Continues from previous week.

Welcome to the Perl review for Week 053 of the Weekly Challenge! For a quick overview, go through the original tasks and recap of the weekly challenge.

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Table of Contents

[ Alicia Bielsa | Andrezgz | Athanasius | Cheok-Yin Fung | Colin Crain | Cristina Heredia | Dave Cross | Dave Jacoby | Duncan C. White | E. Choroba | Jaldhar H. Vyas | Javier Luque | Laurent Rosenfeld | Lubos Kolouch | Mohammad S Anwar | Roger Bell West | Ruben Westerberg | Ryan Thompson | Saif Ahmed | User Person | Wanderdoc | Yet Ebreo ]

[ Alicia Bielsa | Andrezgz | Athanasius | Cheok-Yin Fung | Colin Crain | Dave Cross | Dave Jacoby | Duncan C. White | E. Choroba | Jaldhar H. Vyas | Javier Luque | Laurent Rosenfeld | Lubos Kolouch | Markus Holzer | Mohammad S Anwar | Pete Houston | Roger Bell West | Ruben Westerberg | Ryan Thompson | Saif Ahmed | User Person | Wanderdoc | Yet Ebreo ]

Task #1 › Rotate Matrix

The original task description:

Write a script to rotate the following matrix by given 90/180/270 degrees clockwise

[[ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ]]

Since the task asks us to rotate the matrix clockwise, what we have isn’t quite the same as a matrix transposition (where rows and columns are swapped), but it’s also not that far off, and can be solved in much the same way, looping over each cell and placing it in its correct position in the new array.

Most hackers wrote just one rotation subroutine, and then called it one, two, or three times, corresponding to 90, 180, or 270 degrees of rotation. While this is a bit slower, it avoids near-duplicated code.

Supported Inputs

There was some variation in what shapes of matrices are supported. There were solutions with the following:

Task matrix only: Some solutions only support the specific matrix as given by the task description, meaning, the values are hard-coded.

Some solutions only support the specific matrix as given by the task description, meaning, the values are hard-coded. 3x3 matrices: Some solutions support any 3x3 matrix, but other sizes are not supported.

Some solutions support any 3x3 matrix, but other sizes are not supported. NxN square matrices: Some solutions accept any “square” matrix (i.e., same number of rows and columns)

Some solutions accept any “square” matrix (i.e., same number of rows and columns) MxN matrices: The most general solutions support any arbitrary number of rows, and columns.

If your program accepted an MxN matrix but produced incorrect results, I generally assumed you did not intend to support MxN matrices.

Stats

Number of submissions: 22

Total SLOC: 1287

Average SLOC: 58

Alicia Bielsa

Alicia Bielsa’s solution supports NxN (square) matrices. She defines a rotateMatrix90Degrees sub that does the hard work:

sub rotateMatrix90Degrees { my $refMatrix = shift; my @aNewMatrix = (); foreach my $x ( 0 .. $#{$refMatrix}){ foreach my $y ( 0 .. $#{$$refMatrix[$x]}){ $aNewMatrix[$y][$#aMatrix - $x] = $$refMatrix[$x][$y] ; } } return @aNewMatrix; }

She then defines a rotateMatrix sub that accepts the matrix, and a rotation angle in degrees:

sub rotateMatrix { my $refMatrix = shift; my $degrees = shift; my @aMatrixRotating = @{$refMatrix}; while ( $degrees / 90 >= 1 ) { @aMatrixRotating = rotateMatrix90Degrees( \ @aMatrixRotating); $degrees -= 90 ; } return @aMatrixRotating; }

And, finally, drawMatrix is a nice touch:

sub drawMatrix { my $refMatrix = shift; foreach my $row (@{$refMatrix}){ print "[ " . join( ', ' ,@{$row}) . " ]

" ; } }

Andrezgz

Andrezgz’s solution supports MxN matrices, by calling their 90-degree rotate sub as many times as needed:

# Rotate matrix clockwise the number of times specified $matrix = rotate($matrix) for ( 1 .. $rotation); # Rotated matrix is printed print '[ ' , join( ' , ' , $matrix -> [$_] -> @ * ) , " ]

" for ( 0 .. $matrix -> @ * - 1 ); sub rotate { my $input = shift; my $output = [] ; foreach my $r ( 0 .. $input -> @ * - 1 ){ foreach my $c ( 0 .. $input -> [ 0 ] -> @ * - 1 ){ # Each element of the input matrix is appended to the output matrix # at the beginning of the row defined by its column from the input matrix unshift @{$output -> [$c]}, $input -> [$r] -> [$c]; } } return $output; }

Athanasius

Athanasius’s solution supports 3x3 matrices:

sub rotate { my ( $degrees, $old_matrix ) = @_; exists $ROTATIONS{$degrees} or die "ERROR: Rotation of $degrees° is not supported

" ; my @new_matrix; for my $r_new ( 0 .. 2 ) # Rows { for my $c_new ( 0 .. 2 ) # Columns { my ( $r_old, $c_old ) = $ROTATIONS{$degrees} -> [$r_new][$c_new] -> @ *; $ new_matrix[$r_new] -> [$c_new] = $old_matrix -> [$r_old][$c_old]; } } return \ @new_matrix; }

Cheok-Yin Fung

Cheok-Yin Fung’s solution gives us rcaqx which is short for “Rotation_Clockwise_A_Quarter, x for multiple”. Rolls right off the tongue! It supports 3x3 matrices:

sub rcaqx { if ($_[ 0 ] >= 1 ) { my %nhash; for ( 0 .. 8 ) { if ( $cp[$_] >= 0 ) { $nhash{ $cp[$_] } = $hash{ ($cp[($_ )] + 2 ) % 8 }; } } $nhash{ - 1 } = $hash{ - 1 }; %hash = %nhash; rcaqx($_[ 0 ] - 1 ); } } rcaqx($ANGLE / 90 );

However, that’s not all! Cheok Yin submitted a second solution for Task #1, which is more advanced. It supports any square (NxN) matrix, and makes use of a custom xy class:

package xy; use strict; sub new { my ($class) = @_; bless{ _value => $_[ 1 ], _x => $_[ 2 ], _y => $_[ 3 ], }, $class; } sub x { $_[ 0 ] -> {_x}} sub y { $_[ 0 ] -> {_y}} sub value { $_[ 0 ] -> {_value} }

The new and improved rcaqx looks like this:

sub rcaqx { if ($_[ 2 ] >= 1 ) { my ($xcoord, $ycoord) = ($_[ 0 ], $_[ 1 ]); $_[ 0 ] = $ycoord; $_[ 1 ] = - $xcoord; return rcaqx($_[ 0 ], $_[ 1 ], $_[ 2 ] - 1 ); } else { return ($_[ 0 ], $_[ 1 ])} }

Coordinate translation helpers:

sub translation_add_negT { $_[ 0 ] -= $T -> [ 0 ]; $_[ 1 ] -= $T -> [ 1 ]; return ($_[ 0 ], $_[ 1 ]) } sub translation_add_T { $_[ 0 ] += $T -> [ 0 ]; $_[ 1 ] += $T -> [ 1 ]; return ($_[ 0 ], $_[ 1 ]) }

And finally, here is how all of the above routines come together to actually perform the rotation:

for $i ( 1 .. $N * $N) { $newmatrix -> [$i] = xy -> new ($matrix -> [$i] -> value, translation_add_negT(rcaqx ((translation_add_T( $matrix -> [$i] -> x, $matrix -> [$i] -> y) ), $ANGLE / 90 )) ); $coordinateplane[position( $newmatrix -> [$i] -> x, $newmatrix -> [$i] -> y )] = $newmatrix -> [$i] -> value; }

Cheok Yin is now blogging twice per week about the PWC! (See Cheok Yin’s Task #2 solution for a link to her second blog post.)

