## Appendix A  
This appendix provides an example of the recommendations provided by our system for both forum conversations and reinforcement activities. Specifically, the examples presented here are obtained when embeddings are used to represent the text. Question posed by the student  
Message no. 1 Sent by: XXX on XXX Title: Prim vs. Kruskal - Good morning. On page 71, at the end of the section on the cost of the Kruskal algorithm, it states:  
''... if the graph is dense, the Prim algorithm is preferable since its cost is 0(n^2). However, if the graph is sparse, the Kruskal algorithm is more suitable.'' In the case of a dense graph, it is clear. But in the case of a sparse graph, if we use adjacency lists in the Prim algorithm, wouldn't it be the same as using Prim or Kruskal? Both have a cost of 0(a log n). Thank you. First recommendation  
Message no. 1 Sent by: XXX on XXX Tittle: Minimum Spanning Trees: Prim vs. Kruskal Algorithm - I have two questions:  
(1)-Regarding the cost of the two algorithms, I read (and I believe I understand) that, in the case of Prim, when implemented with adjacency matrices, the cost is 0(n^2), while if implemented with adjacency lists and heaps, the cost is 0(n log(n)). This implementation will mainly affect the Distance(x, y) function, is that correct? Therefore, in the case of dense graphs, where the number of edges approaches n^2, it is preferable to implement it with matrices. When studying the cost of the [PERSON] algorithm, at the end of the section (page 71), it is said that if the graph is dense, it is better to use Prim, and if it is sparse, Kruskal is better, but always when implemented with matrices, right? (2)-Regarding the optimality proof of both algorithms, they are based on Lemma 3.2.1 (page 65). When reading it, I do not under- stand the phrase, ''Let (u, v) be the edge of the smallest weight leaving NA...'' How can an edge ''leave a set of nodes??' Does it mean that it is the edge of the smallest weight leaving a node in NA (u) and going to another that does not belong to NA (v)? Thank you in advance. Second recommendation Message no. 1  Sent by: XXX on XXX  Tittle: Cost of [PERSON]'s Algorithm, page 71  -  Hello,  
Regarding the cost of the algorithm, you mention that the ''Buscar  Componente Conexa'' (Connected Component Search) function will be  executed 2*a times, and you assign it an implicit constant cost  in order to disregard it compared to the sorting cost. However,  I understand that in the worst case, the ''Buscar Componente Conexa''  function will have a cost of ''n'' because it will be necessary to  search the node in all components, and in each component, check  each of its nodes unless there is some additional data structure  in the node that allows knowing to which component it belongs. But  in that case, we would be increasing the cost of ''Fusionar'' (Merge)  to ''n'' to update the information of all nodes in the components  that are merged. Greetings. Third recommendation  
Message no. 1  Sent by: XXX on XXX  Title: Question about [PERSON]'s Algorithm  -  In [PERSON]'s algorithm, on page 69, the line reads:  
if Distance(j, node) < costeMinimo[j] \textLambda costeMinimo[j] \textLambda -1 then  
Isn't the condition \textLambda costeMinimo[j] \textLambda -1 redundant? In other words, could it be eliminated since, assuming costeMinimo[j]=-1,  this condition implies that Distancia(j, node) < costeMinimo[j] is not  satisfied (since Distancia(j, node) is always greater than or equal  to 0), and therefore, it would not enter the if statement? In case I am mistaken and the condition \textLambda costeMinimo[j] \textLambda -1 is indeed not redundant, could you provide an example  where this condition is necessary? Greetings. Next, we showcase the first recommended reinforcement activities for the same student's question (again, translated from Spanish):  
First recommendation  
The [PERSON] and Kruskal algorithms are greedy algorithms applied when  calculating a minimum spanning tree. Regarding both algorithms,  which of the following statements is true? A.