Data commit

Task/Pascals-triangle-Puzzle/Perl/pascals-triangle-puzzle.pl

@@ -0,0 +1,40 @@
+# set up triangle
+my $rows = 5;
+my @tri = map { [ map { {x=>0,z=>0,v=>0,rhs=>undef} } 1..$_ ] } 1..$rows;
+$tri[0][0]{rhs} = 151;
+$tri[2][0]{rhs} = 40;
+$tri[4][0]{x} = 1;
+$tri[4][1]{v} = 11;
+$tri[4][2]{x} = 1;
+$tri[4][2]{z} = 1;
+$tri[4][3]{v} = 4;
+$tri[4][4]{z} = 1;
+
+# aggregate from bottom to top
+for my $row ( reverse 0..@tri-2 ) {
+    for my $col ( 0..@{$tri[$row]}-1 ){
+        $tri[$row][$col]{$_} = $tri[$row+1][$col]{$_}+$tri[$row+1][$col+1]{$_} for 'x','z','v';
+    }
+}
+# find equations
+my @eqn;
+for my $row ( @tri ) {
+    for my $col ( @$row ){
+        push @eqn, [ $$col{x}, $$col{z}, $$col{rhs}-$$col{v} ] if defined $$col{rhs};
+    }
+}
+# print equations
+print "Equations:\n";
+print "  x +   z = y\n";
+printf "%d x + %d z = %d\n", @$_ for @eqn;
+# solve
+my $f = $eqn[0][1] / $eqn[1][1];
+$eqn[0][$_] -=  $f * $eqn[1][$_] for 0..2;
+$f = $eqn[1][0] / $eqn[0][0];
+$eqn[1][$_] -=  $f * $eqn[0][$_] for 0..2;
+# print solution
+print "Solution:\n";
+my $x = $eqn[0][2]/$eqn[0][0];
+my $z = $eqn[1][2]/$eqn[1][1];
+my $y = $x+$z;
+printf "x=%d, y=%d, z=%d\n", $x, $y, $z;