Blog › Rotation in R^2 - CY’s take on PWC#053 Task 1

Colin Crain

Colin Crain’s solution went the extra mile and implemented separate routines, optimized for each of the 90, 180, and 270 degree rotations, and his is the first solution we’ve seen that supports MxN matrices:

sub rotate90 { ## matrix is an array ref of array refs ## zip and reverse subarray elements my $matrix = shift; my $output; my $cols = scalar $matrix -> [ 0 ] -> @ *; ## subarray elements, or num of cols my $rows = scalar $matrix -> @ *; ## array elements, or num of rows for my $idx ( 0 .. $cols - 1 ) { ## for each index in a row my @newrow; for my $row ( 0 .. $rows - 1 ) { ## for each row unshift @newrow, $matrix -> [$row] -> [$idx]; ## reverse rows } push $output -> @ * , \ @newrow; ## forward cols } return $output; }

sub rotate180 { ## matrix is an array ref of array refs ## reverse each subarray, then reverse the outer array my $matrix = shift; my $output; for my $row ( $matrix -> @ * ) { my @newrow = reverse $row -> @ *; unshift $output -> @ * , \ @newrow; } return $output; }

sub rotate270 { ## matrix is an array ref of array refs ## zip and reverse subarrays in outer array my $matrix = shift; my $output; my $cols = scalar $matrix -> [ 0 ] -> @ *; ## subarray elements, or num of cols my $rows = scalar $matrix -> @ *; ## array elements, or num of rows for my $idx ( 0 .. $cols - 1 ) { my @newrow; for my $row ( 0 .. $rows - 1 ) { push @newrow, $matrix -> [$row] -> [$idx]; ## forward rows } unshift $output -> @ * , \ @newrow; ## reverse cols } return $output; }

Cristina Heredia

Cristina Heredia’s solution has all three allowed rotations for the task’s matrix hard-coded:

sub rotateMatix { if ($choise == '90' ) { @array = ( [ 7 , 4 , 1 ], [ 8 , 5 , 2 ], [ 9 , 6 , 3 ] ); printArray(); } elsif ($choise == '180' ) { @array = ( [ 9 , 8 , 7 ], [ 6 , 5 , 4 ], [ 3 , 2 , 1 ] ); printArray(); } elsif ($choise == '270' ) { @array = ( [ 3 , 6 , 9 ], [ 2 , 5 , 8 ], [ 1 , 4 , 7 ] ); printArray(); } else { print "The value $choise isn't valid, please choose between: 90, 180 or 270

" ; $choise = <> ; $choise =~ s/^\s+|\s+$//g ; rotateMatix(); } }

She provides a printArray sub to pretty-print the output matrix:

sub printArray { for ( my $i = 0 ; $i < 3 ; $i ++ ) { for ( my $j = 0 ; $j < 3 ; $j ++ ) { print "$array[$i][$j] " ; } print "

" ; } }

Dave Cross

Dave Cross’s solution supports square (NxN) matrices. The rotate_matrix sub handles rotations by any of 90, 180, and 270 degrees:

sub rotate_matrix { my ( $matrix, $degrees ) = @_; die "Must give rotation in degrees

" unless $degrees; die "Must rotate by 90, 180 or 270 degrees

" if $degrees =~ /\D/ or $degrees % 90 or $degrees > 270 ; my $rotated_matrix; for ( 1 .. $degrees / 90 ) { $rotated_matrix = [] ; for my $i ( 0 .. $#$matrix ) { for my $j ( 0 .. $#{ $matrix -> [$i] } ) { $rotated_matrix -> [$j][ $#{ $matrix -> [$i] } - $i ] = $matrix -> [$i][$j]; } } $matrix = $rotated_matrix; } return $rotated_matrix; }

Dave Jacoby

Dave Jacoby’s solution supports MxN matrices, and provides separate routines for each rotation amount:

sub rotate_90 ( $array ) { my $x = - 1 + scalar $array -> @ *; my $y = - 1 + scalar $array -> [ 0 ] -> @ *; my $output = [] ; for my $i ( 0 .. $x ) { my $jj = $i; for my $j ( 0 .. $y ) { my $ii = $y - $j; $output -> [$i][$j] = int $array -> [$ii][$jj]; } } return $output; } sub rotate_180 ( $array ) { my $x = - 1 + scalar $array -> @ *; my $y = - 1 + scalar $array -> [ 0 ] -> @ *; my $output = [] ; for my $i ( 0 .. $x ) { my $jj = $x - $i; for my $j ( 0 .. $y ) { my $ii = $y - $j; $output -> [$i][$j] = int $array -> [$ii][$jj]; } } return $output; } sub rotate_270 ($array) { my $x = - 1 + scalar $array -> @ *; my $y = - 1 + scalar $array -> [ 0 ] -> @ *; my $output = [] ; for my $i ( 0 .. $x ) { my $jj = $x - $i; for my $j ( 0 .. $y ) { my $ii = $j; $output -> [$i][$j] = int $array -> [$ii][$jj]; } } return $output; }

Blog › Rotate Your Matrix and String Your Vowels

Duncan C. White

Duncan C. White’s solution supports 3x3 matrices, but the fun part is his OO implementation which overrides stringification to handle the matrix pretty-printing:

package Matrix; use parent "Clone" ; use overload '""' => \& as_str; sub as_str ($) { my ( $self ) = @_; my @r = map { join( ', ' , @$_ ) } @$self; my $str = "

" . join( "

" , @r ) . "

" ; #say "debug: $str"; return $str; }

The constructor accepts a string such as 1 2 3/4 5 6/7 8 9 :

method new ( $class: $matrixstr ) { my $mat = [] ; if ( $matrixstr ) { my @row = split( m |/| , $matrixstr ); die "Matrix->new( $matrixstr ): badly formed matrix string, should be 2 '/'s

" unless @row == 3 ; foreach my $rowstr (@row) { my @col = split( /\s+/ , $rowstr ); die "Matrix->new( $matrixstr ): badly formed matrix string, row $rowstr

" unless @col == 3 ; push @$mat, \ @col; } } return bless $mat, $class; }

And finally the rotate90 method does $n clockwise rotation(s):

method rotate90( $n ) { $n % = 4; for my $i ( 1 .. $n) { my $mat = Matrix -> new ( "" ); foreach my $col ( 0 .. 2 ) { my @newrow = (); foreach my $row ( 2 , 1 , 0 ) { push @newrow, $self -> [$row][$col]; } $mat -> [$col] = \ @newrow; } @$self = @$mat; } }

The package is then used like this:

# initial matrix my $initmat = Matrix -> new ( "1 2 3/4 5 6/7 8 9" ); say "initmat is $initmat" ; $mat -> rotate90( $times ); say "$initmat rotated $times time(s) is $mat" ;

E. Choroba

E. Choroba’s solution uses an old favourite, PDL , to assist with the matrix transposition:

use PDL; my $matrix = pdl([ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ]); for my $rotation ( 0 , 90 , 180 , 270 ) { my $times = $rotation / 90 ; my $result = $matrix; $result = $result -> transpose -> slice([ - 1 , 0 ]) for 1 .. $times; print "$rotation:$result" ; }

Since the clockwise rotation we are tasked with is different from a true matrix transposition, Choroba uses PDL’s slice to flip the matrix and get the correct result.

