! 56003, 56113, 56333, 56443, 56663, 56773, and 56993.
! Consequently 56003, being the first member of this family,
! is the smallest prime with this property.
-!
+!
! Find the smallest prime which, by replacing part of the number
! (not necessarily adjacent digits) with the same digit,
! is part of an eight prime value family.
<PRIVATE
SYMBOL: family-count
SYMBOL: large-families
-: reset-globals ( -- )
+: reset-globals ( -- )
H{ } clone family-count set
H{ } clone large-families set ;
-: digits-positions ( str -- positions )
+: digits-positions ( str -- positions )
H{ } clone [ '[ swap _ push-at ] each-index ] keep ;
: *-if-index ( char combination index -- char )
dup length [1,b] [ all-combinations ] with map concat ;
: families ( stra -- seq )
- dup digits-positions values
+ dup digits-positions values
[ all-positions-combinations [ replace-positions-with-* ] with map ] with map concat ;
: save-family ( family -- )
! Test all primes that have length n
: n-digits-primes ( n -- primes )
- [ 1 - 10^ ] [ 10^ ] bi primes-between ;
+ [ 1 - 10^ ] [ 10^ ] bi primes-between ;
: test-n-digits-primes ( n -- seq )
- reset-globals
- n-digits-primes
+ reset-globals
+ n-digits-primes
[ number>string families [ handle-family ] each ] each
large-families get ;
! recursively test all primes by length until we find an answer
: (euler051) ( i -- answer )
- dup test-n-digits-primes
- dup assoc-size 0 >
+ dup test-n-digits-primes
+ dup assoc-size 0 >
[ nip values [ fill-*-with-ones string>number ] [ min ] map-reduce ]
[ drop 1 + (euler051) ] if ;
PRIVATE>