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Euler question 14 - start

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Bill Ewanick 2023-09-19 16:31:12 -04:00
parent 970c584d0a
commit e6e3cfbccc
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{ {
"cSpell.words": [ "cSpell.words": [
"Collatz",
"concat", "concat",
"coprime", "coprime",
"elems", "elems",

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{-
The following iterative sequence is defined for the set of positive integers:
n -> n/2 (n is even)
n -> 3n+1 (n is odd )
Using the rule above and starting with 13, we generate the following sequence:
13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms.
Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
-}
module Main where
-- import Data.Set (Set)
-- import qualified Data.Set as Set
import Data.IntSet (IntSet)
import qualified Data.IntSet as IntSet
main :: IO ()
main = print ans
ans :: Integer
ans = 42
nextCollatz n
| n == 1 = 0
| even n = n `div` 2
| odd n = 3*n + 1
collatzChainStartingAt n = takeWhile (/= 0) $ iterate nextCollatz n
-- solve limit = (n, chain)
-- where
-- s = maximum
-- $ map length
-- $ map collatzChainStartingAt [1..limit]
limit = 1_000_000
wholePositiveNumbers :: IntSet
wholePositiveNumbers = IntSet.fromDistinctAscList [1..limit]
f = IntSet.foldl (\acc key -> collatzChainStartingAt key : acc) []