Blog › Perl Weekly Challenge 053: Rotate Matrix and Vowel Strings

Jaldhar H. Vyas

Jaldhar H. Vyas’s solution supports NxN square matrices, specified within the rotate sub:

sub rotate { my ($angle) = @_; my @matrix = ( [ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ], ); my $side = scalar @matrix; for ( 1 .. $angle / 90 ) { for my $row ( 0 .. ($side / 2 ) - 1 ) { for my $col ($row .. ($side - $row - 1 ) - 1 ) { my $temp = $matrix[$row][$col]; $matrix[$row][$col] = $matrix[$side - 1 - $col][$row]; $matrix[$side - 1 - $col][$row] = $matrix[$side - 1 - $row][$side - 1 - $col]; $matrix[$side - 1 - $row][$side - 1 - $col] = $matrix[$col][$side - 1 - $row]; $matrix[$col][$side - 1 - $row] = $temp; } } } return @matrix; }

The code operates by spiraling inward from all four corners, in the following order:

[ 0 , 1 , 2 , 3 , 0 ] [ 3 , 4 , 5 , 4 , 1 ] [ 2 , 5 , 13 , 5 , 2 ] [ 1 , 4 , 5 , 4 , 3 ] [ 0 , 3 , 2 , 1 , 0 ]

The numbers shown are a simple count of the number of times the inner loop has run. The 13 in the middle is a side-effect of the loop bounds.

Blog › Jaldhar’s Week #053 Blog

Javier Luque

Javier Luque’s solution supports NxN square matrices, and is called multiple times to effect rotations in multiples of 90 degrees:

sub rotate_matrix { my $m = shift; # Size of the matrix my $n = scalar(@$m); for ( my $i = 0 ; $i < int($n / 2 ); $i ++ ) { for ( my $j = $i; $j < $n - $i - 1 ; $j ++ ) { my $temp = $m -> [$i] -> [$j]; $m -> [$i] -> [$j] = $m -> [$n - $j - 1 ] -> [$i]; $m -> [$n - $j - 1 ] -> [$i] = $m -> [$n - $i - 1 ] -> [$n - $j - 1 ]; $m -> [$n - $i - 1 ] -> [$n - $j - 1 ] = $m -> [$j] -> [$n - $i - 1 ]; $m -> [$j] -> [$n - $i - 1 ] = $temp; } } }

This rotation also spirals inward.

Blog › 053 – Perl Weekly Challenge

Laurent Rosenfeld

Laurent Rosenfeld’s solution supports NxN matrices, via repeated calls to rotate_90 :

sub rotate_90 { my $input = shift; my @output; for my $row ( 0 .. $#$input) { for my $col ( 0 .. $#{@$input[$row]}) { $output[$col][$#{@$input[$row]} - $row] = $input -> [$row][$col]; } } return \ @output; } sub rotate_180 {rotate_90 rotate_90 @_} sub rotate_270 {rotate_90 rotate_180 @_}

Blog › Rotate Matrix and Vowel Strings

Lubos Kolouch

Lubos Kolouch’s solution also uses PDL :

use PDL; my $m = sequence( 3 , 3 ) + 1 ; print ($m); for ( 0 .. 2 ) { say( 90 * ($_ + 1 )); $m = $m -> transpose -> slice([ - 1 , 0 ]); print ($m); }

Lubos credits the StackOverflow question Use Perl PDL to rotate a matrix for figuring out the rotation, and also credits Choroba’s solution for the use of ->slice . Doing the research and crediting sources is the mark of a good programmer, and I really appreciate it.

Mohammad S Anwar

Mohammad S Anwar’s solution supports 3x3 matrices only. Mohammad has been doing good work with the Test family, providing unit tests for his solutions. Here is how he organized the tests for this task:

use Test::More; use Test::Deep; my $unit_tests = { 90 => { in => [ [ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ] ], out => [ [ 7 , 4 , 1 ], [ 8 , 5 , 2 ], [ 9 , 6 , 3 ] ], }, 180 => { in => [ [ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ] ], out => [ [ 9 , 8 , 7 ], [ 6 , 5 , 4 ], [ 3 , 2 , 1 ] ], }, 270 => { in => [ [ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ] ], out => [ [ 3 , 6 , 9 ], [ 2 , 5 , 8 ], [ 1 , 4 , 7 ] ], }, }; foreach my $degree (sort { $a <=> $b } keys %$unit_tests) { my $in = $unit_tests -> {$degree} -> {in}; my $out = $unit_tests -> {$degree} -> {out}; cmp_deeply(rotate_matrix($in, $degree), $out, "rotation by $degree." ); } done_testing;

I can’t count the number of times I’ve opened up a CPAN distribution and looked at the unit tests, only to see an unorganized mess of individual tests with duplicated code. It’s easy to forget that unit tests are code, too. Mohammad hasn’t forgotten that, and took the time to factor out the common code in his tests, for a more maintainable and readable result.

Here is the rotate_matrix that handles any 3x3 matrix:

sub rotate_matrix { my ($matrix, $degree) = @_; foreach my $i ( 1 .. int($degree / 90 ) ) { my $rows = @$matrix; my $cols = @{$matrix -> [ 0 ]}; my $_matrix = [] ; foreach my $i ( 0 .. $rows - 1 ) { my $k = 2 ; foreach my $j ( 0 .. $cols - 1 ) { $_matrix -> [$i][$j] = $matrix -> [$k][$i]; $k -- ; } } $matrix = $_matrix; } return $matrix; }

Blog › BLOG: The Weekly Challenge #053

Roger Bell West

Roger Bell West’s solution works with any NxN (square) matrix:

sub rotate { my ( $rotations, @in ) = @_; my $xs = $#in; foreach my $ya (@in) { if ( $#{$ya} != $xs ) { die "not a square matrix

" ; } } my @out = @in; foreach ( 1 .. $rotations ) { my @im = @out; my @tmp; foreach my $x ( 0 .. $xs ) { foreach my $y ( 0 .. $xs ) { $tmp[$y][ $xs - $x ] = $im[$x][$y]; } } @out = @tmp; } return @out; }

Ruben Westerberg

Ruben Westerberg’s solution supports 3x3 matrices only, but does so in style, with trigonometry. I suppose we should have held this task just a little sooner, so it would line up with Pi Day, March 14th!

Ruben uses core module Math::Trig for its pi routines only, and POSIX ‘s round :

use Math::Trig ':pi' ; use POSIX qw<round> ;

With basic trigonometry, @ir and @ic give the input rows and columns, for a respective 0..7 index into the 3x3 array. ( pip4 is a Math::Trig equivalent for pi*4 .)

sub rotate { my ($input,$angle) = @_; #input indexing my @ip = map {pip4 * $_} 0 .. 7 ; my @ir = map { 1 + round sin} @ip; my @ic = map { 1 + round cos} @ip; #output indexing my @polar = map {($angle / 180 * pi) + pip4 * $_} 0 .. 7 ; my @row = map { 1 + round sin} @polar; my @col = map { 1 + round cos} @polar;

For a 90 degree rotation, the arrays look like this:

@ir = ( 1 , 2 , 2 , 2 , 1 , 0 , 0 , 0 ); @ic = ( 2 , 2 , 1 , 0 , 0 , 0 , 1 , 2 ); @row = ( 2 , 2 , 1 , 0 , 0 , 0 , 1 , 2 ); @col = ( 1 , 0 , 0 , 0 , 1 , 2 , 2 , 2 );

Thus, each column in the above gives a coordinate mapping from input to output, for a single element in the 3x3 array. For example, the first column gives you a mapping from [1,2] to [2,1].

