Question

Union-find algorithm.

1.when doing union by size, what extra information is kept at the root of each subtree?

  

the height of the tree   

the number of children each node has    

the number of nodes in the tree

2.What is true of the union (a,b) operation using union by rank?

  

You need to do find(a) but not a find(b) before unioning.

You need to do find(a) and find(b) before unioning.

3.When using path compression, when does path compression happen?

when specifically called   

continually     

during find

4.What is the motivation behind union by rank (height)?

  

As long as you are touching a node, you may as well point it directly to the current root (which you know)   

Answer is not mentioned   

Making trees shorter makes access faster

Answer 1

1. When doing union by size, we keep the number of children each node has as the count, this helps in avoiding tall trees,and makes trees more flat.
2. We need to find(a) and find(b) before union .
3. Path compression happens when finding root of an element , here we make every other node in path point to its grandparent.
4. Motivation behind union by rank is that we do not want tall trees, because we need to traverse from the child to the root of the tree, if the tree is very tall, suppose with n elements tree has a height of n then we need to traverse every element and find operation becomes too expensive, but if trees are flat we can traverse from child to root in log(n) time, hence we want flat trees, which can be achieved by linking small tree below large one.