diff options
Diffstat (limited to 'challenge-146')
| -rwxr-xr-x | challenge-146/colin-crain/perl/ch-1.pl | 39 | ||||
| -rwxr-xr-x | challenge-146/colin-crain/perl/ch-2.pl | 163 | ||||
| -rwxr-xr-x | challenge-146/colin-crain/raku/ch-1.raku | 40 | ||||
| -rwxr-xr-x | challenge-146/colin-crain/raku/ch-2.raku | 33 |
4 files changed, 275 insertions, 0 deletions
diff --git a/challenge-146/colin-crain/perl/ch-1.pl b/challenge-146/colin-crain/perl/ch-1.pl new file mode 100755 index 0000000000..34757b15f0 --- /dev/null +++ b/challenge-146/colin-crain/perl/ch-1.pl @@ -0,0 +1,39 @@ +#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl
+#
+# ten-thousand-and-one-nights.pl
+#
+# 10001st Prime Number
+# Submitted by: Mohammad S Anwar
+# Write a script to generate the 10001st prime number
+#
+# © 2021 colin crain
+## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
+
+
+
+use warnings;
+use strict;
+use utf8;
+use feature ":5.26";
+use feature qw(signatures);
+no warnings 'experimental::signatures';
+
+
+say make_primes_quantity( 10001 )->[-1];
+
+
+sub make_primes_quantity ( $quantity ) {
+## creates a list of the first $quantity primes
+ my ($candidate, @primes) = ( 1, 2 );
+
+ CANDIDATE: while ( $candidate += 2 and @primes < $quantity ) {
+ my $sqrt_candidate = sqrt( $candidate );
+ for my $test ( @primes ) {
+ next CANDIDATE if $candidate % $test == 0;
+ last if $test > $sqrt_candidate;
+ }
+ push @primes, $candidate;
+ }
+ return \@primes;
+}
+
diff --git a/challenge-146/colin-crain/perl/ch-2.pl b/challenge-146/colin-crain/perl/ch-2.pl new file mode 100755 index 0000000000..fe74302411 --- /dev/null +++ b/challenge-146/colin-crain/perl/ch-2.pl @@ -0,0 +1,163 @@ +#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl
+#
+# curiously-arboreal.pl
+#
+# Curious Fraction Tree
+# Submitted by: Mohammad S Anwar
+# Consider the following Curious Fraction Tree:
+#
+#
+# ┏━━━━━━━━━━━━┫1/1┣━━━━━━━━━━━━┓
+# ┃ ┃
+# ┏━━━━┫1/2┣━━━━┓ ┏━━━━┫2/1┣━━━━┓
+# ┃ ┃ ┃ ┃
+# ┏┫1/3┣┓ ┏┫3/2┣┓ ┏┫2/3┣┓ ┏┫3/1┣┓
+# ┃ ┃ ┃ ┃ ┃ ┃ ┃ ┃
+# ┃1/4┃ ┃4/3┃ ┃3/5┃ ┃5/2┃ ┃2/5┃ ┃5/3┃ ┃3/4┃ ┃4/1┃
+#
+# (A Curious Fraction Tree)
+#
+#
+# You are given a fraction, member of the tree created similar to the above sample.
+#
+# Write a script to find out the parent and grandparent of the given member.
+#
+# Example 1:
+# Input: $member = '3/5';
+# Output: parent = '3/2' and grandparent = '1/2'
+# Example 2:
+# Input: $member = '4/3';
+# Output: parent = '1/3' and grandparent = '1/2'
+
+
+# analysis:
+#
+# Oooh, a proper puzzle! Mystery! Intrigue! Suspense!
+#
+# What's going on here? Welll we notice first the numbers
+# involved are getting larger as we descend, sometimes in the
+# numerator, sometimes the denominator. But going down the left
+# hand side we can plainly see 1,2,3 and the 4. This suggests a
+# progression from top to bottom. Further playing around reveals
+# the larger number in the child node is the sum of the
+# components of the parent: 1 + 1 = 2, 1 + 3 = 4, 3 + 2 = 5.
+#
+# The next deduction is that the left child is, with respect to
+# the parent values, the numerator over the sum, and the right is
+# the sum over the denominator.
+#
+# The next row would thus start:
+#
+# 1/5, 5/4, 4/7, 7/3, 3/8, 8/5, 5/7, 7/2, 2/7, 7/5, 5/8, 8/3 ...
+#
+# Curiouser and curiouser.
+#
+# Now when given one of these values what are we to do? How can
+# we run the machine in reverse?
+#
+# Can we assume we are limited to positive numbers for a moment?
+# The use of the word "similar" in the description suggests we
+# might in a broader sense use differing starting values, but I'm
+# going to understand things as meaning that in a the tree shown,
+# extended using the same rules of construction. In that case is
+# can easily seen that the numbers always increase as more nodes
+# are added. The values are another thing to study, but the
+# numbers used above and below the fraction line are always going
+# to go up, and so will always be positive.
+#
+# The left child is the numerator over that value plus some other
+# positive value, so the numerator will always be less than the
+# denominator. Likewise, the same logic can be reversed and
+# applied to the right side to conclude that for those nodes the
+# numerator will always be greater.
