85 lines
2.8 KiB
Factor
85 lines
2.8 KiB
Factor
! Copyright (C) 2009 Jon Harper.
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! See http://factorcode.org/license.txt for BSD license.
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! http://projecteuler.net/index.php?section=problems&id=1
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! DESCRIPTION
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! -----------
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! By replacing the first digit of *3, it turns out that
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! six of the nine possible values:
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! 13, 23, 43, 53, 73, and 83, are all prime.
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! By replacing the third and fourth digits of 56**3 with the same digit,
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! this 5-digit number is the first example having seven primes among
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! the ten generated numbers, yielding the family:
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! 56003, 56113, 56333, 56443, 56663, 56773, and 56993.
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! Consequently 56003, being the first member of this family,
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! is the smallest prime with this property.
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!
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! Find the smallest prime which, by replacing part of the number
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! (not necessarily adjacent digits) with the same digit,
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! is part of an eight prime value family.
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! SOLUTION
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! --------
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! for each prime number, count the families it belongs to. When one reaches count of 8, stop, and get the smallest number by replacing * with ones.
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USING: assocs kernel math math.combinatorics math.functions
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math.parser math.primes namespaces project-euler.common
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sequences sets strings grouping math.ranges arrays fry math.order ;
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IN: project-euler.051
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<PRIVATE
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SYMBOL: family-count
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SYMBOL: large-families
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: reset-globals ( -- )
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H{ } clone family-count namespaces:set
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H{ } clone large-families namespaces:set ;
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: digits-positions ( str -- positions )
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H{ } clone [ '[ swap _ push-at ] each-index ] keep ;
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: *-if-index ( char combination index -- char )
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member? [ drop CHAR: * ] when ;
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: replace-positions-with-* ( str positions -- str )
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[ *-if-index ] curry map-index ;
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: all-positions-combinations ( seq -- combinations )
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dup length [1,b] [ all-combinations ] with map concat ;
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: families ( stra -- seq )
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dup digits-positions values
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[ all-positions-combinations [ replace-positions-with-* ] with map ] with map concat ;
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: save-family ( family -- )
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dup family-count get at 8 = [ large-families get conjoin ] [ drop ] if ;
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: increment-family ( family -- )
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family-count get inc-at ;
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: handle-family ( family -- )
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[ increment-family ] [ save-family ] bi ;
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! Test all primes that have length n
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: n-digits-primes ( n -- primes )
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[ 1 - 10^ ] [ 10^ ] bi primes-between ;
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: test-n-digits-primes ( n -- seq )
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reset-globals
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n-digits-primes
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[ number>string families [ handle-family ] each ] each
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large-families get ;
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: fill-*-with-ones ( str -- str )
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[ dup CHAR: * = [ drop CHAR: 1 ] when ] map ;
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! recursively test all primes by length until we find an answer
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: (euler051) ( i -- answer )
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dup test-n-digits-primes
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dup assoc-size 0 >
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[ nip values [ fill-*-with-ones string>number ] [ min ] map-reduce ]
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[ drop 1 + (euler051) ] if ;
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PRIVATE>
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: euler051 ( -- answer )
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2 (euler051) ;
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SOLUTION: euler051
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