Merge pull request #5564 from pjcs00/wk149

My solutions for week 149

3 files changed, 130 insertions, 0 deletions

diff --git a/challenge-149/peter-campbell-smith/blog.txt b/challenge-149/peter-campbell-smith/blog.txt
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+https://www.blogger.com/blog/post/edit/6451878819927982087/2815995642365863231
diff --git a/challenge-149/peter-campbell-smith/perl/ch-1.pl b/challenge-149/peter-campbell-smith/perl/ch-1.pl
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+#!/usr/bin/perl
+
+# Peter Campbell Smith - 2022-01-24
+# PWC 149 task 2
+
+use v5.28;
+use strict;
+use warnings;
+use utf8;
+
+# Given an input $n, generate the first $n numbers for which the sum of their digits is a Fibonacci number.
+
+# Note: eval(join('+', split(//, $i))) splits $i into individual digits, joins them with '+' signs and 
+# evaluates the resulting sum of the digits.
+
+my ($n, $i, @fibs, @results);
+
+$n = 20;
+
+@fibs = (0, 1);   # initial fibonacci series
+@results = ();
+
+# count up until we have the required quantity of results
+for ($i = 0; $#results < $n - 1; $i++) {
+	push(@results, $i) if is_a_fib(eval(join('+', split(//, $i))));   # see note above
+}
+
+say qq[f($n) = (] . join(', ', @results) . ')';
+
+sub is_a_fib {
+	
+	# returns true if the argument is a fibonacci number
+	
+	my ($arg, $i);
+	$arg = $_[0];
+	
+	# make sure @fibs is long enough
+	while ($arg > $fibs[$#fibs]) {
+		$fibs[$#fibs + 1] = $fibs[$#fibs] + $fibs[$#fibs - 1];   # add one fib to @fibs
+	}
+	
+	# check if $arg is in @fibs (binary chop would be faster but why bother?)
+	for ($i = $#fibs; $i >= 0; $i--) {
+		return 1 if $arg == $fibs[$i];
+	}
+	return 0;
+}
+		
+
+
diff --git a/challenge-149/peter-campbell-smith/perl/ch-2.pl b/challenge-149/peter-campbell-smith/perl/ch-2.pl
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+#!/usr/bin/perl
+
+# Peter Campbell Smith - 2022-01-24
+# PWC 149 task 2
+
+use v5.28;
+use strict;
+use warnings;
+use utf8;
+
+# Given a number base, derive the largest perfect square with no repeated digits and return 
+# it as a string.
+
+# The largest non-repeating number in eg base 4 is: 3210 = (3 * 4**3) + (2 * 4**2) + 1 * (4**1) + (0 * 4**0)
+# So the largest non-repeating number in base n is: sum (j = 1 .. n-1) of j * n**j
+
+my ($i, $square, $string, $test, @tests, $largest, $start);
+
+# bases to try
+@tests = (2, 4, 10, 12, 16, 17);
+
+for $test (@tests) {
+	
+	# get largest possible number in base $test with no repeating digits (see above)
+	$largest = 0;
+	for $i (1 .. $test - 1) {
+		$largest += $i * $test ** $i;
+	}
+	
+	# can't do this if $largest can't be represented as an integer
+	if ($largest > ~1 + 1) {
+		say qq[$test is too large];
+		next;
+	}
+	
+	# find the largest square <= $largest
+	$start = int(sqrt($largest));
+	
+	# generate squares down from there
+	for ($i = $start; $i > 0; $i--) {
+		$square = $i * $i;
+		$string = basify($square, $test);    # convert to required format (eg 123AB)
+		last if no_repeats($string);         # the answer!
+	}
+	say qq[f($test) = $string]
+}
+
+sub basify {   # ($integer, $base)
+
+	my ($base, $digit, $digits, $integer, $result);
+	
+	# converts $integer to 123AB representation in base $base
+	
+	($integer, $base) = @_;
+	$digits = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ';
+	$result = '';
+	
+	# strip digits 1 at a time
+	while ($integer) {
+		$digit = $integer % $base;
+		$integer = ($integer - $digit) / $base;
+		$result = substr($digits, $digit, 1) . $result;
+	}
+	return $result;
+}
+
+sub no_repeats {   # ($string)
+
+	my ($string, %seen);
+	$string = $_[0];
+
+	while ($string =~ m|(.)|g) {
+		return 0 if $seen{$1};
+		$seen{$1} = 1;
+	}
+	return 1;
+}
+
+