Two lines are indeed enough.

# Build a hash of word counts
foreach ( map @$_, @all ) { $words{$_} ++ }

# Create a list of arrays showing repeats
@out = map { [ map $words{$_} > 1 ? 1 : 0, @$_ ] } @all;
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With regards to map, I find it easiest to think of it as a rolled-up form of the common foreach ... push idiom:

# List processing with foreach/push  
foreach ( @input ) {
  push @out, lc($_);
}
print @out;

# Equivalent "rolled-up" map expression:
print map { lc($_) } @input;
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