ii Find the union of the sets. 11, 3U12, 4) Choose the correct answer below. O A. {1, 3U12, 4t - 12, 4) O D. {1, 3)UK2, 4) (1, 2, 3, 4) Solution 1. {1,3}U{2,4} combining of all the distinct elements of the two sets is the union of the two sets. {AUB}={x|xA or xB} For ex : A={red,blue,green} and B ={yellow , green} Then {A}U{B} = { red ,blue ,green,yellow} Therefore, the answer of this question is (D) : {1,3}U{2,4}={1,2,3,4}. 2. {x|x^2=81} x^2=81; x=-9,+9. So, this resulting set represents the value of x and is equal to {-9,+9}..

1. Implement a minimum spanning tree using Boruvka's algorithm.
Implement a minimum spanning tree using Boruvka's algorithm.
Solution
The psuedo code is as follows:
1 Graph input = /* read input */;
2 UnionFind uf (input.getNodes ());
3 Workset ws = input.getNodes();
4 foreach (Node n : ws) {
5 Edge e = minWeight (input.getOutEdges (n));
6 Node rep1 = uf.find (e.src);
7 Node rep2 = uf.find (e.dst);
8 if (rep1 != rep2) {
9 e.markInMST();
10 Node rep = uf.union (rep1, rep2);
11 ws.add (rep)
12 }
13 }