XSLT Cookbook

Computing Combinatorial Functions

Problem

You need to compute the number of permutations or combinations of size r of a given set.

Solution

If you know the formula for permutations of size r is N! / r! and you know that the formula for combinations is N! / r! * (N-r)!, then you might disregard this example; this book already gave an example for factorial. However, since factorials get very big quickly, you need to be a little crafty to get the best bang for your calculating buck:

<xsl:template name="math:P"> <xsl:param name="n" select="1"/> <xsl:param name="r" select="1"/> <xsl:choose> <xsl:when test="$n &lt; 0 or $r &lt; 0">NaN</xsl:when> <xsl:when test="$n = 0">0</xsl:when> <xsl:otherwise> <xsl:call-template name="prod-range"> <xsl:with-param name="start" select="$r + 1"/> <xsl:with-param name="end" select="$n"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="math:C"> <xsl:param name="n" select="1"/> <xsl:param name="r" select="1"/> <xsl:choose> <xsl:when test="$n &lt; 0 or $r &lt; 0">NaN</xsl:when> <xsl:when test="$n = 0">0</xsl:when> <xsl:otherwise> <xsl:variable name="min" select="($r &lt;= $n - $r) * $r + ($r > $n - $r) * $n - $r"/> <xsl:variable name="max" select="($r >= $n - $r) * $r + ($r &lt; $n - $r) * $n - $r"/> <xsl:variable name="numerator"> <xsl:call-template name="prod-range"> <xsl:with-param name="start" select="$max + 1"/> <xsl:with-param name="end" select="$n"/> </xsl:call-template> </xsl:variable> <xsl:variable name="denominator"> ...