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Antti H S Laaksonen 2017-02-17 00:50:04 +02:00
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luku10.tex
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@ -468,9 +468,9 @@ for (int i = 0; i < n; i++) {
\subsubsection{Counting subsets}
Our last problem in this chapter is as follows:
We are given a collection $C$ of $m$ sets,
We are given a collection $C$ that consists of $m$ sets,
and our task is to determine for each set
the number of sets that are its subsets.
the number of sets in $C$ that are its subsets.
For example, consider the following collection:
\[C = \{\{0\}, \{0,2\}, \{1,4\}, \{0,1,4\}, \{1,4,5\}\}\]
For any set $x$ in $C$,
@ -492,7 +492,7 @@ However, a more efficient solution is possible
using dynamic programming.
Let $c(x,k)$ denote the number of sets in
$C$ that equal to a set $x$
$C$ that equal a set $x$
if we are allowed to remove any subset of
$\{0,1,\ldots,k\}$ from $x$.
For example, in the above collection,