##DESCRIPTION
##  stuff here
##ENDDESCRIPTION

##KEYWORDS('tree', 'forest', 'word3')

## DBsubject('Graph theory')
## DBchapter('Trees')


## Level('2')
## Date('06/08/2023')   
## Author('Cynthia Loten')
## Institution('University of the Fraser Valley')
## TitleText1('Discrete and Combinatorial Mathematics')
## EditionText1('5')
## AuthorText1('Grimaldi')
## Section1('12.2')



########################################################################

DOCUMENT();      

loadMacros(
   "PGstandard.pl",     # Standard macros for PG language
   "MathObjects.pl",
   "PGML.pl",
   "PGtikz.pl", 
#   "niceTables.pl",
   "parserRadioButtons.pl",
 #  "unionTables.pl",
   "PGnauGraphCatalog.pl",
   "PGnauGraphtheory.pl",
   "PGcourse.pl",      # Customization file for the course
);

#PGnauGraphtheory.pl loads PGnauGraphics.pl
#PGnuaGraphpics.pl loads PGgraphmacros.pl and unionTables.pl and PGchoicemacros.pl
#PGnuaGraphpics.pl contains checkbox_table and radio_table
# Print problem number and point value (weight) for the problem
TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect, set to 0 for no information
$showPartialCorrectAnswers = 1;

##############################################################
#
#  Setup
#
#
Context("Numeric");
Context()->flags->set(tolerance => 0.01);

$pick = random(0,3);
#$pick = 0; 
# pick 5 letters from p to z
@possible_vars = ('p' .. 'z');
@vars = map { splice(@possible_vars, random(0, $#possible_vars), 1) } 1..4;

#### ((x + y) / u ) * v
$exp[0] = "(($vars[0] + $vars[1]) / $vars[2] ) * $vars[3]";
$pn[0] = "* / + $vars[0] $vars[1] $vars[2] $vars[3]";
$tree[0]= createTikZImage(); 
$tree[0]->BEGIN_TIKZ 
  [thick, every node/.style = {fill = green!20, circle, inner sep = 2pt},
  level 1/.style = {sibling distance = 25mm},
  level 2/.style = {sibling distance = 15mm},
  level 3/.style = {sibling distance = 13mm}, ]
   \node {\(*\)}
     child {node {/}
       child {node{\(+\)}
         child {node{\($vars[0]\)}}
         child {node{\($vars[1]\)}}        
       }
      child {node{\($vars[2]\)}}
     }
     child {node {\($vars[3]\)} };
END_TIKZ 
#using testing suggestion 
$image[0] = image($tree[0], width => 150, tex_size => 500); #  width was 300, text size was 1000 

####  (x + y) / (u  * v )
$exp[1] = "($vars[0] + $vars[1]) / ($vars[2]  * $vars[3])";
$pn[1] = "/ + $vars[0] $vars[1] * $vars[2] $vars[3]";
$tree[1]= createTikZImage(); 
$tree[1]->BEGIN_TIKZ 
  [thick, every node/.style = {fill = green!20, circle, inner sep = 2pt},
  level 1/.style = {sibling distance = 25mm},
  level 2/.style = {sibling distance = 15mm},
  level 3/.style = {sibling distance = 13mm}, ]
  \node {/}
    child {node {\(+\)}
      child {node {\($vars[0]\)}}
      child {node {\($vars[1]\)}}
    }
    child {node {\(*\)}
      child {node{\( $vars[2]\)}}
      child {node{\( $vars[3]\)}}
    };
END_TIKZ 
#using testing suggestion 
$image[1] = image($tree[1], width => 150, tex_size => 500); #  width was 300, text size was 1000 

####  x + ((y/u) * v)
$exp[2] = "$vars[0] + (( $vars[1] / $vars[2] ) * $vars[3])";
$pn[2] = "+ $vars[0] * / $vars[1] $vars[2] $vars[3]";
$tree[2]= createTikZImage(); 
$tree[2]->BEGIN_TIKZ 
  [thick, every node/.style = {fill = green!20, circle, inner sep = 2pt},
  level 1/.style = {sibling distance = 25mm},
  level 2/.style = {sibling distance = 15mm},
  level 3/.style = {sibling distance = 13mm}, ]
  \node {\(+\)}
    child {node {\($vars[0]\)}}
    child {node {\(*\)}
      child {node{ / }
        child {node{\($vars[1]\) }}
        child {node{\( $vars[2]\)}}
      }
      child {node {\( $vars[3]\)}}
    };
END_TIKZ 
#using testing suggestion 
$image[2] = image($tree[2], width => 150, tex_size => 500); #  width was 300, text size was 1000 

####  x + (y / (u *v))
$exp[3] = "$vars[0] + ($vars[1] / ($vars[2]  * $vars[3]))";
$pn[3] = "+ $vars[0] / $vars[1] * $vars[2] $vars[3]";
$tree[3]= createTikZImage(); 
$tree[3]->BEGIN_TIKZ 
  [thick, every node/.style = {fill = green!20, circle, inner sep = 2pt},
  level 1/.style = {sibling distance = 25mm},
  level 2/.style = {sibling distance = 15mm},
  level 3/.style = {sibling distance = 13mm}, ]
  \node {\(+\)}
    child {node {\($vars[0]\)}}
    child {node {/ }
      child {node { \($vars[1]\) } }
      child {node {\(*\)}
        child {node{\($vars[2]\) }}
        child {node{\( $vars[3]\)}}
      }
    };
END_TIKZ 
#using testing suggestion 
$image[3] = image($tree[3], width => 150, tex_size => 500); #  width was 300, text size was 1000 


##### radio buttons
$radio_tree =RadioButtons(
  [ "A","B","C","D"
  ],
  $pick,                       #index of correct answer
   separator => "$SPACE$SPACE$SPACE$SPACE",
);

$radio_pn = RadioButtons(
  [
    ["\($pn[0]\)",
    "\($pn[1]\)",
    "\($pn[2]\)",
    "\($pn[3]\)",
    ],
  ],
  $pick,            #index of correct answer
);

@indices = (0,0,0,0);
$indices[$pick] = 1;  #set index of correct tree to 1
($table,$ans) = radio_table([ @image], [@indices], geometry => [2,2], border => 1);
# ($table,$ans) = radio_table([@pics], [0,0,1], geometry => [1,3]);
#got this command from 
#FindIsomorphism.pg
#Graph Theory, Terminology
##############################################################
#
#  Text
#
#


BEGIN_PGML
Consider the algebraic expression given below.

		[`[$exp[$pick]]`]

(a) Select the binary tree that corresponds to the  algebraic expression.

		[@ $table @]*

END_PGML
$ans;
BEGIN_PGML
(b) Now (using part (a))  convert the algebraic expression to Polish notation.

		[_]{$radio_pn}

END_PGML



##############################################################
#
# Hints 
#
#

$showHint = 2; # default is 1

BEGIN_PGML
If you don't get this in [$showHint] tries, you can get a hint.
END_PGML

BEGIN_PGML_HINT
   hints here if wanted
END_PGML_HINT



##############################################################
#
# Solutions
#
#

BEGIN_PGML_SOLUTION
stuff
END_PGML_SOLUTION
COMMENT('MathObject version. Uses PGML.');
ENDDOCUMENT();