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