bibin/cphb
1
0
Fork 0
Code Issues Pull requests Releases Wiki Activity

Improvements for graph algorithms

Browse source
This commit is contained in:
Antti H S Laaksonen 2017-04-17 13:58:04 +03:00
parent 086d0e61cd
commit 31ff123f33
4 changed files with 58 additions and 56 deletions
Download patch file Download diff file Expand all files Collapse all files

16
chapter15.tex
View file

@ -504,17 +504,17 @@ efficiently by following the corresponding chain.
The union-find structure can be implemented
using arrays.
In the following implementation,
the array \texttt{k} contains for each element
the array \texttt{link} contains for each element
the next element
in the chain or the element itself if it is
a representative,
and the array \texttt{s} indicates for each representative
and the array \texttt{size} indicates for each representative
the size of the corresponding set.
Initially, each element belongs to a separate set:
\begin{lstlisting}
for (int i = 1; i <= n; i++) k[i] = i;
for (int i = 1; i <= n; i++) s[i] = 1;
for (int i = 1; i <= n; i++) link[i] = i;
for (int i = 1; i <= n; i++) size[i] = 1;
\end{lstlisting}
The function \texttt{find} returns
@ -524,7 +524,7 @@ the chain that begins at $x$.
\begin{lstlisting}
int find(int x) {
while (x != k[x]) x = k[x];
while (x != link[x]) x = link[x];
return x;
}
\end{lstlisting}
@ -552,9 +552,9 @@ set to the larger set.
void unite(int a, int b) {
a = find(a);
b = find(b);
if (s[a] < s[b]) swap(a,b);
s[a] += s[b];
k[b] = a;
if (size[a] < size[b]) swap(a,b);
size[a] += size[b];
link[b] = a;
}
\end{lstlisting}
\end{samepage}