If you were wondering, “why index 0..7, instead of 0..8?", you are right to wonder that. Ruben handles the middle element (1,1) separately:

my $out = [ [] , [] , [] ]; $out -> [ 1 ] -> [ 1 ] = $matrix -> [ 1 ] -> [ 1 ];

Meanwhile, here is the line that handles the rest of the assignments from the input array¹ to the output array:

$out -> [$row[$_]] -> [$col[$_]] = $matrix -> [$ir[$_]] -> [$ic[$_]] for ( 0 .. @col - 1 );

¹. Despite taking an $input argument, rotate always uses $matrix . I suspect this is a simple oversight.

Ryan Thompson

My solution handles any MxN matrix:

sub rotate90_cw { my @A = reverse @{$_[ 0 ]}; my @T; for my $x ( 0 .. $#A) { $T[$_][$x] = $A[$x][$_] for 0 .. $#{$A[ 0 ]}; } \ @T; }

You might notice I reverse the rows in the input array first. That’s a stylistic choice so the rest of the function could be a simple transpose, much like my Raku submission; I could have instead mirrored the output columns.

The additional rotations are simply defined in terms of rotate90_cw :

# Convenience sub rotate180 { rotate90_cw( rotate90_cw (@_) ) } sub rotate_ccw { rotate90_cw( rotate180( @_) ) }

I also provided a number of unit tests, making sure I hit the important edge cases like 1xN, Mx1, and non-numeric cell contents:

# 1xN, Nx1 is_deeply rotate90_cw( [[ 1 , 2 , 3 ]]), [[ 1 ],[ 2 ],[ 3 ]]; is_deeply rotate90_cw( [[ 1 ],[ 2 ],[ 3 ]]), [[ 3 , 2 , 1 ]]; # Non-numeric, because why not is_deeply rotate90_cw ( [[ 'a' , 'b' , 'c' ], [ 'd' , 'e' , 'f' ]] ), [[ 'd' , 'a' ],[ 'e' , 'b' ],[ 'f' , 'c' ]];

Blog › Matrix Rotation

Saif Ahmed

Saif Ahmed’s solution works on any MxN matrix, and also does more than just rotate. Here are the supported “rotation” options:

0 , 90 , 180 , 270 : Clockwise rotation by degrees

, , , : Clockwise rotation by degrees cw , ht, ccw`: Aliases for above. “ Clockwise "," Half Turn ", “ Counter-Clockwise ”

, ccw`: Aliases for above. “ "," ", “ ” v , h : Flip vertically or horizontally

, : Flip or lr : Flip top left to bottom right diagonal

: Flip top left to bottom right diagonal rl : Flip bottom right to top left diagonal

Here is the flip sub in its entirety:

sub flip { my $arr = shift; my $direction = shift; my @flipped = (); return $arr unless $direction; # return original list for 0 deg trun if ( $direction =~ /^cw|ccw|lr|rl|90|270$/ ) { foreach my $row ( 0 .. scalar @{ $$arr[ 0 ] } - 1 ) { # for each row $flipped[$row] = [] ; # initialise empty row foreach my $col ( 0 .. scalar @$arr - 1 ) { # for each column push @{ $flipped[$row] }, $$arr[$col][$row]; # this does a diagonal flip } @{ $flipped[$row] } = reverse @{ $flipped[$row] } if $direction =~ /^cw|90|rl$/ ; } @flipped = reverse @flipped if $direction =~ /^ccw|270|rl$/ ; } elsif ( $direction eq 'v' ) { @flipped = reverse(@$arr); } elsif ( $direction eq 'h' ) { my $row = 0 ; foreach (@$arr) { @{ $flipped[ $row ++ ] } = reverse @$_; } } elsif ( $direction =~ /^180|ht$/ ) { @flipped = @{ flip( flip( $arr, "v" ), "h" ) }; } return \ @flipped; }

The factorization of logic for cw|ccw|lr|rl|90|270 all into the same block is rather elegant.

The real star of the show, however, has to be Saif’s second set of test cases. While everyone else had me staring at numbers to try and figure out if they all rotated into their proper places, Saif eschewed from such eyestrain-inducing numerals, in favour of this majestic bit of ASCII:

my $matrix2 = [[ qw{- - - █ - -} ], [ qw{- - - ░ █ -} ], [ qw{█ █ █ ░ ░ █} ], [ qw{- - - ░ █ -} ], [ qw{- - - █ - -} ]];

The output makes it extremely obvious to verify:

Rotating by 0 ---█-- ---░█- ███░░█ ---░█- ---█-- Rotating by 90 --█-- --█-- --█-- █░░░█ -█░█- --█-- Rotating by 180 --█--- -█░--- █░░███ -█░--- --█--- Rotating by 270 --█-- -█░█- █░░░█ --█-- --█-- --█--

Arrows or not, Saif’s solutions are always a joy to review.

User Person

User Person’s solution works on 3x3 matrices only:

User Person has a recursive array flattener, that they will use:

sub flat { return map { ref eq 'ARRAY' ? flat(@$_) : $_ } @_; }

User Person uses this to flatten the input AoA, @matrix , into @rawNums :

my @rawNums = (); @rawNums = flat @matrix;

Now, depending on the $deg (degrees) input, User Person loops through @newMatrix differently. @rawNums is flat, and is always iterated in order, giving it a row-major traversal every time:

my @newMatrix = (); my $i = 0 ; if ($deg == 0 ) { for ( my $j = 0 ; $j < $width; ++ $j) { for ( my $k = 0 ; $k < $width; ++ $k) { $newMatrix[$j][$k] = $rawNums[$i ++ ]; } } } elsif ( $deg == 90 ) { for ( my $j = $width - 1 ; $j >= 0 ; -- $j) { for ( my $k = 0 ; $k < $width; ++ $k) { $newMatrix[$k][$j] = $rawNums[$i ++ ]; } } } elsif ( $deg == 180 ) { for ( my $j = $width - 1 ; $j >= 0 ; -- $j) { for ( my $k = $width - 1 ; $k >= 0 ; -- $k) { $newMatrix[$j][$k] = $rawNums[$i ++ ]; } } } elsif ( $deg == 270 ) { for ( my $j = 0 ; $j < $width; ++ $j) { for ( my $k = $width - 1 ; $k >= 0 ; -- $k) { $newMatrix[$k][$j] = $rawNums[$i ++ ]; } } }

Wanderdoc

Wanderdoc’s solution includes a rotate sub that supports any MxN matrix:

sub rotate { my ( $aref, $angle ) = @_; my $rotated; for my $row_idx ( 0 .. $#$aref ) { for my $col_idx ( 0 .. $#{ $aref -> [$row_idx] } ) { if ( 90 == $angle ) { $rotated -> [$col_idx][ $#$aref - $row_idx ] = $aref -> [$row_idx][$col_idx]; } elsif ( 180 == $angle ) { $rotated -> [ $#$aref - $row_idx ] [ $#{ $aref -> [$row_idx] } - $col_idx ] = $aref -> [$row_idx][$col_idx]; } elsif ( 270 == $angle ) { $rotated -> [ $#{ $aref -> [$row_idx] } - $col_idx ][$row_idx] = $aref -> [$row_idx][$col_idx]; } else { die "Can only rotate a matrix by 90/180/270 degrees clockwise!$/" ; } } } return $rotated; }

The sub also directly implements the three different rotation angles, so this is also an optimally efficient solution. Nice!

