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#!/usr/bin/env perl
use strict;
use warnings;
use feature qw'say state signatures';
use bignum;
no warnings qw'experimental::signatures';
# TASK #2 › Largest Square
# Submitted by: Roger Bell_West
#
# Given a number base, derive the largest perfect square with no repeated digits and return it as a string. (For base>10, use ‘A’..‘Z’.)
# Example:
#
# f(2)="1"
# f(4)="3201"
# f(10)="9814072356"
# f(12)="B8750A649321"
use List::Util qw(uniq);
run() unless caller();
sub run() {
my ($N) = @ARGV;
if ( !$N || $N !~ m/^\d+$/ || $N < 2 || $N > 36 ) {
die <<EOF;
Usage:
$0 N
Options:
N - a number base (between 2 and 36)
EOF
}
say "f($N) = " . largest_perfet_square_without_repeated_digits_in_base($N);
}
sub largest_perfet_square_without_repeated_digits_in_base($base) {
my @digits = ( 0 .. 9, 'A' .. 'Z' )[ 0 .. $base - 1 ];
for (
my $i =
int( sqrt( base_to_dec( $base, join( '', reverse @digits ) ) ) ) ;
$i > 0 ;
$i--
)
{
my $perfect_square = dec_to_base( $base, $i**2 );
my @digits = split( '', $perfect_square );
return $perfect_square if scalar uniq(@digits) == scalar @digits;
}
}
sub dec_to_base ( $base, $n ) {
my @digits = ( 0 .. 9, 'A' .. 'Z' );
return $digits[$n] if $n <= $base - 1;
my $rem = $n % $base;
my $next = int( $n / $base );
dec_to_base( $base, $next ) . $digits[$rem];
}
sub base_to_dec ( $base, $n ) {
my $power = 1;
my $num = 0;
my @digits = split( '', $n );
for my $i ( reverse( 0 .. $#digits ) ) {
$num += value( $digits[$i] ) * $power;
$power = $power * $base;
}
return $num;
}
sub value($c) {
if ( $c ge '0' && $c le '9' ) {
return ord($c) - ord('0');
}
return ord($c) - ord('A') + 10;
}
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