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| -rw-r--r-- | challenge-201/bruce-gray/raku/ch-1.raku | 15 | ||||
| -rw-r--r-- | challenge-201/bruce-gray/raku/ch-2.raku | 46 |
2 files changed, 61 insertions, 0 deletions
diff --git a/challenge-201/bruce-gray/raku/ch-1.raku b/challenge-201/bruce-gray/raku/ch-1.raku new file mode 100644 index 0000000000..2b758163f5 --- /dev/null +++ b/challenge-201/bruce-gray/raku/ch-1.raku @@ -0,0 +1,15 @@ +sub task1 ( @ns ) { + my Set $s = @ns.Set; + + return grep { $_ ∉ $s }, 0 .. @ns.elems; +} + + +multi sub MAIN ( *@ns ) { say task1(+«@ns) } +multi sub MAIN ( Bool :$test ) { + use Test; + plan 3; + is-deeply task1([0,1,3]), (2,); + is-deeply task1([0,1 ]), (2,); + is-deeply task1([87,29]), (0,1,2); +} diff --git a/challenge-201/bruce-gray/raku/ch-2.raku b/challenge-201/bruce-gray/raku/ch-2.raku new file mode 100644 index 0000000000..dba0c2caa0 --- /dev/null +++ b/challenge-201/bruce-gray/raku/ch-2.raku @@ -0,0 +1,46 @@ +# https://oeis.org/A001318 +sub positive_and_negative ( UInt $n ) { |( +$n, -$n ) } +sub pentagonal ( Int $n --> UInt ) { $n * ( 3 * $n - 1 ) div 2 } +constant @A001318 = (1 .. Inf).map(&positive_and_negative).map(&pentagonal); + +# PartitionsP uses A001318 in this pattern of signs: ++--++--++-- … +constant @A001318_to_add = flat @A001318.skip(0).rotor(2 => 2); +constant @A001318_to_subtract = flat @A001318.skip(2).rotor(2 => 2); + +# https://oeis.org/A001318/ +constant @PartitionsP = 1, -> *@P { + @P[+@P X- @A001318_to_add ].sum + - @P[+@P X- @A001318_to_subtract].sum +} … *; + +sub task2 ( UInt $n ) { return @PartitionsP[$n] } + + +multi sub MAIN ( Bool :$OEIS ) { say "$_ {.&task2}" for 0..10_000 } +multi sub MAIN ( UInt $n ) { say task2($n) } +multi sub MAIN ( Bool :$test ) { + use Test; + plan 3; + is task2( 5), 7; + is task2(666), 11956824258286445517629485; + is-deeply @PartitionsP.head(26), + +«<1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958>; +} +# `ch-2.raku --OEIS` produces exact match of the 10_000 values +# at https://oeis.org/A001318/b001318.txt , in 35 seconds. +# This is twice as fast as Perl's ntheory module, even when it is using GMP! +# Yet another instance of where Raku shines, +# when the design (`Sequences` this time) exactly matches a use case. + +# Illustration at 14m54s of: +# https://youtu.be/iJ8pnCO0nTY?t=894 +# The hardest "What comes next?" (Euler's pentagonal formula) + + +# By the way, I attempted to translate the fastest known method, +# Hardy-Ramanujan-Rademacher formula +# https://fungrim.org/topic/Partition_function/ +# https://fungrim.org/entry/fb7a63/ +# , from http://www.flintlib.org/ into Raku, +# but my code returned zero for every input, +# so clearly I did something wrong! |