Yet Ebreo

Yet Ebreo’s solution supports MxN matrices:

#Obfuscated routine to rotate array 90cw, because it's perl. :D sub rotate {@{$_[ 0 ]} = map[map$_[ 0 ] -> [ - $_][$'], // .. @{$_[ 0 ]}], 0 ..~- @{$_[ 0 ] -> [ 0 ]}}

Again, with a little whitespace:

# De-obfuscated [Ryan] sub rotate { my ($matrix) = @_; @$matrix = map [ map $matrix -> [ - $_ ][ $' ] => // .. @$matrix ], 0 .. $#{ $matrix -> [ 0 ] }; }

We can now clearly see the rotation is done in-place. Once you run it through perltidy , there isn’t anything too unusual here. There is one old Perl golf trick, with $' ( $POSTMATCH ) and the empty regex ( // ) as the start of a .. range. This is a way to (sort of) access the outer $_ loop variable in the inner loop, without having to assign either of them to a different named variable. After // , $' effectively becomes an alias for the outer $_ .

Task #2 › Vowel Strings

Here is Mohammad’s description, abridged:

Write a script to accept an integer 1 <= N <= 5 that would print all possible strings of size N formed by using only vowels (a, e, i, o, u).

The string should follow the following rules:

a can only be followed by e and i .

can only be followed by and . e can only be followed by i .

can only be followed by . i can only be followed by a , e , o , and u .

can only be followed by , , , and . o can only be followed by a and u .

can only be followed by and . u can only be followed by o and e .

For example, if the given integer N = 2 then script should print the following strings:

ae ai ei ia io iu ie oa ou uo ue

Solution Types

This task is a directed graph traversal. The “rules,” above, define the valid edges. With that in mind, one can implement the graph traversal in any number of ways, or, indeed, go a completely different direction, as we’ll see.

Dispatch Tables

Most people used a dispatch table to store the graph edges. The hash key is the current node, and the value is an array of nodes that may be visited from the current node. For example, if $edges{a} = ['e','i'] , that means there are directed edges from a to e , and also from a to i .

Traversal

Traversing the graph can be done breadth-first or depth-first if you don’t care about the ordering (or if you sort at the end). BFS will preserve the ordering.

BFS can be done with a queue, which in Perl is any old array with push and shift (or pop and unshift , if you prefer). You shift a string off the queue, look at the last character, and then push all strings that can be reached from the current string. For example, if you shift the string aei from the array, you would then push aeia , aeie , aeio , and aeiu , because the vowels allowed after i are a, e, o, u .

DFS is done with a stack, which makes it natural for recursive solutions. The operations are very similar, but the stack is implicit with recursion. The strings will be in a depth-first order at the end, but that can be managed with sort (or not at all, if the order is unimportant).

Alternatives

There were a few alternative solutions. Several people used modules like Algorithm::Combinatorics to generate all variations of the five vowels, and then filter the results with regexps or other means. While these solutions end up throwing out 95-99.5% of strings (it gets worse the longer the strings are), they are fast enough for small inputs.

Stats

Number of submissions: 23

Total SLOC: 1129

Average SLOC: 49

Alicia Bielsa

Alicia Bielsa’s solution uses recursion to populate a global list of vowel strings.

She stores the next vowel edges in a hash, and the result vowel strings in @aStrings :

my %hNodes = (); $hNodes{ 'a' } = [ 'e' , 'i' ]; $hNodes{ 'e' } = [ 'i' ]; $hNodes{ 'i' } = [ 'a' , 'e' , 'o' , 'u' ]; $hNodes{ 'o' } = [ 'a' , 'u' ]; $hNodes{ 'u' } = [ 'a' , 'e' ]; my @aStrings = ();

$hNodes{'u'} should be ['o','e'] , not ['a','e'] . When that is changed, Alicia’s output is correct.

Alicia calls the recursive addVowel once for each vowel, to start the recursion:

foreach my $vowel ( keys(%hNodes)){ addVowel($size, $vowel, '' ); } sub addVowel { my $currentLevel = shift; my $currentVowel = shift; my $currentString = shift; $currentString .= $currentVowel; if ($currentLevel == 1 ){ push (@aStrings , $currentString); return 0 ; } else { $currentLevel -- ; } foreach my $nextVowel (@{$hNodes{$currentVowel}}){ addVowel($currentLevel, $nextVowel,$currentString ); } return 0 ; }

This is a solid recursive implementation.

Andrezgz

Andrezgz’s solution uses a %vowels hash to store the next vowels:

my %vowels = ( a => [ 'e' , 'i' ], e => [ 'i' ], i => [ 'a' , 'e' , 'o' , 'u' ], o => [ 'a' , 'u' ], u => [ 'o' , 'e' ] );

Then things get interesting. Here is the main loop, which initializes a @comb array to the starting five vowels, and then calls add_vowel LENGTH-1 times:

my @comb = keys %vowels; @comb = add_vowel(@comb) for ( 2 .. $n); print $_ . $/ for sort @comb;

And here is the add_vowel sub, which takes a list of strings, and returns a new list of strings:

sub add_vowel { my @output; for my $c (@_) { my $v = substr $c, - 1 ; push @output, map { $c . $_ } @{$vowels{$v}}; } return @output }

The branching required for this problem happens when add_vowel appends to @output . For each input string, @output gets a copy of that string concatenated with each vowel that may follow the last character in the string.

This is a nice alternative to recursion.

Athanasius

Athanasius’s solution builds up a @temp array using a BFS that becomes the @solution :

my @solution = qw( a e i o u ) ; # The solution for N = 1 for ( 2 .. $n ) { my @temp; for my $string (@solution) { my $last = substr $string, - 1 ; push @temp, $string . $_ for $FOLLOWERS{$last} -> @ *; } @ solution = @temp; } printf "For N = %d, the %d possible distinct vowel strings are:

%s

" , $n, scalar @solution, join "

" , @solution;

Cheok-Yin Fung

Cheok-Yin Fung’s solution uses the Tree distribution to create an m-ary trees of depth $N , where $N is the desired vowel string length.

With Tree (as with most computer science trees, actually), every child node is also a Tree , so the initialization creates a forest of trees and then adds each of those to the root $vowel tree. This is a pattern that will be repeated in the rest of the program:

my $vowel = Tree -> new ( "" ); $vowel -> add_child( Tree -> new ($_) ) for qw<a e i o u> ; # [Simplified for brevity --RyanT]

Cheok-Yin then calls the following functions:

grow($vowel, 5 ); traverse_and_named($vowel, $N, "" );

The second argument to grow() is apparently the depth, which is hard-coded at 5 for some reason, despite $N being the user-specified depth. I am not sure why grow($vowel, $N) would not suffice, but maybe there is a reason I did not notice.

