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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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commit eecaab61fc
16 changed files with 110 additions and 109 deletions
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8
semester1/algorithms-and-datastructures/parts/graphs/shortest-path.tex
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@@ -29,8 +29,8 @@
\begin{itemize}
\item \textbf{Time Complexity:}
\begin{itemize}
\item \tco{|V|^2} for a simple implementation.
\item \tco{(|V| + |E|) \log |V|} using a priority queue.
\item $\tco{|V|^2}$ for a simple implementation.
\item $\tco{(|V| + |E|) \log |V|}$ using a priority queue.
\end{itemize}
\item Only works with non-negative edge weights.
\item Greedy algorithm that processes vertices in increasing order of distance.
@@ -112,7 +112,7 @@
\begin{properties}[]{Characteristics of Bellman-Ford Algorithm}
\begin{itemize}
\item \textbf{Time Complexity:} \tco{|V| \cdot |E|}.
\item \textbf{Time Complexity:} $\tco{|V| \cdot |E|}$.
\item Can handle graphs with negative edge weights but not graphs with negative weight cycles.
\item Used for:
\begin{itemize}
@@ -161,7 +161,7 @@
\midrule
Handles Negative Weights & No & Yes \\
Detects Negative Cycles & No & Yes \\
Time Complexity & \tco{(|V| + |E|) \log |V|} & \tco{|V| \cdot |E|} \\
Time Complexity & $\tco{(|V| + |E|) \log |V|}$ & $\tco{|V| \cdot |E|}$ \\
Algorithm Type & Greedy & Dynamic Programming \\
\bottomrule
\end{tabular}