Hi guys, as the title stated, I really need some help with a problem (It appeared in my country's OI years ago). I remember it being a problem on Codeforces, the statement goes something like this:

Given N knowledges, numbered from 1 to N, each knowledge i has a cost of S[i] for you to be proficient in it. There are M tests, for each test from 1 to M, it gives you A[i] money, but it has a set of knowledges that require you to be proficient in all of it. Calculate the maximum benefit, if you learn knowledges optimally. For example,
N = 5
1 2 2 1 3
M = 4
A[1] = 2, knowledge requirements of 1 : (1,2)
A[2] = 5, knowledge requirements of 2 : (2,3)
A[3] = 1, knowledge requirements of 3 : (5)
A[4] = 1, knowledge requirements of 4 : (1)

The maximum benefit will be 3, since you learn knowledges (1,2,3) costs 1+2+2 = 5, and the tests 1,2,4 will give you 2+5+1 = 8 profit — cost = 8 — 5 = 3

Thanks for any help in advance!!!

In an undirected graph, we define that the cost of a path is the minimum value of AN EDGE that lies in the path. For example, there is a path like this: 1->2->4, and the weight of the edge between (1,2),(2,4) are 9 and 13 consecutively, so the cost of this path is 9. Consider the cost of two vertices (u,v), in every path that connects u and v, choose the path that has the highest cost, and that cost is the cost of (u,v).
For example, we have this graph:
https://ibb.co/tmg1xkN
The cost of 1 and 4 is 10, there are 2 paths, 1->2->4 (cost 10) and 1->3->4 (cost 5) so the cost is 10 Given an undirected graph, find the cost between 1 and all other vertices from 2 to N, with N <= 10^5, and the number of edges is smaller than 5.10^6

Can anyone please help me with this? What type of problem is this? Many thanks in advance!!! (Also, pardon me because of my bad English)

How do I go from pupil to candidate master in just 3-4 months? Is this possible? If this is possible, please tell me some ways to do it. Thank you!

Do you guys have any plans to learn competitive programming effectively? I've studied CP for almost 2 years but my rating is still Pupil.