Trying to Develop PostFix Notation in Tree Using Perl - perl

Question

I'm using Perl to run through a tree, and then calculate the leaf nodes of the tree using the internal nodes as operators. I want to be able to print this in a postfix manner, and I managed to this this fairly easily with the basic operands (simply call the left and right nodes respectively before calling the parent) but I am having trouble producing the desired output for an average function. I don't have any trouble printing the actual result of the calculation, but I want to be able to print the operators and operands in postfix notation.
For example, 1 + average(3, 4, 5) will be shown as 1 ; 3 4 5 average +.
Here is my code:
use strict;
use warnings;
use Data::Dumper;
$Data::Dumper::Indent = 0;
$Data::Dumper::Terse = 1;
my $debug = 0;
# an arithmetic expression tree is a reference to a list, which can
# be of two kinds as follows:
# [ 'leaf', value ]
# [ 'internal', operation, leftarg, rightarg ]
# Evaluate($ex) takes an arithmetic expression tree and returns its
# evaluated value.
sub Evaluate {
my ($ex) = #_;
$debug and
print "evaluating: ", Dumper($ex), "\n";
# the kind of node is given in the first element of the array
my $node_type = $ex->[0];
# if a leaf, then the value is a number
if ( $node_type eq 'leaf' ) {
# base case
my $value = $ex->[1];
$debug and
print "returning leaf: $value\n";
return $value;
}
# if not a leaf, then is internal,
if ( $node_type ne 'internal' ) {
die "Eval: Strange node type '$node_type' when evaluating tree";
}
# should now have an operation and two arguments
my $operation = $ex->[1];
my $left_ex = $ex->[2];
my $right_ex = $ex->[3];
# evaluate the left and right arguments;
my $left_value = Evaluate($left_ex);
my $right_value = Evaluate($right_ex);
# if any arguments are undefined, our value is undefined.
return undef unless
defined($left_value) and defined($right_value);
my $result;
# or do it explicitly for the required operators ...
if ($operation eq 'average') {
$result = ($left_value + $right_value) / 2;
}
if ($operation eq '+') {
$result = $left_value + $right_value;
} elsif ($operation eq '-') {
$result = $left_value - $right_value;
} elsif ($operation eq '*') {
$result = $left_value * $right_value;
} elsif ($operation eq 'div') {
if ($right_value != 0 ) {
$result = int ($left_value / $right_value);
} else {
$result = undef;
}
} elsif ($operation eq 'mod') {
$result = $left_value % $right_value;
} elsif ($operation eq '/') {
if ( $right_value != 0 ) {
$result = $left_value / $right_value;
}
else {
$result = undef;
}
}
$debug and
print "returning '$operation' on $left_value and $right_value result: $result\n";
return $result;
}
# Display($ex, $style) takes an arithmetic expression tree and a style
# parameter ('infix' or 'postfix') and returns a string that represents
# printable form of the expression in the given style.
sub Display {
my ($ex, $style) = #_;
# the kind of node is given in the first element of the array
my $node_type = $ex->[0];
# if a leaf, then the value is a number
if ( $node_type eq 'leaf' ) {
# base case
my $value = $ex->[1];
return $value;
}
# if not a leaf, then is internal,
if ( $node_type ne 'internal' ) {
die "Display: Strange node type '$node_type' when evaluating tree";
}
# should now have an operation and two arguments
my $operation = $ex->[1];
my $left_ex = $ex->[2];
my $right_ex = $ex->[3];
# evaluate the left and right arguments;
my $left_value = Display($left_ex, $style);
my $right_value = Display($right_ex, $style);
my $result;
if ($operation ne 'average') {
$result = "($left_value $operation $right_value) \n $left_value $right_value $operation";
} else {
$result = "($left_value $operation $right_value) \n $left_value $right_value $operation";
}
return $result;
}
# module end;
1;
And here is a test:
use strict;
use warnings;
use Display;
use arith;
my $ex1 = [ 'leaf', 42];
my $ex2 = [ 'internal', '+', [ 'leaf', 42], [ 'leaf', 10 ] ];
my $ex3 = [ 'internal', 'average', $ex2, [ 'leaf', 1 ] ];
print "ex1 is ", Evaluate($ex1), "\n";
print "ex1: ", Display($ex1), "\n";
print "\n";
print "ex2 is ", Evaluate($ex2), "\n";
print "ex2: ", Display($ex2), "\n";
print "\n";
print "ex3 is ", Evaluate($ex3), "\n";
print "ex3: ", Display($ex3), "\n";
print "\n";
Display::Render(\$ex3);
In order to do this, I realize I will have to change the subroutine "Display", but I'm not sure how to get the output --> value value ; #to indicate values that aren't averaged# value value average operand etc.
Any ideas?

