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[AD] Update summary to new version of helpers

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2025-09-26 12:31:55 +02:00
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semester1/algorithms-and-datastructures/parts/search/heap-sort.tex
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@@ -9,11 +9,11 @@
\item \textbf{Efficiency:} Excellent for in-place sorting with predictable performance.
\item \textbf{Time Complexity:}
\begin{itemize}
\item Best case: \tcl{n \log n}
\item Worst case: \tco{n \log n}
\item Average case: \tct{n \log n}
\item Best case: $\tcl{n \log n}$
\item Worst case: $\tco{n \log n}$
\item Average case: $\tct{n \log n}$
\end{itemize}
\item \textbf{Space Complexity:} In-place sorting requires \tct{1} additional space.
\item \textbf{Space Complexity:} In-place sorting requires $\tct{1}$ additional space.
\item \textbf{Limitations:} Inefficient compared to Quick Sort for most practical datasets.
\end{itemize}
\end{properties}
@@ -46,11 +46,11 @@ The lecture does not cover the implementation of a heap tree. See the specific s
\item \textbf{Efficiency:} Performs well for uniformly distributed datasets.
\item \textbf{Time Complexity:}
\begin{itemize}
\item Best case: \tcl{n + k} (for uniform distribution and $k$ buckets)
\item Worst case: \tco{n^2} (when all elements fall into a single bucket)
\item Average case: \tct{n + k}
\item Best case: $\tcl{n + k}$ (for uniform distribution and $k$ buckets)
\item Worst case: $\tco{n^2}$ (when all elements fall into a single bucket)
\item Average case: $\tct{n + k}$
\end{itemize}
\item \textbf{Space Complexity:} Requires \tct{n + k} additional space.
\item \textbf{Space Complexity:} Requires $\tct{n + k}$ additional space.
\item \textbf{Limitations:} Performance depends on the choice of bucket size and distribution of input elements.
\end{itemize}
\end{properties}
@@ -99,9 +99,9 @@ The lecture does not cover the implementation of a heap tree. See the specific s
\end{itemize}
\item \textbf{Time Complexity:}
\begin{itemize}
\item Insert: \tct{\log n}.
\item Extract Min/Max: \tct{\log n}.
\item Build Heap: \tct{n}.
\item Insert: $\tct{\log n}$.
\item Extract Min/Max: $\tct{\log n}$.
\item Build Heap: $\tct{n}$.
\end{itemize}
\end{itemize}
\end{properties}