Lecture 8 - Problems

1. Here’s the very simple general tree class we saw in lecture:

   /** A general tree */
   public class Tree {
     int value;
     List<Tree> children;
   }

   Implement the following method, which is the analogue of the binary tree findVal method you saw in the lecture video.

   /** Return true if tree T contains value v. */
   boolean findVal(Tree t, int v) {
    // your code here 
   }

   Pro tip: the easiest way to loop through a List is using an “enhanced for loop”, also known as a “foreach loop”, such as for (Thing t : listOfThings) { // do stuff with t }

2. What’s the worst-case runtime of findVal if t has \(n\) nodes in it?

3. What’s the worst-case runtime of a pre-order, in-order, and post-order traversal in which whatever is being done to each node takes constant time?

4. Suppose that you have two binary trees. You print each tree’s nodes using a pre-order traversal and find that the output is identical for both trees. Are the trees identical? Make an argument for why this is the case if so, or give a counterexample if not.

5. Suppose a binary tree has height \(h\). What’s the smallest number of nodes it could have? What’s the largest number of nodes it can have?