Corrections to GA4

GA4/ga4.tex

@@ -35,6 +35,7 @@
 \maketitle
 \tableofcontents
 \lstlistoflistings
+{\color{white}{Will these be the right solutions? 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):
+  P[w] = NIL
-    $\textit{delete edge where IS-MST-MINIMAL stopped from T}$
+  DEFINE-PARENT(T, P, Adj[w], w)
-    $\textit{add (v, w) to T}$
+  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}