+#
+# So from this, when given a fraction, say 7/5, we can determine
+# that it is a right child, as 7 is greater than 5.
+#
+# So far so good. In fact, 7 isn't just greater than 5, it's 2
+# greater than 5. Now a right side child is the sum of the
+# parents over the denominator, so 5 is the parent denominator,
+# which means 2 must be the numerator. The parent is thus 2/5.
+#
+# Ok let's keep going. Now, of course, 5, the denominator, is
+# greater than 2, indicating this is a left-hand child. This
+# allows us to explore the other case. In a left child, the
+# parent numerator is over the sum. So for the parent of 2/5, the
+# numerator is 2 and the sum is 5, making the denominator 3. So
+# the parent is 2/3.
+#
+# Thus the parent of 7/5 is 2/5, and the grandparent is 2/3.
+# Applying a left rule followed by a right says the next parents
+# up the chain are 2/1 and 1/1, which we can see from the diagram
+# is the case.
+#
+# Neat.
+#
+# method:
+#
+# Based on whether the numerator is greater than the denominator,
+# we will select one of two courses of action, for a left child
+# or a right.
+#
+# * For the left-child parent the numerator will continue to
+# be the numerator, and the new denominator the denominator
+# minus the numerator.
+#
+# * For the right-child parent the numerator will be the
+# numerator minus the denominator, and the denominator will
+# remain unchanged.
+#
+# post-analysis:
+#
+# It appears that most fractions are found somewhere on the tree.
+# Looping and ascending until we find 1/1 usualy finds its way
+# home, but not in every case. 105/1452 (some arbitrary mid-sized
+# numbers) degenerates into 0/3 without passing go. So its
+# unclear what exactly the rules are governing which values are
+# part of the 1/1 root and which are not, and if not, where they
+# end up.
+
+# Curiouser still. What an unusual tree.
+
+# © 2021 colin crain
+## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
+
+
+
+use warnings;
+use strict;
+use utf8;
+use feature ":5.26";
+use feature qw(signatures);
+no warnings 'experimental::signatures';
+
+my $input = shift // '101/1452';
+
+my ($num, $den) = $input =~ /(\d+)\/(\d+)/;
+say "input $num/$den";
+
+my @parent = get_parent( $num, $den);
+say "parent is ", join '/', @parent;
+say "grandparent is ", join '/', get_parent( @parent );
+
+my $count = 0;
+while ( 1 ) {
+ my @prev = @parent;
+ @parent = get_parent( @parent );
+ if ( $parent[0] == $prev[0] and $parent[1] == $prev[1] ) {
+ say "--> repeats";
+ last;
+ }
+ last if $parent[0] == 1 and $parent[1] == 1 ;
+ say "--> next upwards is ", join '/', get_parent( @parent );
+}
+
+
+sub get_parent ( $num, $den ) {
+ return ( $num < $den )
+ ? ( $num, $den - $num ) ## left child
+ : ( $num - $den, $den ) ; ## right child
+}
+
+
+
diff --git a/challenge-146/colin-crain/raku/ch-1.raku b/challenge-146/colin-crain/raku/ch-1.raku new file mode 100755 index 0000000000..d6f6470030 --- /dev/null +++ b/challenge-146/colin-crain/raku/ch-1.raku @@ -0,0 +1,40 @@ +#!/usr/bin/env perl6 +# +# +# ten-thousand-and-one-nights.raku +# +# +# +# © 2021 colin crain +## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## + + + +unit sub MAIN ( $nth = 10001, $slow = Nil ) ; + +## we could do this but it's s-l-o-w +## so we won't. +defined $slow and do { + last unless defined $slow; + my @primes = grep { .is-prime }, 1..* ; + say @primes[ $nth ] ; +} + +## so instead we do this, and +## eliminate large swaths of useless searching + +nth-prime( $nth ).say; + +sub nth-prime ( $nth ) { +## creates a list of the first $quantity primes + my ($candidate, @primes) = 1, 2 ; + CANDIDATE: while ( $candidate += 2 and @primes.elems < $nth ) { + my $sqrt_candidate = sqrt( $candidate ); + for @primes -> $test { + next CANDIDATE if $candidate %% $test ; + last if $test > $sqrt_candidate; + } + @primes.push: $candidate; + } + return @primes[*-1]; +} diff --git a/challenge-146/colin-crain/raku/ch-2.raku b/challenge-146/colin-crain/raku/ch-2.raku new file mode 100755 index 0000000000..3b0570e1ec --- /dev/null +++ b/challenge-146/colin-crain/raku/ch-2.raku @@ -0,0 +1,33 @@ +#!/usr/bin/env perl6 +# +# +# curiously-arboreal.raku +# +# +# +# © 2021 colin crain +## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## + + + +unit sub MAIN ( Str $input = "9/13" ) ; + + + + +$input ~~ m{ (\d+) \/ (\d+) }; +my ($num, $den) = $0, $1; +say "input is $num/$den"; + +my @parent = get_parent( $num, $den); +say "parent is ", @parent.join: '/'; +say "grandparent is ", (get_parent( |@parent )).join: '/',; + + + +sub get_parent ( $num, $den ) { + return ( $num < $den ) + ?? ( $num, $den - $num ) ## left child + !! ( $num - $den, $den ) ; ## right child +} + |