php - Sort algorithm: Magento checkout totals sorted wrongly causing wrong shipping tax calculation

Question

In Magento there is a functionality where you can define the order of total calculation by specifing before and after which totals a total should be run.

I added a custom total and if I add the following lines to the config.xml, the sorting is wrong. Wrong means: tax_shipping comes before shipping. This causes the tax for the shipping cost to be added twice.

But this violates the condition

tax_shipping
after: shipping

My guess: There must be some contradiction in the full set of rules. But how can I find it?

This is the only rule I add. Without this rule, tax_shipping is sorted after shipping.

<shippingprotectiontax>
    <class>n98_shippingprotection/quote_address_total_shippingprotectionTax</class>
    <after>subtotal,discount,shipping,tax</after>
    <before>grand_total</before>
</shippingprotectiontax>

Below I paste the sorted array that is returned by the usort call in Mage_Sales_Model_Quote_Address_Total_Collector::_getSortedCollectorCodes() For those who do not have a Magento installation, the code is like this:

/**
 * uasort callback function
 *
 * @param   array $a
 * @param   array $b
 * @return  int
 */
protected function _compareTotals($a, $b)
{
    $aCode = $a['_code'];
    $bCode = $b['_code'];
    if (in_array($aCode, $b['after']) || in_array($bCode, $a['before'])) {
        $res = -1;
    } elseif (in_array($bCode, $a['after']) || in_array($aCode, $b['before'])) {
        $res = 1;
    } else {
        $res = 0;
    }
    return $res;
}

protected function _getSortedCollectorCodes()
{

    ...

    uasort($configArray, array($this, '_compareTotals'));
    Mage::log('Sorted:');

    // this produces the output below
    $loginfo = "";
    foreach($configArray as $code=>$data) {
        $loginfo .= "$code
";
        $loginfo .= "after: ".implode(',',$data['after'])."
";
        $loginfo .= "before: ".implode(',',$data['before'])."
";
        $loginfo .= "
";
    }
    Mage::log($loginfo);

    ...

Log output:

nominal
after: 
before: subtotal,grand_total

subtotal
after: nominal
before: grand_total,shipping,freeshipping,tax_subtotal,discount,tax,weee,giftwrapping,cashondelivery,cashondelivery_tax,shippingprotection,shippingprotectiontax

freeshipping
after: subtotal,nominal
before: tax_subtotal,shipping,grand_total,tax,discount

tax_shipping
after: shipping,subtotal,freeshipping,tax_subtotal,nominal
before: tax,discount,grand_total,grand_total

giftwrapping
after: subtotal,nominal
before: 

tax_subtotal
after: freeshipping,subtotal,subtotal,nominal
before: tax,discount,shipping,grand_total,weee,customerbalance,giftcardaccount,reward

weee
after: subtotal,tax_subtotal,nominal,freeshipping,subtotal,subtotal,nominal
before: tax,discount,grand_total,grand_total,tax

shipping
after: subtotal,freeshipping,tax_subtotal,nominal
before: grand_total,discount,tax_shipping,tax,cashondelivery,cashondelivery_tax,shippingprotection,shippingprotectiontax

discount
after: subtotal,shipping,nominal,freeshipping,tax_subtotal,tax_shipping,weee
before: grand_total,tax,customerbalance,giftcardaccount,reward,cashondelivery,cashondelivery_tax,shippingprotection,shippingprotectiontax

cashondelivery
after: subtotal,discount,shipping,nominal,subtotal,shipping,nominal,freeshipping,tax_subtotal,tax_shipping,weee,subtotal,freeshipping,tax_subtotal,nominal
before: tax,grand_total,grand_total,customerbalance,giftcardaccount,tax_giftwrapping,reward,customerbalance,giftcardaccount,reward

shippingprotection
after: subtotal,discount,shipping,nominal,subtotal,shipping,nominal,freeshipping,tax_subtotal,tax_shipping,weee,subtotal,freeshipping,tax_subtotal,nominal
before: tax,grand_total,grand_total,customerbalance,giftcardaccount,tax_giftwrapping,reward,cashondelivery_tax,customerbalance,giftcardaccount,reward

tax
after: subtotal,shipping,discount,tax_subtotal,freeshipping,tax_shipping,nominal,weee,cashondelivery,shippingprotection
before: grand_total,customerbalance,giftcardaccount,tax_giftwrapping,reward,cashondelivery_tax,shippingprotectiontax

shippingprotectiontax
after: subtotal,discount,shipping,tax,nominal,subtotal,shipping,nominal,freeshipping,tax_subtotal,tax_shipping,weee,subtotal,freeshipping,tax_subtotal,nominal,subtotal,shipping,discount,tax_subtotal,freeshipping,tax_shipping,nominal,weee,cashondelivery,shippingprotection
before: grand_total,customerbalance,giftcardaccount,reward

