Merge pull request #6309 from pjcs00/wk170

Week 170 submission

3 files changed, 147 insertions, 0 deletions

diff --git a/challenge-170/peter-campbell-smith/blog.txt b/challenge-170/peter-campbell-smith/blog.txt
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+https://pjcs-pwc.blogspot.com/2022/06/primorials-and-kronecker-products.html
diff --git a/challenge-170/peter-campbell-smith/perl/ch-1.pl b/challenge-170/peter-campbell-smith/perl/ch-1.pl
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+#!/usr/bin/perl
+
+# Peter Campbell Smith - 2022-06-20
+# PWC 170 task 1
+
+use v5.28;
+use strict;
+use warnings;
+use utf8;
+
+# Write a script to generate first 10 Primorial Numbers.
+# Primorial numbers are those formed by multiplying successive prime numbers.
+
+# Blog: https://pjcs-pwc.blogspot.com/2022/06/primorials-and-kronecker-products.html
+
+my (@primes, $j, $p, @pm, $k);
+
+@primes = ();
+$p = 1;
+$pm[0] = 1;
+say qq[P(0) = 1];
+
+OUTER: for $j (2 .. 99999) {
+	for $k (@primes) {
+		next OUTER if $j % $k == 0;   # $j is not prime if divisible by a smaller prime
+	}
+	
+	# found a prime, create next primorial
+	push @primes, $j;
+	$pm[$p] = $pm[$p - 1] * $j;
+	say qq[P($p) = $pm[$p]];
+	$p ++;
+	exit if $p == 10;
+}
diff --git a/challenge-170/peter-campbell-smith/perl/ch-2.pl b/challenge-170/peter-campbell-smith/perl/ch-2.pl
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+#!/usr/bin/perl
+
+# Peter Campbell Smith - 2022-06-20
+# PWC 170 task 2
+
+use v5.28;
+use strict;
+use warnings;
+use utf8;
+
+# You are given 2 matrices.
+# Write a script to generate the Kronecker Product of the given 2 matrices.
+
+# Blog: https://pjcs-pwc.blogspot.com/2022/06/primorials-and-kronecker-products.html
+
+my ($test, $A, $B, $K, $m, $n, $p, $q, $i, $j, $i_quo_p, $i_rem_p, $j_quo_q, $j_rem_q);
+
+for $test (1, 2) {
+	
+	if ($test == 1) {   # Mohammad's example
+
+		$A = [[ 1, 2 ],
+			  [ 3, 4 ]];
+
+		$B = [[ 5, 6 ],
+			  [ 7, 8 ]];
+			  
+	} else {   # Wikipedia's 2nd example
+
+		$A = [[ 1, -4, 7],
+			  [-2,  3, 3]];
+			  
+		$B = [[8, -9, -6,  5],
+			  [1, -3, -4,  7],
+			  [2,  8, -8, -3],
+			  [1,  2, -5, -1]];
+	}
+	
+	# display input
+	show('A', $A);
+	show('B', $B);
+		  
+	$m = scalar(@$A);			# no of rows in A (0 to $m - 1)
+	$n = scalar(@{$A->[0]});   	# no of columns in A
+	$p = scalar(@$B);			# no of rows in B 
+	$q = scalar(@{$B->[0]});	# no of columns in B
+
+	# loop over the rows and cols of product matrix $K ($m * $p rows, $n * $q cols)
+	for $i (0 .. $m * $p - 1) {
+		for $j (0 .. $n * $q - 1) {
+			
+			# get the quotient and remainder on dividing i by p and j by q
+			($i_quo_p, $i_rem_p) = quorem($i, $p);
+			($j_quo_q, $j_rem_q) = quorem($j, $q);
+			
+			# Wikipedia formula for element i, j of K
+			$K->[$i]->[$j] = $A->[$i_quo_p]->[$j_quo_q] * $B->[$i_rem_p]->[$j_rem_q];
+		}
+	}
+	
+	# display the result
+	show('A x B', $K);
+	print qq[-----\n\n];
+}
+		
+sub quorem {
+
+	my ($dividend, $divisor, $quotient, $remainder);
+
+	# returns the integer quotient and remainder from dividend / divisor (both integers > 0)
+	$dividend = shift;
+	$divisor = shift;
+	
+	$quotient = int($dividend / $divisor);
+	$remainder = $dividend - $quotient * $divisor;
+	
+	return ($quotient, $remainder);
+}
+
+sub show {
+	
+	my ($caption, $M, $margin, $i, $j, $this_width, $cell_width);
+	
+	# pretty print matrix
+	($caption, $M) = @_;
+	
+	$caption .= ' = ';
+	$margin = length($caption);
+	
+	# first pass to get width of cells
+	$cell_width = 0;
+	for $i (0 .. scalar(@$M) - 1) {
+		for $j (0 .. scalar(@{$M->[0]}) - 1) {
+			$this_width = length($M->[$i]->[$j]);
+			$cell_width = $this_width if $this_width > $cell_width;
+		}
+	}
+	$cell_width += 1;
+	
+	# second pass to print out - loop over rows
+	for $i (0 .. scalar(@$M) - 1) {
+		print qq{$caption\[};       # first line
+		$caption = ' ' x $margin;   # subsequent lines
+		
+		# and over columns, padding each value to $cell_width
+		for $j (0 .. scalar(@{$M->[0]}) - 1) {
+			printf("%${cell_width}s", $M->[$i]->[$j]);
+		}
+		print qq[ \]\n];
+	}
+	print qq[\n];
+}