Task — Max number

You are given a list of positive integers. Write a script to concatenate the integers to form the highest possible value.

Analysis

This is a rather frustrating problem in that it's hard to see a simple alternative to just trying all possible concatenations. I have done that using recursion, which has the usual issue of being quite slow when the number of numbers exceeds, in this case, around 9.

It would be faster using one of the modules that generates permutations, but my free web hosting doesn't have those installed and doesn't allow me access to cpan, and I don't have time to write one myself.

Try it 

#!/usr/bin/perl

use v5.16;    # The Weekly Challenge - 2023-05-15
use utf8;     # Week 217 task 2 - Max number
use strict;   # Peter Campbell Smith
use warnings; # Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

max_number(1, 23);
max_number(10, 3, 2);
max_number(31, 2, 4, 10);
max_number(5, 11, 4, 1, 2);
max_number(1, 10);
max_number(9900, 1, 99, 88);
max_number(47, 53, 99, 82, 9, 21, 36, 76, 77);

sub max_number {
    
    my (%left, $max);
    
    # put the numbers in a hash (as keys)
    $left{$_} = 1 for @_;

    # show result
    say qq[\nInput: (] . join(', ', @_) . ')';
    say qq[Output: ] . add_a_number(0, '', \%left);
}

sub add_a_number {
    
    my ($max, $so_far, $so_far2, %left, %more, $this);
    
    # initialise
    $max = $_[0];
    $so_far = $_[1];
    %left = %{$_[2]};
    
    # added all numbers
    unless (%left) {
        $max = $so_far if $so_far > $max;
    
    # add the next number
    } else {    
        for $this (keys %left) {
            %more = %left;
            delete $more{$this};            
            $max = add_a_number($max, $so_far . $this, \%more);
        }
    }
    
    # return the best so far
    return $max;
}

Output

Input: (1, 23)
Output: 231

Input: (10, 3, 2)
Output: 3210

Input: (31, 2, 4, 10)
Output: 431210

Input: (5, 11, 4, 1, 2)
Output: 542111

Input: (1, 10)
Output: 110

Input: (9900, 1, 99, 88)
Output: 999900881

Input: (47, 53, 99, 82, 9, 21, 36, 76, 77)
Output: 99982777653473621