# ETOOBUSY ðŸš€ minimal blogging for the impatient

# PWC154 - Missing Permutation

**TL;DR**

Here we are with TASK #1 from The Weekly Challenge #154. Enjoy!

# The challenge

You are given possible permutations of the string

`'PERL'`

.`PELR, PREL, PERL, PRLE, PLER, PLRE, EPRL, EPLR, ERPL, ERLP, ELPR, ELRP, RPEL, RPLE, REPL, RELP, RLPE, RLEP, LPER, LPRE, LEPR, LRPE, LREP`

Write a script to find any permutations missing from the list.

# The questions

One thing thatâ€™s not entirely clear is whether one permutation should be found or more. The title seems to imply the former, while the wording seems to point to the latter.

In a generalization of the challenge, it would be interesting to know how to deal with repeated letters. But weâ€™re not in that generazation, right?

# The solution

Our approach will be some plain brute force: iterate through all possible permutations and print out only the ones that are not present in the inputs.

Raku goes first and it provides us with a fantastic built-in
`permutations`

. which does the heavy lifting. It does the permutations
magic acting over an input list-y thing, so we `comb`

one of the
*present* combinations (it does not matter which, they all contain the
same letters). Assembling each permutation back to a string is a
fantastic option to brag about hyperoperators:

```
#!/usr/bin/env raku
use v6;
sub MAIN (*@args) { .put for missing-permutations(@args) }
sub missing-permutations (@present) {
my %present = @present.map({$_ => 1});
permutations( # consider all permutations
@present[0].comb(/./) # over letters of the first item
)Â».join('') # merge each back to a string
.grep({!%present{$_}++}); # and keep only the unseen
}
```

The astute reader might object to the use of an additional hash to test
the presence of a combination, and they would be right in suggesting
that the final `grep`

might just be:

```
...
.grep({!($_ âˆˆ @present)}); # and keep only the unseen
...
```

Only I liked to code a generalizable solution, and this takes care of filtering out duplicates in case of input words with duplicate lettersâ€¦

The Perl alternative goes on the same wavelength, except that now we
have to code our own `permutations`

(stolen from Permutations with
Heapâ€™s Algorithm) and the hyperoperator is substitued with a `map`

:

```
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
say for missing_permutations(@ARGV);
sub missing_permutations (@present) {
my %present = map { $_ => 1 } @present;
return grep {!$present{$_}++}
map { join '', $_->@* }
permutations(split m{}mxs, $present[0]);
}
sub permutations (@present) {
my @indexes = 0 .. $#present;
my @stack = (0) x @indexes;
my @retval = [@present[@indexes]];
my $sp = 0;
while ($sp < @indexes) {
if ($stack[$sp] < $sp) {
my $other = $sp % 2 ? $stack[$sp] : 0;
@indexes[$sp, $other] = @indexes[$other, $sp];
push @retval, [@present[@indexes]];
$stack[$sp]++;
$sp = 0;
}
else {
$stack[$sp++] = 0;
}
}
return @retval;
}
```

I guess itâ€™s everything for this post, stay safe!

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