cashondelivery_tax
after: subtotal,discount,shipping,tax,nominal,subtotal,shipping,nominal,freeshipping,tax_subtotal,tax_shipping,weee,subtotal,freeshipping,tax_subtotal,nominal,subtotal,shipping,discount,tax_subtotal,freeshipping,tax_shipping,nominal,weee,cashondelivery
before: grand_total,customerbalance,giftcardaccount,reward

tax_giftwrapping
after: tax,subtotal,shipping,discount,tax_subtotal,freeshipping,tax_shipping,nominal,weee
before: grand_total,customerbalance,giftcardaccount

grand_total
after: subtotal,nominal,shipping,freeshipping,tax_subtotal,discount,tax,tax_giftwrapping,cashondelivery,cashondelivery_tax,shippingprotection,shippingprotectiontax
before: customerbalance,giftcardaccount,reward

reward
after: wee,discount,tax,tax_subtotal,grand_total,subtotal,shipping,nominal,freeshipping,tax_subtotal,tax_shipping,weee,subtotal,shipping,discount,tax_subtotal,freeshipping,tax_shipping,nominal,weee,freeshipping,subtotal,subtotal,nominal,subtotal,nominal,shipping,freeshipping,tax_subtotal,discount,tax,tax_giftwrapping
before: giftcardaccount,customerbalance,customerbalance

giftcardaccount
after: wee,discount,tax,tax_subtotal,grand_total,reward,subtotal,shipping,nominal,freeshipping,tax_shipping,weee
before: customerbalance

customerbalance
after: wee,discount,tax,tax_subtotal,grand_total,reward,giftcardaccount,subtotal,shipping,nominal,freeshipping,tax_shipping,weee
before: 

EDIT:

After Vinai's answer I added more debug code

$fp = fopen('/tmp/dotfile','w');
fwrite($fp,"digraph TotalOrder
");
fwrite($fp,"{
");
foreach($configArray as $code=>$data) {
    $_code = $data['_code'];
    foreach($data['before'] as $beforeCode) {
        fwrite($fp,"$beforeCode -> $_code;
");
    }
    foreach($data['after'] as $afterCode) {
        fwrite($fp,"$_code -> $afterCode;
");
    }
}
fwrite($fp,"}
");
fclose($fp);

And visualized it with graphviz: dot -Tpng dotfile > viz.png. That's the result of the first try. Called after the sorting.

EDIT2:

I think this is pretty useless.

So I made a visualization of the array before merging the after/before entries. (right after $configArray = $this->_modelsConfig;)

This is it without my shippingprotectiontax entry:

This is it with my shippingprotectiontax entry:

I do not see any clear contradictions.

EDIT3:

Config array just before uasort:

