == 3 = s + 1 |
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+ | | otherwise = s + sumdiags (i-2) |
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+ | where s = sumcorners i |
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+ | |||
⚫ | |||
</haskell> |
</haskell> |
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Revision as of 12:46, 25 May 2007
Problem 21
Evaluate the sum of all amicable pairs under 10000.
Solution: This is a little slow because of the naive method used to compute the divisors.
problem_21 = sum [m+n | m <- [2..9999], let n = divisorsSum ! m, amicable m n]
where amicable m n = m < n && n < 10000 && divisorsSum ! n == m
divisorsSum = array (1,9999)
[(i, sum (divisors i)) | i <- [1..9999]]
divisors n = [j | j <- [1..n `div` 2], n `mod` j == 0]
Problem 22
What is the total of all the name scores in the file of first names?
Solution:
-- apply to a list of names
problem_22 :: [String] -> Int
problem_22 = sum . zipWith (*) [ 1 .. ] . map score
where score = sum . map ( subtract 64 . ord )
Problem 23
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
Solution:
problem_23 = undefined
Problem 24
What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
Solution:
perms [] = [[]]
perms xs = do
x <- xs
map ( x: ) ( perms . delete x $ xs )
problem_24 = ( perms "0123456789" ) !! 999999
Problem 25
What is the first term in the Fibonacci sequence to contain 1000 digits?
Solution:
valid ( i, n ) = length ( show n ) == 1000
problem_25 = fst . head . filter valid . zip [ 1 .. ] $ fibs
where fibs = 1 : 1 : 2 : zipWith (+) fibs ( tail fibs )
Problem 26
Find the value of d < 1000 for which 1/d contains the longest recurring cycle.
Solution:
problem_26 = fst $ maximumBy (\a b -> snd a `compare` snd b)
[(n,recurringCycle n) | n <- [1..999]]
where recurringCycle d = remainders d 10 []
remainders d 0 rs = 0
remainders d r rs = let r' = r `mod` d
in case findIndex (== r') rs of
Just i -> i + 1
Nothing -> remainders d (10*r') (r':rs)
Problem 27
Find a quadratic formula that produces the maximum number of primes for consecutive values of n.
Solution:
problem_27 = undefined
Problem 28
What is the sum of both diagonals in a 1001 by 1001 spiral?
Solution:
corners :: Int -> (Int, Int, Int, Int)
corners i = (n*n, 1+(n*(2*m)), 2+(n*(2*m-1)), 3+(n*(2*m-2)))
where m = (i-1) `div` 2
n = 2*m+1
sumcorners :: Int -> Int
sumcorners i = a+b+c+d where (a, b, c, d) = corners i
sumdiags :: Int -> Int
sumdiags i | even i = error "not a spiral"
| i == 3 = s + 1
| otherwise = s + sumdiags (i-2)
where s = sumcorners i
problem_28 = sumdiags 1001
Problem 29
How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
Solution:
problem_29 = length . group . sort $ [a^b | a <- [2..100], b <- [2..100]]
Problem 30
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
Solution:
problem_30 = undefined