# Powerful digit counts

*Author: polettix*

https://projecteuler.net/problem=63

The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number, 134217728=8^9, is a ninth power.

How many n-digit positive integers exist which are also an nth power?

Source code: prob063-polettix.pl

use v6; # As of August 24th, 2009 we don't have big integers, so we'll have # to conjure up something. We'll represent each number with an # array of digits, base 10-exp for ease of length computation. The most # significant part is at the end of the array, i.e. the array should # be read in reverse. # Setting '1' for the number of digits means representing the base-10 # system with one digit in each array position. my $digits = 5; my $limit = 10 ** $digits; my $count = 0; # 9 is the maximum possible base for this problem. 9**22 has 21 digits sub MAIN(Bool :$verbose = False) { for 1 .. 9 -> $x { my @x = (1); for 1 .. * -> $y { @x = multby(@x, $x); my $px = printable(@x); if ($px.encode('utf-8').bytes == $y) { say "$x ** $y = $px (", $px.encode('utf-8').bytes, ')' if $verbose; $count++; } elsif ($px.encode('utf-8').bytes < $y) { last; } } } say $count; } sub printable (@x is copy) { my $msb = pop @x; return $msb ~ @x.reverse.map({sprintf '%0'~$digits~'d', $_ }).join(''); } # Add a "number" to another, modifies first parameter in place. # This assumes that length(@y) <= length(@x), which will be true in # our program because @y is lower than @x sub add (@x is copy, @y) { my $rest = 0; return add(@y, @x) if +@x < +@y; for @x Z (@y, 0, *) -> $x is rw, $y { $x += $y + $rest; $rest = int($x / $limit); $x %= $limit; } push @x, $rest if $rest; return @x; } sub multby (@x is copy, $y) { my $rest = 0; for @x -> $x is rw { $x = $x * $y + $rest; $rest = $x div $limit; $x %= $limit; } push @x, $rest if $rest; return @x; } # Not really needed... sub mult (@x is copy, @y) { my @result = (0); for @y -> $y { my @addend = multby(@x, $y); @result = add(@result, @addend); @x.unshift(0); } return @result; }