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