Homework 7

The diagrams that you should draw for the following questions should be conceptual. That is, you should draw lines between nodes to indicate parent-child relationships rather than sibling relationships.

1. (1 point) Draw a diagram of a binomial tree of rank 2.

2. (1 point) Draw a diagram of a binomial tree of rank 3.

3. (1 point) A binomial heap has 14 nodes. What are the ranks of the binomial trees it contains?

4. (1 point) You are given two binomial trees:

   • a binomial tree that contains two nodes with priorities 3 and 7, and
   • a binomial tree that contains two nodes with priorities 4 and 5.

   Show the binomial tree that results from merging these two trees.

5. (1 point) Suppose you are given a binomial heap containing two binomial trees:

   • the merged binomial tree from the previous problem, and
   • a binomial tree that contains two nodes with priorities 6 and 8.

   Show the binomial heap after removing the highest priority node.