Rare numbers: Difference between revisions

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<lang perl6># 20220315 Raku programming solution

sub rare (\target where ( target > 1 and target ~~ Int )) {

sub rare (\target where ( target > 0 and target ~~ Int )) {

my \digit = $ = 2;

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my @diffs1 = 0,1,4,5,6;

# all possible digits pairs to ~~calaculate~~ potential diffs

# all possible digits pairs to calculate potential diffs

my @pairs = 0..9 X 0..9;

my @all_diffs = -9..9;

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# lookup table for all the remaining diffs

given my %lookup_n { for @pairs -> \pair { $_{ [-] pair.values }.push: pair } }

my %lookup_n;

for @pairs { %lookup_n{ .[0] - .[1] }.push: $_ }

loop {

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my @terms = (@powers.reverse Z- @powers).grep: * > 0 ;

# create a cartesian product for all ~~potetential~~ diff numbers

# create a cartesian product for all potential diff numbers

# for the first use the very short one, for all other the complete 19 element

my @diff_list = do ~~given~~ @all_diffs xx (digit div 2 - 1) {

my @diff_list = digit == 2 ?? @diffs1 !! [X] @diffs1, |(@all_diffs xx digit div 2 - 1);

when $_.Bool { [X] @diffs1, |$_ }

default { @diffs1 } }

my @diff_list_iter = gather for @diff_list -> \k {

# remove invalid first diff/second diff combinations

{ take k ; next } if k.elems == 1 ;

{ take k andthen next } if k.elems == 1 ;

given (my (\a,\b) = k~~[0,1]~~) {

given (my (\a,\b) = k.values) {

when a == 0 && b != 0 { next }

when a == 1 && b ∉ [ -7, -5, -3, -1, 1, 3, 5, 7 ] { next }

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# placeholder for the digits

my \dig = @ = 0 xx digit;

# generate a cartesian product for each identified diff using the lookup tables

my @~~terms1toN~~ = ~~(1..(+diffs + (~~digit % 2 ~~- 1))).map: -> \k {~~

my @c_iter = digit == 2

~~k != +diffs~~ ?? do { ~~%lookup_n{~~$_} ~~with diffs[k~~] }

?? @lookup_1[diffs[0]].map: { [ $_ ] }

!! ~~do {~~ @~~numeric_digits~~ ~~} }~~

!! [X] @lookup_1[diffs[0]], |(1..(+diffs + (digit % 2 - 1))).map: -> \k {

k == diffs ?? @numeric_digits !! %lookup_n{diffs[k]} }

my @c_iter = digit == 2 ?? @lookup_1[diffs[0]].map: { [ $_ ] }

!! [X] @lookup_1[diffs[0]], |@terms1toN;

# check each H (n+r) by using digit combination

for @c_iter -> \elt {

for elt.kv -> \i, \pair { dig[i,digit-1-i] = pair~~[0,1]~~ }

for elt.kv -> \i, \pair { dig[i,digit-1-i] = pair.values }

# for numbers with odd # digits restore the middle digit

# which has been overwritten at the end of the previous cycle