Here is the recursive grow , and the produce_child sub it calls:

# grow : traverse and force the tree nodes produce child(ren) sub grow { my ($t, $d) = ($_[ 0 ], $_[ 1 ]); produce_child($t); my @t_baby = $t -> children; foreach (@t_baby) { grow($_, $d) if $_ -> depth < $d; } } sub produce_child { my $t = $_[ 0 ]; if ($t -> size == 1 ) { switch($t -> value) { case ( "a" ) {$t -> add_child(Tree -> new ( "e" )); $t -> add_child(Tree -> new ( "i" ));} case ( "e" ) {$t -> add_child(Tree -> new ( "i" ));} case ( "i" ) {$t -> add_child(Tree -> new ( "a" )); $t -> add_child(Tree -> new ( "e" )); $t -> add_child(Tree -> new ( "o" )); $t -> add_child(Tree -> new ( "u" ));} case ( "o" ) {$t -> add_child(Tree -> new ( "a" )); $t -> add_child(Tree -> new ( "u" ));} case ( "u" ) {$t -> add_child(Tree -> new ( "e" )); $t -> add_child(Tree -> new ( "o" ));} } } }

Finally, the traverse_and_named function traverses the tree and prints all the nodes at the specified depth:

sub traverse_and_named { my ($t, $d, $str) = ($_[ 0 ], $_[ 1 ], $_[ 2 ]); print $str . "

" if length($str) == $d; my @t_baby = $t -> children; foreach (@t_baby) { traverse_and_named($_, $d, $str . $_ -> value) if $_ -> depth <= $d; } }

Blog › Tree as a tool for enumeration - CY’s take on PWC#053 Task 2

Colin Crain

Colin Crain’s solution also uses a BFS queue:

my @output = qw( a e i o u ) ; my %following = ( a => [ qw( e i ) ], e => [ qw( i ) ], i => [ qw( a e o u ) ], o => [ qw( a u ) ], u => [ qw( o e ) ] ); my $count = 1 ; while ($count < $length) { my $num_clusters = scalar @output; ## memoize this now because we will add elements for ( 1 .. $num_clusters) { my $vowel_cluster = shift @output; ## shift off a cluster my $vowel = substr $vowel_cluster, - 1 , 1 ; ## get the last letter for ($following{$vowel} -> @ * ) { ## build new combinations from that letter push @output, "$vowel_cluster" . "$_" ; ## and add them to the end of the list } } $count ++ ; ## keep track of the cluster length } say $_ for @output;

Dave Cross

Dave Cross’s solution sets up the %strings map, initializes @words with the five starting nodes, and then calls his add_letter function on @words $count-1 times to get “words” of the correct length:

my $count = get_arg(); my %strings = ( a => [ qw[e i] ], e => [ qw[i] ], i => [ qw[a e o u] ], o => [ qw[a u] ], u => [ qw[o e] ], ); my @words = map { [ $_ ] } keys %strings; @words = add_letter(@words) for 2 .. $count; say @$_ for sort { "@$a" cmp "@$b" } @words;

Here is the add_letter function that appends the new word(s) based on the last vowel:

sub add_letter { my @input = @_; my @output; for my $in (@input) { push @output, map { [ @$in, $_ ] } @{ $strings{ $in -> [ - 1 ] } }; } return @output; }

Dave Jacoby

Dave Jacoby’s solution lets his vowel_strings function do all of the heavy lifting:

my @strings = vowel_strings($l); say join "

" , @strings;

sub vowel_strings ( $l, $string = '' ) { if ( length $string == $l ) { return $string; } my @next; my $m = length $string == 0 ? '' : substr $string, - 1 ; if ( $string eq '' ) { @next = qw{ a e i o u} ; } elsif ( $m eq 'a' ) { @next = qw{ e i } ; } elsif ( $m eq 'e' ) { @next = qw{ i } ; } elsif ( $m eq 'i' ) { @next = qw{ a o u e } ; } elsif ( $m eq 'o' ) { @next = qw{ a u } ; } elsif ( $m eq 'u' ) { @next = qw{ o e } ; } my @output; for my $n (@next) { push @output, vowel_strings( $l, $string . $n ); } return @output; }

This is a great recursive DFS implementation. Stylsitically, I might consider using a dispatch table or turnstyle operator to eliminate the if .. elsif .. else , but that’s just me. Computationally, I wouldn’t change a thing!

Blog › Rotate Your Matrix and String Your Vowels

Duncan C. White

Duncan C. White’s solution is also recursive, but uses regexps instead of substr or arrays, to find the last character in each string:

use Function::Parameters; die "vowel-strings N

" unless @ARGV == 1 ; my $n = shift; die "vowel-strings: N ($n) should be 1..5

" unless $n >= 1 && $n <= 5 ; my @vow = qw(a e i o u) ; # # generate( $prefix, $moresteps ); # Generate and print all vowel strings starting with $prefix, # and taking $moresteps more generative steps, applying # the above rules at each step to extend the prefix. # fun generate( $prefix, $moresteps ) { if ( $moresteps == 0 ) { say $prefix; return ; } # 'a' can only be followed by 'e' or 'i'. if ( $prefix =~ /a$/ ) { generate( $prefix . 'e' , $moresteps - 1 ); generate( $prefix . 'i' , $moresteps - 1 ); } # 'e' can only be followed by 'i'. elsif ( $prefix =~ /e$/ ) { generate( $prefix . 'i' , $moresteps - 1 ); } # 'i' can only be followed by 'a', 'e', 'o', or 'u'. elsif ( $prefix =~ /i$/ ) { foreach my $vowel (@vow) { next if $vowel eq 'i' ; generate( $prefix . $vowel, $moresteps - 1 ); } } # 'o' can only be followed by 'a' or 'u'. elsif ( $prefix =~ /o$/ ) { generate( $prefix . 'a' , $moresteps - 1 ); generate( $prefix . 'u' , $moresteps - 1 ); } # 'u' can only be followed by 'o' or 'e'. elsif ( $prefix =~ /u$/ ) { generate( $prefix . 'o' , $moresteps - 1 ); generate( $prefix . 'e' , $moresteps - 1 ); } } foreach my $firstvowel (@vow) { generate( $firstvowel, $n - 1 ); }

Again, a lot of this duplicated code could be eliminated with a dispatch table, but apart from that, I love it.

E. Choroba

E. Choroba’s solution ought to look familiar by now (BFS queue):

my %next = ( a => [ qw[ e i ] ], e => [ qw[ i ] ], i => [ qw[ a e o u ] ], o => [ qw[ a u ] ], u => [ qw[ o e ] ]); my $n = shift; die "Invalid argument" unless ($n // "" ) =~ /^[1-5]$/ ; my @agenda = sort keys %next; while ($n > length $agenda[ 0 ]) { my @next; for my $string (@agenda) { my $last = substr $string, - 1 ; push @next, map $string . $_, @{ $next{$last} }; } @agenda = @next; } say for @agenda;

Blog › Rotate Matrix and Vowel Strings

Jaldhar H. Vyas

Jaldhar H. Vyas’s solution is another good example of a BFS queue:

sub generate { my ($n) = @_; my %rules = ( a => [ qw/ e i / ], e => [ qw/ i / ], i => [ qw/ a e o u / ], o => [ qw/ a u / ], u => [ qw/ e o / ] ); my @generated; for my $i ( 1 .. $n) { if ($i == 1 ) { @generated = sort keys %rules; } else { @generated = map { my $e = $_; map { $e . $_; } @{ $rules{substr $e, - 1 , 1 } }; } @generated; } } return @generated; }

