pic $1$ is requirement, pic $2$ is a$4.$ py need to complete followed pic $1$ requirement. pic $3$ is all the file contain, only need to write a$4.$ py can be implemented and pass test. The expected output is $3\mathrm{.}44$ of $8$ node graph, $26\mathrm{.}71$ of $100$ node graph, $53\mathrm{.}96$ of $250$ node graph, $223\mathrm{.}83$ of $1000$ node graph.

pic $4$ and pic $5$ are same type question with requirement and code successfully pass the test, so it might be helpful to use same style and idea to do pic $1-3$ question. something might important to know :

Some of the edges in the test cases may have a weight of $0\mathrm{.}000.$ You should still treat this as a valid edge.

You can assume the graph doesn't contain any self $-$ loops or parallel edges

You can assume the problem is always solvable

You shouldn't need to import any libraries but if you do$,$ it should not trivialise the problem e$.$ g$.$ you cannot import network libraries like networkx

For the graph files, the edges in E are formatted so that they are given from node $0$ to upwards $[$u$,$ v$,$ weight$]$ and so u

when you are constructive set A$,$ you want to make sure that you check if u $>$ v$,$ if it is then you want to make u$,$ v $=$ v$,$ u$.$ While u$,$v in set E are ordered properly, those in A are not garunteed to$.$

$2)$ Start off with including all of the elements in A$.$ It should be a no brainier that you have a loop that says for u$,$ v in edges; if its in A i want it to be in my graph. A basic $3$ lines is all you need to achieve the first part. I believe from your output, you arent doing that cuz that number was the same I was getting.

$3)$ After you include all of A with no exception, you need to make make sure that you look for all $($u$,$ v$)$ not in set$\_$A$,$ then for each of those $($u$,$v$)$ you need to check if adding them in the Union set causes a cycle to form. A simple if statement that checks if u$,$v has the same root node would suffice. If they do then adding them leads to a cycle and you dont want that; if not then you include them. It should not take you more than $4-5$ lines. You can make it easier by returning true or false from your union set operation. If the result of the function, unionSet$($u$,$v$)$ is false then you know its gonna form a cycle and if its true then it wont and you want to keep those edges.