69 lines
1.7 KiB
Factor
69 lines
1.7 KiB
Factor
! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: assocs hashtables kernel math math.ranges
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project-euler.common sequences sets ;
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IN: project-euler.074
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! http://projecteuler.net/index.php?section=problems&id=074
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! DESCRIPTION
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! -----------
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! The number 145 is well known for the property that the sum of the factorial
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! of its digits is equal to 145:
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! 1! + 4! + 5! = 1 + 24 + 120 = 145
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! Perhaps less well known is 169, in that it produces the longest chain of
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! numbers that link back to 169; it turns out that there are only three such
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! loops that exist:
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! 169 → 363601 → 1454 → 169
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! 871 → 45361 → 871
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! 872 → 45362 → 872
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! It is not difficult to prove that EVERY starting number will eventually get
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! stuck in a loop. For example,
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! 69 → 363600 → 1454 → 169 → 363601 (→ 1454)
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! 78 → 45360 → 871 → 45361 (→ 871)
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! 540 → 145 (→ 145)
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! Starting with 69 produces a chain of five non-repeating terms, but the
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! longest non-repeating chain with a starting number below one million is sixty
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! terms.
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! How many chains, with a starting number below one million, contain exactly
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! sixty non-repeating terms?
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! SOLUTION
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! --------
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! Brute force
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<PRIVATE
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: digit-factorial ( n -- n! )
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{ 1 1 2 6 24 120 720 5040 40320 362880 } nth ;
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: digits-factorial-sum ( n -- n )
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number>digits [ digit-factorial ] map-sum ;
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: chain-length ( n -- n )
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61 <hashtable>
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[ 2dup key? not ]
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[ [ conjoin ] [ [ digits-factorial-sum ] dip ] 2bi ]
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while nip assoc-size ;
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PRIVATE>
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: euler074 ( -- answer )
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1000000 [1,b] [ chain-length 60 = ] count ;
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! [ euler074 ] 10 ave-time
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! 25134 ms ave run time - 31.96 SD (10 trials)
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SOLUTION: euler074
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