# RogerBW's Blog

 The Weekly Challenge 220: Square Commoners 11 June 2023 I’ve been doing the Weekly Challenges. The latest involved word breakdowns and perfect squares. (Note that this is open until 11 June 2023.) Task 1: Common Characters You are given a list of words. Write a script to return the list of common characters (sorted alphabeticall) found in every word of the given list. Some languages have sets with full function support. Some don't. I took `word2set` from challenge 216 task #1. Python: ``````def word2set(word): r = set() for c in word.lower(): if c >= 'a' and c <= 'z': r.add(c) return r def commoncharacters(lst): c = word2set(lst[0]) for w in lst[1:]: c = c.intersection(word2set(w)) return sorted(list(c)) `````` Probably this could be done with a `reduce` or equivalent, but that's not really part of my standard mental programming toolbox. For languages like Perl, the set intersection is more a matter of looking through the keys of `c` and deleting any that don't appear in the set from the other word. Task 2: Squareful You are given an array of integers, @ints. An array is squareful if the sum of every pair of adjacent elements is a perfect square. Write a script to find all the permutations of the given array that are squareful. For languages without permutation readily available, I borrowed code from challenge 154 task #1. More interesting is the way that in some languages an array is a perfectly good set key and a thing that can be sorted; in others, rather less so. In some cases I changed the sequence into a base-`X` number (`X` being one higher than the highest value) for easier manipulation, then broke it down again for output. I decided to make things a bit more interesting by having a squareness-tester that automatically extended itself as needed. A shorthand function for squaring things: ``````sub squared(\$a) { return \$a * \$a; } `````` Sequence decoder (base-`X` number to sequence): ``````sub decode(\$a0, \$base) { my @eq; my \$a = \$a0; while (\$a > 0) { unshift @eq, \$a % \$base; \$a = int(\$a / \$base); } return \@eq; } `````` Sequence encoder (sequence to base-X number): ``````sub encode(\$sq, \$base) { my \$a = 0; foreach my \$v (@{\$sq}) { \$a *= \$base; \$a += \$v; } return \$a; } `````` The main function. Set up hashest (sets) to catch results, and for the self-extending squares list. ``````sub squareful(\$lst) { my %results; my %squares; `````` Determine the base for sequence encdding. `````` my \$base = max(@{\$lst}) + 1; `````` For each possible permutation of input digits: `````` my \$p = Algorithm::Permute->new(\$lst); while (my @la = \$p->next) { `````` Only one adjacent combination need not be squareful to disqualify this permutation. `````` my \$squareful = 1; `````` Go through the permutation by overlapping digit pairs. `````` foreach my \$i (0 .. \$#la - 1) { my \$cs = \$la[\$i] + \$la[\$i + 1]; `````` What's the highest perfect square we already know about? (Taking the length of the hash and squaring it should be faster than retrieving its maximum value.) `````` my \$mx = squared(scalar keys %squares); `````` If the value under test is higher, extend the `squares` hash until it isn't. `````` while (\$cs > \$mx) { \$mx = squared((scalar keys %squares) + 1); \$squares{\$mx} = 1; } `````` If it's not a perfect square, bail out on this permutation. `````` unless (exists \$squares{\$cs}) { \$squareful = 0; last; } } `````` If this was a squareful permutation, code it up. (If the permutor produces duplicates, this will get rid of them.) `````` if (\$squareful) { \$results{encode(\@la, \$base)} = 1; } } `````` Now take those results, sort them, decode them, and stick them in the output list. `````` return [map {decode(\$_, \$base)} sort {\$a <=> \$b} keys %results]; } `````` Full code on github. Comments on this post are now closed. 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