Answer 1

I am not 100% sure that I understand your problem, but here is a cleanup / improvement of your two functions:
my %ops = ( # dispatch table for operations
average => sub {my $acc; $acc += $_ for #_; $acc / #_},
'+' => sub {$_[0] + $_[1]},
'-' => sub {$_[0] - $_[1]},
'*' => sub {$_[0] * $_[1]},
'mod' => sub {$_[0] % $_[1]},
(map {$_ => sub {$_[1] ? $_[0] / $_[1] : undef}} qw (/ div)),
);
sub Evaluate {
my $ex = shift;
print "evaluating: ", Dumper($ex), "\n" if $debug;
my $node_type = $ex->[0];
if ( $node_type eq 'leaf' ) {
print "returning leaf: $$ex[1]\n" if $debug;
return $$ex[1];
}
elsif ( $node_type ne 'internal' ) {
die "Eval: Strange node type '$node_type' when evaluating tree";
}
my $operation = $ex->[1];
my #values = map {Evaluate($_)} #$ex[2 .. $#$ex];
defined or return for #values;
if (my $op = $ops{$operation}) {
return $op->(#values);
} else {
print "operation $operation not found\n";
return undef;
}
}
Here the large if/elsif block is replaced with a dispatch table. This allows you to separate the logic from the parser. I have also replaced the $left_value and $right_value variables with the #values array, allowing your code to scale to n-arity operations (like average).
The following Display function has also been updated to handle n-arity operations:
my %is_infix = map {$_ => 1} qw( * + / - );
sub Display {
my ($ex, $style) = #_;
my $node_type = $ex->[0];
# if a leaf, then the value is a number
if ( $node_type eq 'leaf' ) {
return $$ex[1];
}
# if not a leaf, then is internal,
if ( $node_type ne 'internal' ) {
die "Display: Strange node type '$node_type' when evaluating tree";
}
# should now have an operation and n arguments
my $operation = $ex->[1];
if ($style and $style eq 'infix') {
my #values = map {Display($_, $style)} #$ex[2 .. $#$ex];
if ($is_infix{$operation}) {
return "$values[0] $operation $values[1]"
} else {
local $" = ', '; # "
return "$operation( #values )"
}
} else { # postfix by default
my #out;
for (#$ex[2 .. $#$ex]) {
if (#out and $_->[0] eq 'internal') {
push #out, ';'
}
push #out, Display($_, $style)
}
return join ' ' => #out, $operation;
}
}
You can call Display as Display($tree) or Display($tree, 'postfix') for postfix notation. And Display($tree, 'infix') for the infix notation.
ex1 is 42
ex1: 42
ex1: 42
ex2 is 52
ex2: 42 10 +
ex2: 42 + 10
ex3 is 26.5
ex3: 42 10 + 1 average
ex3: average( 42 + 10, 1 )
Which I believe is what you are looking for.
Finally, using your first example 1 + average(3, 4, 5):
my $avg = ['internal', 'average', [leaf => 3], [leaf => 4], [leaf => 5] ];
my $ex4 = ['internal', '+', [leaf => 1], $avg ];
print "ex4 is ", Evaluate($ex4), "\n";
print "ex4: ", Display($ex4), "\n";
print "ex4: ", Display($ex4, 'infix'), "\n";
print "\n";
which prints:
ex4 is 5
ex4: 1 ; 3 4 5 average +
ex4: 1 + average( 3, 4, 5 )

Answer 2

Maybe try AlgebraicToRPN?