diff options
| -rw-r--r-- | challenge-169/paulo-custodio/perl/ch-1.pl | 80 | ||||
| -rw-r--r-- | challenge-169/paulo-custodio/perl/ch-2.pl | 103 | ||||
| -rw-r--r-- | challenge-169/paulo-custodio/t/test-1.yaml | 5 | ||||
| -rw-r--r-- | challenge-169/paulo-custodio/t/test-2.yaml | 5 |
4 files changed, 193 insertions, 0 deletions
diff --git a/challenge-169/paulo-custodio/perl/ch-1.pl b/challenge-169/paulo-custodio/perl/ch-1.pl new file mode 100644 index 0000000000..313305f986 --- /dev/null +++ b/challenge-169/paulo-custodio/perl/ch-1.pl @@ -0,0 +1,80 @@ +#!/usr/bin/perl + +# Challenge 169 +# +# Task 1: Brilliant Numbers +# Submitted by: Mohammad S Anwar +# +# Write a script to generate first 20 Brilliant Numbers. +# +# Brilliant numbers are numbers with two prime factors of the same length. +# +# The number should have exactly two prime factors, i.e. it’s the product of two +# primes of the same length. +# +# For example, +# +# 24287 = 149 x 163 +# 24289 = 107 x 227 +# +# Therefore 24287 and 24289 are 2-brilliant numbers. +# These two brilliant numbers happen to be consecutive as there are no even +# brilliant numbers greater than 14. +# +# +# Output +# +# 4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, +# 289, 299 + +use Modern::Perl; + +sub is_prime { + my($n) = @_; + return 0 if $n <= 1; + return 1 if $n <= 3; + return 0 if ($n % 2)==0 || ($n % 3)==0; + for (my $i = 5; $i*$i <= $n; $i += 6) { + return 0 if ($n % $i)==0 || ($n % ($i+2))==0; + } + return 1; +} + +sub prime_factors { + my($n) = @_; + my @factors; + my $p = 0; + while ($n > 1) { + do { $p++; } while (!is_prime($p)); + while ($n % $p == 0) { + push @factors, $p; + $n /= $p; + } + } + return @factors; +} + +sub is_brillant { + my($n) = @_; + my @factors = prime_factors($n); + return @factors==2 && + is_prime($factors[0]) && is_prime($factors[1]) && + length($factors[0]) == length($factors[1]); +} + +sub brillant_seq { + my $n = 1; + return sub { + while (1) { + $n++; + return $n if is_brillant($n); + } + }; +} + +@ARGV==1 or die "usage: ch-1.pl n\n"; +my $n=shift; +my @brillant; +my $it = brillant_seq(); +push @brillant, $it->() while @brillant < $n; +say join ", ", @brillant; diff --git a/challenge-169/paulo-custodio/perl/ch-2.pl b/challenge-169/paulo-custodio/perl/ch-2.pl new file mode 100644 index 0000000000..e049f4f458 --- /dev/null +++ b/challenge-169/paulo-custodio/perl/ch-2.pl @@ -0,0 +1,103 @@ +#!/usr/bin/perl + +# Challenge 169 +# +# Task 2: Achilles Numbers +# Submitted by: Mohammad S Anwar +# +# Write a script to generate first 20 Achilles Numbers. Please checkout wikipedia +# for more information. +# +# An Achilles number is a number that is powerful but imperfect (not a +# perfect power). Named after Achilles, a hero of the Trojan war, who was +# also powerful but imperfect. +# +# A positive integer n is a powerful number if, for every prime factor p of +# n, p^2 is also a divisor. +# +# A number is a perfect power if it has any integer roots (square root, cube +# root, etc.). +# +# For example 36 factors to (2, 2, 3, 3) - every prime factor (2, 3) also has its +# square as a divisor (4, 9). But 36 has an integer square root, 6, so the number +# is a perfect power. +# +# But 72 factors to (2, 2, 2, 3, 3); it similarly has 4 and 9 as divisors, but it +# has no integer roots. This is an Achilles number. +# +# Output +# +# 72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, +# 1152, 1323, 1352, 1372, 1568, 1800 + +use Modern::Perl; + +sub is_prime { + my($n) = @_; + return 0 if $n <= 1; + return 1 if $n <= 3; + return 0 if ($n % 2)==0 || ($n % 3)==0; + for (my $i = 5; $i*$i <= $n; $i += 6) { + return 0 if ($n % $i)==0 || ($n % ($i+2))==0; + } + return 1; +} + +sub prime_factors { + my($n) = @_; + my @factors; + my $p = 0; + while ($n > 1) { + do { $p++; } while (!is_prime($p)); + while ($n % $p == 0) { + push @factors, $p; + $n /= $p; + } + } + return @factors; +} + +sub is_powerfull { + my($n) = @_; + my @factors = prime_factors($n); + for (@factors) { + return 0 if $n % ($_*$_) != 0; + } + return 1; +} + +sub is_perfect { + my($n) = @_; + for my $e (2..$n) { + my $b = 1; + for my $b (1..$n) { + my $power = $b ** $e; + return 1 if $power == $n; + last if $power > $n; + $b++; + } + } + return 0; +} + +sub is_aquilles { + my($n) = @_; + return is_powerfull($n) && !is_perfect($n); +} + +sub aquilles_seq { + my($n) = 1; + return sub { + while (1) { + $n++; + return $n if is_aquilles($n); + } + }; +} + +@ARGV==1 or die "usage: ch-2.pl n\n"; +my $n=shift; +my @aquilles; +my $it = aquilles_seq(); +push @aquilles, $it->() while @aquilles < $n; +say join ", ", @aquilles; diff --git a/challenge-169/paulo-custodio/t/test-1.yaml b/challenge-169/paulo-custodio/t/test-1.yaml new file mode 100644 index 0000000000..986b1d3daa --- /dev/null +++ b/challenge-169/paulo-custodio/t/test-1.yaml @@ -0,0 +1,5 @@ +- setup: + cleanup: + args: 20 + input: + output: 4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299 diff --git a/challenge-169/paulo-custodio/t/test-2.yaml b/challenge-169/paulo-custodio/t/test-2.yaml new file mode 100644 index 0000000000..4d75cc9bf2 --- /dev/null +++ b/challenge-169/paulo-custodio/t/test-2.yaml @@ -0,0 +1,5 @@ +- setup: + cleanup: + args: 20 + input: + output: 72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800 |