########################################################################
## DESCRIPTION
## A WeBWorK problem that asks students to construct a back to back stem and leaf display.
## WeBWorK problem written by JoAnne Taormina, <joanne(dot)taormina(at)ncc(dot)edu>
## ENDDESCRIPTION
##
## KEYWORDS('back to back', 'stem and leaf display')
##
## Author('JoAnne Taormina')
## Institution('Nassau Community College')
########################################################################

DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"PGchoicemacros.pl",
"unionTables.pl",
"weightedGrader.pl",
);
$refreshCachedImages=1;

# make sure we're in the context we want
Context("Numeric");


# the data
@alldata = ();
@row10=();
$j=0;
for($i = 0; $i < 5; $i ++)
{
  $alldata[$j]= random(100, 109, 1);
  $row10[$i] = $alldata[$j++]-100;
}
@row12=();
for($i = 0; $i < 9; $i ++)
{
  $alldata[$j]=random(120, 129, 1);
  $row12[$i] = $alldata[$j++]-120;
}
@row13=();
for($i = 0; $i < 8; $i ++)
{
  $alldata[$j] = random(130, 139, 1);
  $row13[$i] = $alldata[$j++]-130;
}
@row14=();
for($i = 0; $i < 7; $i ++)
{
  $alldata[$j] = random(140, 149, 1);
  $row14[$i] = $alldata[$j++]-140;
}
@row15=();
for($i = 0; $i < 6; $i ++)
{
  $alldata[$j] = random(150, 159, 1);
  $row15[$i] = $alldata[$j++]-150;
}
@row10=reverse num_sort(@row10);
@row12=reverse num_sort(@row12);
@row13=reverse num_sort(@row13);
@row14=reverse num_sort(@row14);
@row15=reverse num_sort(@row15);

@alldata2 = ();
$j=0;
for($i = 0; $i < 3; $i ++)
{
  $alldata2[$j] = random(80, 89, 1);
  $row8b[$i] = $alldata2[$j++]-80;
}
for($i = 0; $i < 3; $i ++)
{
  $alldata2[$j] = random(90, 99, 1);
  $row9b[$i] = $alldata2[$j++]-90;
}
for($i = 0; $i < 7; $i ++)
{
  $alldata2[$j] = random(100, 109, 1);
  $row10b[$i] = $alldata2[$j++]-100;
}
for($i = 0; $i < 8; $i ++)
{
  $alldata2[$j] = random(110, 119, 1);
  $row11b[$i] = $alldata2[$j++]-110;
}
for($i = 0; $i < 9; $i ++)
{
  $alldata2[$j] = random(120, 129, 1);
  $row12b[$i] =  $alldata2[$j++]-120;
}
for($i = 0; $i < 5; $i ++)
{
  $alldata2[$j] = random(130, 139, 1);
  $row13b[$i] = $alldata2[$j++]-130;
}
@row8b = num_sort(@row8b);
@row9b = num_sort(@row9b);
@row10b = num_sort(@row10b);
@row11b = num_sort(@row11b);
@row12b = num_sort(@row12b);
@row13b = num_sort(@row13b);

# the table data
$table_start2 = begintable(21);
$table_row2[0] = row("","","","","","","","","","","Stem","","","","","","","","","","","");
for ( $i = 1; $i <9; $i++ )
{
   $table_row2[$i]  = row( ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(8),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2),ans_rule(2)  );
}

$table_end2   = endtable();

TEXT(beginproblem());
install_weighted_grader();

Context()->texStrings;
BEGIN_TEXT
Create a back to back stem and leaf display from the following two data sets. $BR$BR
Put a single stem in the center column labeled $BBOLD "stem." $EBOLD Put the leaves for data set 1 in the blanks on the left of the stem, and the leaves for data set 2 in the blanks on the right of the stem.  
$BR$BR
$BBOLD Each leaf has its own blank. $EBOLD
$BR$BR
Unused blanks should remain empty.
$BR$BR
DATA SET 1
$BR
\[ $alldata[0], \ $alldata[1], \ $alldata[2], \ $alldata[3], \ $alldata[4], \ $alldata[5], \ $alldata[6], \ $alldata[7], \ $alldata[8], \ $alldata[9] \] 
\[ $alldata[10], \ $alldata[11], \ $alldata[12], \ $alldata[13], \ $alldata[14], \ $alldata[15], \ $alldata[16], \ $alldata[17], \ $alldata[18], \ $alldata[19] \] 
\[ $alldata[20], \ $alldata[21], \ $alldata[22], \ $alldata[23], \ $alldata[24], \ $alldata[25], \ $alldata[26], \ $alldata[27], \ $alldata[28], \ $alldata[29] \]
\[ $alldata[30], \ $alldata[31], \ $alldata[32], \ $alldata[33], \ $alldata[34] \]
$BR $BR
DATA SET 2
$BR
\[ $alldata2[0], \ $alldata2[1], \ $alldata2[2], \ $alldata2[3], \ $alldata2[4], \ $alldata2[5], \ $alldata2[6], \ $alldata2[7], \ $alldata2[8], \ $alldata2[9] \] 
\[ $alldata2[10], \ $alldata2[11], \ $alldata2[12], \ $alldata2[13], \ $alldata2[14], \ $alldata2[15], \ $alldata2[16], \ $alldata2[17], \ $alldata2[18], \ $alldata2[19] \] 
\[ $alldata2[20], \ $alldata2[21], \ $alldata2[22], \ $alldata2[23], \ $alldata2[24], \ $alldata2[25], \ $alldata2[26], \ $alldata2[27], \ $alldata2[28], \ $alldata2[29] \]
\[ $alldata2[30], \ $alldata2[31], \ $alldata2[32], \ $alldata2[33], \ $alldata2[34] \]
$BR

Put a single stem in the center column labeled $BBOLD "stem." $EBOLD Put the leaves for data set 1 in the blanks on the left of the stem, and the leaves for data set 2 in the blanks on the right of the stem.  You may need to scroll right to view the entire display.
$BR$BR

$BCENTER


$table_start1
$table_row1[0]
$table_end1


$table_start2
$table_row2[0]
$table_row2[1]
$table_row2[2]
$table_row2[3]
$table_row2[4]
$table_row2[5]
$table_row2[6]
$table_row2[7]
$table_row2[8]
$table_end2

$ECENTER
END_TEXT

Context()->normalStrings;
@rows=("","","","","","","","","","",8,@row8b,"","","","","","","","","","","","","","","","","",9,@row9b,"","","","","","","","","","","","",@row10,10,@row10b,"","","","","","","","","","","","","",11,@row11b,"","","",@row12,12,@row12b,"","","",@row13,13,@row13b,"","","","","","","","",@row14,14,"","","","","","","","","","","","","","",@row15,15,"","","","","","","","","","");

for ( $i = 0; $i<168; $i++ )
{
  if($rows[$i] eq "")
  {
    WEIGHTED_ANS( str_cmp($rows[$i]), 0 );
  }
  else
  {
    WEIGHTED_ANS( str_cmp($rows[$i]), 1.2821 );
  }
}

ENDDOCUMENT();