array (
  'nominal' => 
  array (
    'class' => 'sales/quote_address_total_nominal',
    'before' => 
    array (
      0 => 'subtotal',
      1 => 'grand_total',
    ),
    'renderer' => 'checkout/total_nominal',
    'after' => 
    array (
    ),
    '_code' => 'nominal',
  ),
  'subtotal' => 
  array (
    'class' => 'sales/quote_address_total_subtotal',
    'after' => 
    array (
      0 => 'nominal',
    ),
    'before' => 
    array (
      0 => 'grand_total',
      1 => 'shipping',
      2 => 'freeshipping',
      3 => 'tax_subtotal',
      4 => 'discount',
      5 => 'tax',
      6 => 'weee',
      7 => 'giftwrapping',
      8 => 'cashondelivery',
      9 => 'cashondelivery_tax',
      10 => 'shippingprotection',
      11 => 'shippingprotectiontax',
    ),
    'renderer' => 'tax/checkout_subtotal',
    'admin_renderer' => 'adminhtml/sales_order_create_totals_subtotal',
    '_code' => 'subtotal',
  ),
  'shipping' => 
  array (
    'class' => 'sales/quote_address_total_shipping',
    'after' => 
    array (
      0 => 'subtotal',
      1 => 'freeshipping',
      2 => 'tax_subtotal',
      3 => 'nominal',
    ),
    'before' => 
    array (
      0 => 'grand_total',
      1 => 'discount',
      2 => 'tax_shipping',
      3 => 'tax',
      4 => 'cashondelivery',
      5 => 'cashondelivery_tax',
      6 => 'shippingprotection',
      7 => 'shippingprotectiontax',
    ),
    'renderer' => 'tax/checkout_shipping',
    'admin_renderer' => 'adminhtml/sales_order_create_totals_shipping',
    '_code' => 'shipping',
  ),
  'grand_total' => 
  array (
    'class' => 'sales/quote_address_total_grand',
    'after' => 
    array (
      0 => 'subtotal',
      1 => 'nominal',
      2 => 'shipping',
      3 => 'freeshipping',
      4 => 'tax_subtotal',
      5 => 'discount',
      6 => 'tax',
      7 => 'tax_giftwrapping',
      8 => 'cashondelivery',
      9 => 'cashondelivery_tax',
      10 => 'shippingprotection',
      11 => 'shippingprotectiontax',
    ),
    'renderer' => 'tax/checkout_grandtotal',
    'admin_renderer' => 'adminhtml/sales_order_create_totals_grandtotal',
    'before' => 
    array (
      0 => 'customerbalance',
      1 => 'giftcardaccount',
      2 => 'reward',
    ),
    '_code' => 'grand_total',
  ),
  'freeshipping' => 
  array (
    'class' => 'salesrule/quote_freeshipping',
    'after' => 
    array (
      0 => 'subtotal',
      1 => 'nominal',
    ),
    'before' => 
    array (
      0 => 'tax_subtotal',
      1 => 'shipping',
      2 => 'grand_total',
      3 => 'tax',
      4 => 'discount',
    ),
    '_code' => 'freeshipping',
  ),
  'discount' => 
  array (
    'class' => 'salesrule/quote_discount',
    'after' => 
    array (
      0 => 'subtotal',
      1 => 'shipping',
      2 => 'nominal',
      3 => 'freeshipping',
      4 => 'tax_subtotal',
      5 => 'tax_shipping',
      6 => 'weee',
    ),
    'before' => 
    array (
      0 => 'grand_total',
      1 => 'tax',
      2 => 'customerbalance',
      3 => 'giftcardaccount',
      4 => 'reward',
      5 => 'cashondelivery',
      6 => 'cashondelivery_tax',
      7 => 'shippingprotection',
      8 => 'shippingprotectiontax',
    ),
    'renderer' => 'tax/checkout_discount',
    'admin_renderer' => 'adminhtml/sales_order_create_totals_discount',
    '_code' => 'discount',
  ),
  'tax_subtotal' => 
  array (
    'class' => 'tax/sales_total_quote_subtotal',
    'after' => 
    array (
      0 => 'freeshipping',
      1 => 'subtotal',
      2 => 'subtotal',
      3 => 'nominal',
    ),
    'before' => 
    array (
      0 => 'tax',
      1 => 'discount',
      2 => 'shipping',
      3 => 'grand_total',
      4 => 'weee',
      5 => 'customerbalance',
      6 => 'giftcardaccount',
      7 => 'reward',
    ),
    '_code' => 'tax_subtotal',
  ),
  'tax_shipping' => 
  array (
    'class' => 'tax/sales_total_quote_shipping',
    'after' => 
    array (
      0 => 'shipping',
      1 => 'subtotal',
      2 => 'freeshipping',
      3 => 'tax_subtotal',
      4 => 'nominal',
    ),
    'before' => 
    array (
      0 => 'tax',
      1 => 'discount',
      2 => 'grand_total',
      3 => 'grand_total',
    ),
    '_code' => 'tax_shipping',

Answer 1

Thanks for persisting @Alex, here is a better answer with a better explanation :) My first answer was wrong.

PHP implements the quicksort for all array sorting functions (reference zend_qsort.c).
If two records in the array are identical, their place will be swapped.

The problem is the giftwrap total record, which, according to _compareTotals(), is larger then subtotal and nominal but equal to all other totals.

Depending on the original order of the $confArray input array and on the placement of the pivot element it is legal to swap giftwrap with e.g. discount, because both are equal, even though discount is larger then shipping.

This might make the problem clearer from the sorting algorithms point of view:

• shipping < tax_shipping
• giftwrapping == shipping
• giftwrapping == tax_shipping

There are several possible solutions, even though the original problem is the choice of quicksort to build a directed acyclic dependency graph

• One (bad, shortterm) solution would be to add more dependencies to the giftwrapping total, even though there might still be more problems with other totals that simply didn't surface so far.
• The real solution would be to implement a topological sorting algorithm for the problem.

Interestingly there are not many PHP packages floating around. There is an orphaned PEAR package Structures_Graph. Using that would probably be the quick solution, but it would mean transforming the $confArray into a Structures_Graph structure (so maybe not that quick).

Wikipedia does a good job of explaining the problem, so rolling your own solution might be a fun challenge. The German Wikipedia topological sorting page breaks down the problem into logical steps and also has a great example algorithm in PERL.