From c393a6d332c91be3fd9e552a57ef4351f9a7292d Mon Sep 17 00:00:00 2001 From: Claudio Maggioni Date: Mon, 27 May 2019 16:12:32 +0200 Subject: [PATCH] Corrections to GA4 --- .DS_Store | Bin 0 -> 6148 bytes GA4/ga4.pdf | Bin 311152 -> 315639 bytes GA4/ga4.tex | 24 ++++++++++++++++++++---- 3 files changed, 20 insertions(+), 4 deletions(-) create mode 100644 .DS_Store diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..be1185b31979740bbdf08d4d9c0833c977e874d6 GIT binary patch literal 6148 zcmeHK!A{#i5Zz7E)+SQrN<9RLgC!1JI0TxMtD8c5K`O$C99kOe+G;FWHnN@M5Jj^1 z06u_T3;YM=BRKLCy?17Jf?5TRR0PdPvu`q<8LywMos1Adb_T(k5S9?a07a~ru-qYd z9d$-3$61NiQ$;-h#cTK?$o_ZLTb(QIDJO11Xv`3u8b zsGIedb@RaOrz5xUib3A-vYxf%MnUL%SvLxb{$7}D#o;haK4sfp5oVt;crQ(32++3Y z??>UNXT5%(CWRLzVW#To8eh6m5~QO}I!JKMz;;f-R_G|ZmW7>`@+ z_Nv`#uTNI(@y13I>^E;G6VosjS3c~19UPyW{`h%zesTFr^Dp63Rq~2(3Rhqd6+!+j z_F>-`O0J=sC2^X32hX&?G?9@RU8}-(ir^H@sgC2sS 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I have the answer: \url{https://imgur.com/a/yk9RPFs}}} \newpage \section{Exercise 1} @@ -222,11 +223,26 @@ of vertices (i.e.: $|E_T| = |V| - 1$). \begin{lstlisting}[caption=Solution for exercise 4 point 2, label={lst:ex4p1}] FUNCTION MAKE-MST-MINIMAL(T=(V,E), weight, v, w, c): - if not IS-MST-MINIMAL(T, weight, v, w, c): - $\textit{delete edge where IS-MST-MINIMAL stopped from T}$ - $\textit{add (v, w) to T}$ + P[w] = NIL + DEFINE-PARENT(T, P, Adj[w], w) + s = P[s] + s_max = s + max = weight($\textit{edge}$ (s, P[s])) + while s $\neq$ w: + edge_w = weight($\textit{edge}$ (s, P[s])) + if edge_w > max: + max = edge_w + s_max = s + s = P[s] + + if max < c: + return + else: + $\textit{remove edge (s, P[s]) from T}$ // O(|V|) cost operation + $\textit{add (v, w) to T}$ // constant cost \end{lstlisting} -For what said before, this algorithm updates $T$ to a valid MST and runs in $O(|V_T|)$ which is always $< O(|E|)$. +For what said before, this algorithm updates $T$ to a valid MST and runs in $O(|V_T|)$ which is always $< O(|E|)$. In order to find +the new MST, we need to find remove the edge with highest weight in the path from $v$ to $w$ and add $(v, w)$ to the MST. \end{document} \ No newline at end of file