Blog › Jaldhar’s Week #053 Blog

Javier Luque

Javier Luque’s solution uses Algorithm::Combinatorics ’ variations_with_repetition function. v_w_r(\@data, $k) returns an iterator that will generate all tuples of length $k from @data . Thus:

my @vowels = ( 'a' , 'e' , 'i' , 'o' , 'u' ); my $iter = variations_with_repetition( \ @vowels,$size); while ( my $v = $iter -> next ) { say join '' , @$v if (valid_combination($v)); }

Javier generates all tuples of $size length of @vowels . Many of these will be invalid, but his valid_combination checks each one in turn to see if it follows the rules of the task:

sub valid_combination { my $word = shift; # Faster than a regex for ( my $i = 0 ; $i < scalar(@$word) - 1 ; $i ++ ) { return 0 unless _check_letters($word, $i, 'a' , 'e' , 'i' ) && _check_letters($word, $i, 'e' , 'i' ) && _check_letters($word, $i, 'i' , 'a' , 'e' , 'o' , 'u' ) && _check_letters($word, $i, 'o' , 'a' , 'u' ) && _check_letters($word, $i, 'u' , 'o' , 'e' ); } return 1 ; }

The helper _check_letters is called five times per candidate word, once for each vowel, with a list of the allowed vowels that may follow.

# Check the folowing letters sub _check_letters { my ($word, $i, $letter, @checks) = @_; my $valid = 1 ; if ($word -> [$i] eq $letter) { $valid = 0 ; for my $check (@checks) { $valid = 1 if ($word -> [$i + 1 ] eq $check); } } return $valid; }

This is a unique solution. Despite the extra looping checking more than 95% invalid solutions at N=5 (99.4% at size 7), it performs better than I would have expected. N=7 takes around 0.7 seconds, vs 0.012 seconds for an iterative BFS solution.

Blog › Perl Weekly Challenge

Laurent Rosenfeld

Laurent Rosenfeld’s solution is another recursive DFS example:

my %successors = ( a => [ 'e' , 'i' ], e => [ 'i' ], i => [ qw /a e o u / ], o => [ 'a' , 'u' ], u => [ 'e' , 'o' ] ); my @vowels = sort keys %successors; my $error_msg = "Please pass a parameter between 1 and 5." ; my $str_size = shift or die $error_msg; die $error_msg unless $str_size =~ /^[1-5]$/ ; for my $start (@vowels) { make_str($str_size - 1 , $start, $start); } sub make_str { my ($left, $last, $string) = @_; say $string and return unless $left; # Stop the recursion for my $next (@{$successors{$last}}) { my $new_str = $string . $next; make_str($left - 1 , $next, $new_str); } }

Blog › Rotate Matrix and Vowel Strings

Lubos Kolouch

Lubos Kolouch’s solution uses List::Permute::Limit to generate initial permutations of vowels in his get_permutations sub:

sub get_permutations { my $count = shift; my @wovels = [ 'a' , 'e' , 'i' , 'o' , 'u' ]; my @result; my $iter = permute_iter(items => @wovels, nitems => $count); while ( my $ary = $iter -> ()) { say @$ary if check_perm($ary); } } get_permutations( 2 );

Those permutations are then checked against the task’s rules in check_perm :

my @ok_rules = ( 'ae' , 'ai' , 'ei' , 'ia' , 'ie' , 'io' , 'iu' , 'oa' , 'ou' , 'uo' , 'ue' ); my %ok_hash = map { $_ => 1 } @ok_rules; sub check_perm { my $perm = shift; my @perm_arr = @$perm; for ( 0 .. scalar @perm_arr - 2 ) { return 0 unless $ok_hash{$perm_arr[$_] . $perm_arr[ $_ + 1 ]}; } return 1 ; }

Markus Holzer

Markus Holzer’s solution revolves around the recursive build_str , called initially with the keys of %rules :

my %rules = ( a => [ 'e' , 'i' ], e => [ 'i' ], i => [ 'a' , 'e' , 'o' , 'u' ], o => [ 'a' , 'u' ], u => [ 'e' , 'o' ], ); main( shift @ARGV || 2 ); sub main ( $n ) { my @r; build_str( $_, $n, \ @r ) for ( sort keys %rules ); print join "

" , @r; } sub build_str ( $current, $n, $result ) { my $last = substr( $current, - 1 ); for ( $rules{$last} -> @ * ) { given ( $current . $_ ) { push $result -> @ * , $_ and next if length($_) == $n; build_str( $_, $n, $result ); } } }

Mohammad S Anwar

Mohammad S Anwar’s solution uses Algorithm::Combinatorics to get an iterator that generates $char_sets of the given $count length:

use Algorithm::Combinatorics qw(combinations) ; my $chars = [ qw(a e i o u) ]; my $iter = combinations($chars, $count); my $char_sets = [] ; while ( my $char = $iter -> next ) { push @$char_sets, join "" , @$char; }

There is a problem with this logic. Using combinations means you are selecting elements without repetition. So, for $count = 5 , there is only one possible combination: a e i o u . The results will be incorrect for every count. variations_with_repetition will return all sequences of five vowels, with repetition:

# RyanT my $char_sets = [ map { join '' , @$_ } variations_with_repetition($chars, $count) ];

Once the list of @$char_sets has been generated, Mohammad then checks each one against the following list of $rules regexps:

my $rules = [ qr/a(?=[ie])/ , qr/e(?=[i])/ , qr/i(?=[aeou])/ , qr/o(?=[au])/ , qr/u(?=[oe])/ ]; foreach my $char_set (@$char_sets) { my $pass = 0 ; foreach my $rule (@$rules) { if ($char_set =~ /$rule/ ) { $pass = 1 ; } } print "$char_set

" if ($pass); }

Unfortunately, these rules are too permissive, producing invalid words like uuuo . Notice the loop logic: $char_set passes if it matches any of the regexps in @$rules . Each regexp uses a zero-width positive lookahead, but that doesn’t matter, as each regexp is applied on its own. The problem is that these rules match valid sequences. There is nothing here to notice an invalid sequence, like uu .

To fix the logic with regexps, you have two basic options: match the entire string, or match invalid segments; i.e., an a must be followed by an i or e , so if it is followed by any other character, the string is invalid. The latter choice is probably easier to do.

Blog › BLOG: The Weekly Challenge #053

Pete Houston

Pete Houston’s solution is a concise recursive implementation:

my %rules = ( a => [ qw/e i/ ], e => [ qw/i/ ], i => [ qw/a e o u/ ], o => [ qw/a u/ ], u => [ qw/o e/ ] ); my $n = int shift @ARGV; die "1 <= N <= 5 is the restriction.

