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#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl
#
# waxing-numeric.pl
#
# Brazilian Number
# Submitted by: Mohammad S Anwar
# You are given a number $n > 3.
#
# Write a script to find out if the given number is a Brazilian
# Number.
#
# A positive integer number N has at least one natural number B
# where 1 < B < N-1 where the representation of N in base B has
# same digits.
#
#
# Example 1:
# Input: $n = 7
# Output: 1
#
# Since 7 in base 2 is 111.
#
# Example 2:
# Input: $n = 6
# Output: 0
#
# Since 6 in base 2 is 110,
# 6 in base 3 is 20 and
# 6 in base 4 is 12.
#
# Example 3:
# Input: $n = 8
# Output: 1
#
# Since 8 in base 3 is 22.
#
# © 2022 colin crain
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
use warnings;
use strict;
use utf8;
use feature ":5.26";
use feature qw(signatures);
no warnings 'experimental::signatures';
use constant { ANALYSE => 0 };
use constant { COUNT => 2000 };
if (ANALYSE) {
analyse( COUNT );
}
else {
my $input = shift @ARGV // 1993;
say "input: $input";
say "output: ", brazilian( $input ) ? 1 : 0;
say digit_test_36( 100, 99);
}
## ## ## the task
sub brazilian ( $num ) {
## up/down check if number is a Brazilian number
for ( 2..$num-2 ) {
return $_ if digit_test( $num, $_ );
}
return 0;
}
sub digit_test ( $num, $base ) {
## up/down check for all digits are the same in a given base
## converts from base-10 to any given base
## does not internally store converted number other than
## single digit as base-10 sequence index: conditional
## 1 short-circuits returning 0 if non-repeated digit found,
## otherwise returns 1
my $rem;
my $digit;
while ( $num > 0 ) {
($num, $rem) = (int( $num/$base ), $num % $base);
$digit //= $rem;
return 0 if $digit != $rem;
}
return 1;
}
## ## ## /task
## analysis section
sub analyse ( $count ) {
my $match;
my @coef;
for (2..$count) {
my $b = brazilian( $_ );
next if $b == 0;
push @coef, $b;
my @pdiv = nd_brute( $_ );
for my $div ( 2..42 ) {
next unless $b == $_/$div - 1;
$match = "match 1/${div}-1";
last;
}
$match ||= (sprintf "\t%.2f ", $_/$b);
say sprintf "%3d %-3d %-20s %s", $_, $b, $match, "@pdiv";
$match = undef;
}
my @a = grep { brazilian($_) } (2..200);
say "@a";
say "@coef";
sub nd_brute ( $num, @div ) {
$num % $_ or push @div, $_ for 2..$num/2 ;
return @div;
}
}
## /analysis
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