76 lines
1.7 KiB
Factor
76 lines
1.7 KiB
Factor
! Copyright (c) 2007 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators.short-circuit kernel make math math.ranges sequences ;
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IN: project-euler.014
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! http://projecteuler.net/index.php?section=problems&id=14
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! DESCRIPTION
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! -----------
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! The following iterative sequence is defined for the set of positive integers:
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! n -> n / 2 (n is even)
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! n -> 3n + 1 (n is odd)
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! Using the rule above and starting with 13, we generate the following
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! sequence:
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! 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
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! It can be seen that this sequence (starting at 13 and finishing at 1)
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! contains 10 terms. Although it has not been proved yet (Collatz Problem), it
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! is thought that all starting numbers finish at 1.
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! Which starting number, under one million, produces the longest chain?
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! NOTE: Once the chain starts the terms are allowed to go above one million.
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! SOLUTION
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! --------
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! Brute force
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<PRIVATE
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: next-collatz ( n -- n )
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dup even? [ 2 / ] [ 3 * 1+ ] if ;
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: longest ( seq seq -- seq )
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2dup [ length ] bi@ > [ drop ] [ nip ] if ;
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PRIVATE>
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: collatz ( n -- seq )
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[ [ dup 1 > ] [ dup , next-collatz ] [ ] while , ] { } make ;
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: euler014 ( -- answer )
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1000000 [1,b] 0 [ collatz longest ] reduce first ;
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! [ euler014 ] time
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! 52868 ms run / 483 ms GC time
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! ALTERNATE SOLUTIONS
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! -------------------
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<PRIVATE
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: worth-calculating? ( n -- ? )
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1- 3 { [ mod zero? ] [ / even? ] } 2&& ;
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PRIVATE>
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: euler014a ( -- answer )
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500000 1000000 [a,b] 1 [
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dup worth-calculating? [ collatz longest ] [ drop ] if
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] reduce first ;
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! [ euler014a ] 10 ave-time
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! 4821 ms run / 41 ms GC time
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! TODO: try using memoization
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MAIN: euler014a
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