" unless $n > 0 && $n < 6 ; next_str ($_) for keys %rules; sub next_str { my $string = shift; return say $string if length $string == $n; for my $c (@{$rules{substr ($string, - 1 , 1 )}}) { next_str ( "$string$c" ); } }

Roger Bell West

Roger Bell West’s solution uses a BFS queue, and is decently concise as well:

my %tree = ( '' => [ qw(a e i o u) ], a => [ qw(e i) ], e => [ qw(i) ], i => [ qw(a e o u) ], o => [ qw(a u) ], u => [ qw(o e) ], ); print map { "$_

" } generate( 2 , \ %tree ); sub generate { my ( $len, $tree ) = @_; my @list = ( '' ); while ( 1 ) { if ( length( $list[ 0 ] ) == $len ) { last ; } my $r = shift @list; my $s = substr( $r, - 1 , 1 ) || '' ; foreach my $extension ( @{ $tree{$s} } ) { push @list, $r . $extension; } } return @list; }

Ruben Westerberg

Ruben Westerberg’s solution has me torn. Ruben supplies his own beautiful combinations sub:

sub combinations { my @combinations = (); my ($data,$size) = @_; my @indexes = ( 0 ) x ($size + 1 );; my $i = 0 ; until ($indexes[$size]) { my $count = List::Util::uniq(@indexes[ 0 .. $size - 1 ]); #print $count,"

";; push @combinations, [@$data[@indexes[ 0 .. $size - 1 ]]] if $count == $size; $indexes[ 0 ] ++ ; for ( 0 .. $size - 1 ) { if ($indexes[$_] != 0 and 0 == ($indexes[$_] % @$ data)) { $indexes[$_] = 0 ; $indexes[$_ + 1 ] ++ ; } } } @combinations; }

This combinations sub actually returns permutations, not combinations. Unfortunately, we don’t want permutations or combinations, but something like Algorithm::Combinatorics 's variations_with_repetition , which produces correct results when paired with Ruben’s loop, below. As written, the combinations sub only produces different orderings of the 5 vowels; it will never repeat them, but it needs to. This is fixable.

Here is Ruben’s main loop, which calls combinations and checks the results with regexps:

say for sort map {join "" ,@$_} grep { my $sum = 0 ; my $s = join '' , @$_; given ($s) { my @match; #<<Used to force list context $sum += @match = /a/g ; #<<Count all a $sum -= @match = ( /a[ie]|a$/g ); #<<make sure the rules match #<<Net sum is 0 for success $sum += @match = /e/g ; $sum -= @match = ( /ei|e$/g ); $sum += @match = /i/g ; $sum -= @match = /i[aeou]|i$/g ; $sum += @match = /o/g ; $sum -= @match = /o[au]|o$/g ; $sum += @match = /u/g ; $sum -= @match = /u[oe]|u$/g ; } $sum == 0 ; } combinations( \ @vowels,$n);

The @match array is used here “to force list context”. You can do the same thing without the named array using =()= . For example:

$sum += () = a / g;

Ryan Thompson

My solution has two variations, but first the %edges we’ll use for both:

# Follow rules. Basically graph edges. my %edges = ( a => [ 'i' , 'e' ], e => [ 'i' ], i => [ 'u' , 'o' , 'e' , 'a' ], o => [ 'u' , 'a' ], u => [ 'e' , 'o' ] );

The first example is a BFS queue implementation:

sub vowel_string { my ($len) = @_; my @queue = sort keys %edges; # Pre-load queue my @vstrs; while ( my $str = shift @queue) { push @vstrs, $str and edges if $len <= length $str; push @queue, $str . $_ for @{$edges{ substr $str, - 1 }} } @vstrs; } say for vowel_string( 6 );

For the second variation, I made an iterator version, which returns a code ref that can be called repeatedly to get the next element in the sequence:

sub vowel_iter { my ($len) = @_; my @queue = sort keys %edges; sub { while ( my $str = shift @queue) { return $str if $len <= length $str; push @queue, $str . $_ for @{$edges{ substr $str, - 1 }} } } } my $it = vowel_iter( 3 ); say while $_ = $it -> ();

Both versions have their merits, depending on the application, which is why I included them both.

Blog › PWC 053 › Vowel Strings

Saif Ahmed

Saif Ahmed’s solution uses a BFS queue as well:

sub vowelStrings { my $target = shift; my %following = ( # hash containing lists of valid following vowels a => [ 'e' , 'i' ], e => [ 'i' ], i => [ 'a' , 'e' , 'o' , 'u' ], o => [ 'a' , 'u' ], u => [ 'o' , 'e' ], ); my @list = ( qw{a e i o u } ); # start with list of vowels while ( length $list[ 0 ] < $target ) { my $str = shift @list; push @list, map { $str . $_ } @{ $following{ substr( $str, - 1 , 1 ) } }; } return @list,; }

User Person

User Person’s solution does something a little different, with Math::Int2Base (converts to/from arbitrary bases):

use Math::Int2Base qw( int2base base2int ) ; my @vowels = qw{ a e i o u } ; my $MAX = '4' x $num; my $j = 0 ; for ( my $i = 0 ; $j <= $MAX; ++ $i) { $j = int2base($i, 5 ); $j = sprintf "%0${num}d" , $j; my $string; foreach (split( // ,$j)){ $string .= $vowels[$_]; }

In the C-style for loop, the loop variable ( $i ) is converted to base-5, as there are five vowels. This allows direct indexing within @vowels . All of this is an easy way to emulate the variations_with_repetition function we’ve seen previously.

To see whether $string is a valid vowel string, it is checked against five different regexps in turn:

if ( $string =~ m{a[^ei]} or $string =~ m{e[^i]} or $string =~ m{i[^aeou]} or $string =~ m{o[^au]} or $string =~ m{u[^oe]} ) { next ; } else { print "$string

" ; } }

If any of these regexps match, the string is rejected. For example, a[^ei] means that if a string contains an a followed by anything other than an e or an i , it is rejected.

Wanderdoc

Wanderdoc’s solution uses Algorithm::Combinatorics again, this time using variations .

use Algorithm::Combinatorics qw(variations) ; use Getopt::Std; my @vowels = qw(a e i o u) ; my @pos_patterns = ( qr/a[ei]/ , qr/ei/ , qr/i[aeou]/ , qr/o[au]/ , qr/u[oe]/ ); my @neg_patterns = ( qr/a(?=[aou])/ , qr/e(?=[aeou])/ , qr/i(?=i)/ , qr/o(?=[eio])/ , qr/u(?=[aiu])/ ); my $iter = variations( \ @vowels, $options{n}); my %already_found;

Unfortunately, variations does not include repetitions, and we need repetitions to generate valid strings such as ueiu , so Wanderdoc’s program does not generate all valid solutions. The fix is easy, though: just use variations_with_repetition instead.

Here is the loop, which uses the iterator semantics from Algorithm::Combinatorics :

VAR: while ( my $c = $iter -> next ) { my $str = join( '' , @$c ); for my $pp (@pos_patterns) { if ( $str =~ /$pp/ ) { for my $np (@neg_patterns) { next VAR if $str =~ /$np/ ; } # A string with length > 2 can match > 1 patterns. $already_found{$str} ++ ; print $str, $/ if 1 == $already_found{$str}; } } }

Note the use of positive and negative patterns ( @pos_patterns and @neg_patterns ) to reject invalid strings.

Yet Ebreo

Yet Ebreo’s solution is a one-liner based around regexes and glob :

! ( /a[^ei]/ || /e[^i]/ || /i[^aeou]/ || /o[^au]/ || /u[^oe]/ ) && say for glob "{a,e,i,o,u}" x ($ARGV[ 0 ] || 1 );

The use of glob here is fantastic.

See Also

Blogs this week:

Cheok-Yin Fung › Tree as a tool for enumeration | Rotation in R^2

Dave Jacoby › Rotate Your Matrix and String Your Vowels

E. Choroba › Perl Weekly Challenge 053: Rotate Matrix and Vowel Strings

Jaldhar H. Vyas › Jaldhar’s Week #053 Blog

Javier Luque › 053 – Perl Weekly Challenge

Laurent Rosenfeld › Rotate Matrix and Vowel Strings

Mohammad S Anwar › BLOG: The Weekly Challenge #053

Ryan Thompson › Matrix Rotation | Vowel Strings