Contents:

• Overview
• Problems to be Submitted

Topic: Trees
Related Reading: Ch. 8
Due: Wednesday, 2 May 2007, 2:10pm

Please make sure you adhere to the policies on academic integrity.

1. (4 points)

   Consider the tree shown on the left side of Figure 8.6 (page 452).

   • What order will nodes be visited during a preorder traversal?
   • What order will nodes be visited during a postorder traversal?

2. (4 points)

   On page 463 of Section 8.3, the text discusses how a binary tree can be dumped to text using a preorder traversal, providing an unambiguous representation which can later be used to reconstruct the tree. Demonstrate this principle by drawing a picture of the tree that produced the following text representation:

   T
   R
   NULL
   A
   V
   NULL
   NULL
   E
   R
   NULL
   NULL
   NULL
   S
   A
   NULL
   NULL
   L
   NULL
   NULL
         

3. (4 points)

   Draw a binary tree T such that simultaneously,

   • each node of T stores a single character
   • a preorder traversal of T yields BIGZANYCOMPUTER
   • an inorder traversal of T yields GIAZNBCYPMTUEOR

4. (4 points)

   Consider the tree shown in Figure 8.13 on page 467. If erase("that") were performed based on the code in the text, what would be the resulting tree?

   Note: for ease in providing your solution, you should show the entire subtree rooted at "rat" (but you do not need to draw the left portion of the original tree; that part is unchanged).

5. (4 points)

   It has been a while since we discussed the heap implementation of a priority queue. Please review the general algorithms as described on pages 484-487 of Section 8.5 (you need not concern yourself with the low-level code which is later developed).

   Assume that we start with an initially empty "max heap" (a heap where key of each parent is larger than its child). Show the final heap which results at the very end of the following sequence of keys:

   push(18), push(23), push(16), push(25), push(10), push(19), push(24), push(12), push(22), push(27), push(13), push(17), push(26), push(21).

   (you do not need to show all the intermediate calculations so long as your final result is correct)