Finding Squares in Matrices
I don't usually take part in the Perl Weekly Challenge but one of this week's challenges caught my eye. I thought it could be a fun thing to attempt and decided to use Zydeco to help solve it.
The problem is that you're given a matrix of 0s and 1s:
You need to find any squares (equal length sides) where all four corners are 1s:
Arguably it's not a task best suited for object-oriented programming; a more functional style might suit the problem better, but this is how I did it.
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use strict; | |
use warnings; | |
package Weekly84 { | |
use Zydeco; | |
class Matrix { | |
# public required attribute | |
has cells! ( type => ArrayRef[ArrayRef[Bool, 1], 1] ); | |
# lazy attributes | |
has n, m ( is => lazy, isa => PositiveInt, init_arg => undef ); | |
method _build_m = scalar @{ $self->cells }; | |
method _build_n = scalar @{ $self->cells->[0] }; | |
# private method which acts as helper for factories | |
method $process ( $text ) { | |
[ map [ /([01])/g ], grep /[01]/, split /\n/, $text ] | |
} | |
# factories to make a new Matrix object from an ArrayRef or Str | |
multi factory new_matrix ( ArrayRef $cells ) | |
= $class->new( cells => $cells ); | |
multi factory new_matrix ( Str $text ) | |
= $class->new( cells => $class->$process($text) ); | |
# method to fetch a cell | |
method cell ( PositiveInt $x, PositiveInt $y ) { | |
confess 'Out of range' if $x > $self->m; | |
confess 'Out of range' if $y > $self->n; | |
$self->cells->[$x-1][$y-1]; | |
} | |
# detect a square with size $size and top left corner at $x, $y | |
method has_square ( Int $x, Int $y, PositiveInt $size ) { | |
$self->cell( $x, $y ) and | |
$self->cell( $x+$size, $y ) and | |
$self->cell( $x+$size, $y+$size ) and | |
$self->cell( $x, $y+$size ); | |
} | |
# find all squares within the matrix | |
method find_squares ( Bool $verbose = false ) { | |
my $smallest_axis = ( $self->m < $self->n ) ? 'm' : 'n'; | |
my $max_size = $self->$smallest_axis(); | |
my @found; | |
X: for my $x ( 1 .. $self->m ) { | |
Y: for my $y ( 1 .. $self->n ) { | |
SIZE: for my $size ( 1 .. $max_size ) { | |
next Y if $size + $x > $self->m; | |
next Y if $size + $y > $self->n; | |
if ( $self->has_square( $x, $y, $size ) ) { | |
say "Found size $size square at $x, $y." if $verbose; | |
push @found, [ $x, $y, $size ]; | |
} | |
} | |
} | |
} | |
say "Found ", scalar( @found ), " squares." if $verbose; | |
return @found; | |
} | |
} | |
} | |
'Weekly84'->new_matrix( <<'MATRIX' )->find_squares(1); | |
[ 0 1 0 1 0 1 0 0 1 ] | |
[ 1 0 1 0 0 0 0 0 0 ] | |
[ 1 1 0 1 0 0 0 0 0 ] | |
[ 1 1 1 1 0 1 0 0 1 ] | |
MATRIX |
Sample output:
Found size 2 square at 1, 2. Found size 3 square at 1, 6. Found size 2 square at 2, 1. Found size 1 square at 3, 1. Found 4 squares.
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