Consider the undirected weighted graph below. Run Kruskal's algorithm on it and annotate the sequence of UNION operations that the algorithm performs. -12 -6 0 2 3 6 7 10 12 15 g b d c e a f For each step, write the two vertices being unioned (one vertex label per box). List the unions in the order Kruskal's performs them. If your version of the algorithm performs fewer unions than there are lines, leave the extra lines as empty (their default value). Please enter all union pairs in alphabetical order - so if two nodes x and y are being unioned, enter x,y, not y,x. That is, a < b < c < d < e < f < g. [table] Step 1: UNION(Answer 1 Question 2, Answer 2 Question 2) Step 2: UNION(Answer 3 Question 2, Answer 4 Question 2) Step 3: UNION(Answer 5 Question 2, Answer 6 Question 2) Step 4: UNION(Answer 7 Question 2, Answer 8 Question 2) Step 5: UNION(Answer 9 Question 2, Answer 10 Question 2) Step 6: UNION(Answer 11 Question 2, Answer 12 Question 2) Step 7: UNION(Answer 13 Question 2, Answer 14 Question 2) Step 8: UNION(Answer 15 Question 2, Answer 16 Question 2) Step 9: UNION(Answer 17 Question 2, Answer 18 Question 2) Step 10: UNION(Answer 19 Question 2, Answer 20 Question 2) | If you find it useful, the edge weights in the graph when sorted read [-12, -6, 0, 2, 3, 6, 7, 10, 12, 15]. All edge weights are distinct. In case you do not recall how Kruskal's algorithm works, the pseudocode from the course notes is reproduced below for reference. 1 2 3 4 5 6 7 8 9 function KRUSKAL(G = (V, E)) sort(E, key((u, v)) = w(u, v)) // ascending weight forest = UnionFind.initialise(n) T = (V, ∅) for each edge (u, v) in E do if forest.FIND(u) ≠ forest.FIND(v) then forest.UNION(u, v) T.add_edge(u, v) return T [/table]多项填空题