Weighted union rule

Question

Can someone check with me if I'm using the rule right in the last step (7)?

UPDATE:

Numbers inside the parentheses are the number of elements (weight(?)) of each set that takes part in the Union. Uppercase letters are names of sets.

As I understand this: we are using as our rank the number of elements? This is getting confusing, each one is using different terms for the same stuff.

We have Unions:

U(1,2,A)
U(3,4,B)
U(A,B,C)
U(5,6,D)
U(7,8,E)
U(D,C,F)
U(E,F,G)

enter image description here

score 1 · Answer 1 · answered Feb 15 '14 at 19:22

1

Step 7 (and the others) looks correct, but step 6 doesn't.

In step 6, 4 should be the root, as that's the bigger tree.

answered Feb 15 '14 at 19:22

Bernhard Barker

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1+2+3+4=10 and 5+6=11 , shouldn't 6 be the root in step 6? (cause of the weight) – user2692669 Feb 15 '14 at 19:25
1

I've never seen a union-find algorithm that uses the nodes' values as the weight - this won't make a whole lot of sense either, as the nodes' values don't really correspond to the running time of operations. It usually uses the height / depth of the tree. – Bernhard Barker Feb 15 '14 at 19:38
I updated my problem as you instructed, I think it's correct now(?). – user2692669 Feb 15 '14 at 19:47
Sorry, there is a catch in the problem I did an edit. These things are very tricky! – user2692669 Feb 15 '14 at 22:26

score 0 · Answer 2 · edited Feb 15 '14 at 19:53

void combine(int x,int y)
{
    int xroot=find(x),yroot=find(y);
    if(rank[xroot]<rank[yroot]) 
        parent[xroot]=yroot;
    else if(rank[xroot]>rank[yroot]) 
    parent[yroot]=xroot;
    else 
    {///rank of both is equal..
        parent[yroot]=xroot;
        rank[xroot]++;
    }
}

Using rank, you see the size of set, not sum of vertices, so step 6 is wrong.

But why the size?
Because if we make root of bigger set the root of smaller set , we need to update parents of smaller number of nodes.

For the best explanation, I would recommend CLRS (Introduction to Algorithms).

Hope it helps you!

Weighted union rule

2 Answers2