Re: Re: Keeping a running total?

> What about having a bigger than 2 (variable) number of quotas? How
> would your solution change to tackle this?
>
I suppose a general solution would have a list of quotas (and a
corresponding list of quota names), e.g. :
   <quotas>
       <quota id="Widget" left="{$Widget_quota}" />
       <quota id="Gadget" left="{$Gadget_quota}" />
       ...
   </quotas>

Updating this list on every template call leads to O(Qn)*O(Fn)  time
complexity, where Fn is the number of factories and Qn the number of
quotas.

In the past I've 'cheated' by using the stack as a list, e.g. as follows:

<xsl:template match="xml">
  <xsl:apply-templates select="factory">
      <xsl:with-param name="left0" select="$Widget_quota" />
      <xsl:with-param name="left1" select="$Gadget_quota" />
      ...
      <xsl:with-param name="name0">Widget</xsl:with-param>
      <xsl:with-param name="name1">Gadget</xsl:with-param>
      ...
  </xsl:apply-templates>
</xsl:template>

then in the factory template, each factory would consume $left0 until it
was depleted and then shift by assigning $left1 to $left0, $left2 to
$left1 and so on through parameters.
e.g.
       <xsl:with-param name="left0" select="$left1" />   <!-- shift to
next quota -->
       <xsl:with-param name="left1" select="$left2" />
       <xsl:with-param name="left2" select="$left3" />
       <xsl:with-param name="left3" select="$left4" />

Quota-recursion would end when $left0 was empty then capacity would
accumulate in $excess until factories were depleted.

Having to perform such shifts on template calls again leads to
quadratic-like time complexity.

Better time complexity can be achieved if the running totals for
*both* factories and quotas are calculated with an O(N) (linear)
algorithm.

The implementation I provided could have better than quadratic time
complexity if it used a more efficient way to find overlapping
intervals -- a binary search with an f:binSearch() - like function
would be O(Log2(Qn)). In this case the time complexity would be:

For simplicity, in the implementation I provided the identification of
overlapping intervals traverses all quotas intervals for every
factory.

--
Cheers,
Dimitre Novatchev
---------------------------------------
Truly great madness cannot be achieved without significant intelligence.