Algorithms and Data Structures

Please answer all questions carefully and thoughtfully.
Use as much paper as you wish, but make sure that you label your answers and that you put your name on the top of each page.
In general, you must provide justification for any answer that you give. A simple yes/no is insufficient.

(10 points) Using a stack, write a non-recursive routine which print a binary tree inorder. Use the ATD operations for stack and binary tree provided on the next sheet.
(10 points) Describe how a binary tree can be implemented using an array. Give code for the functions isRoot(), parent(), leftChild() and rightChild(). Draw a binary tree with at least depth 2 and show how it would be stored in an array.
(10 points) Given the following algorithm:
```
Tree_Insert(T, e)
(1)   y = NULL
(2)   x = T.root()
(3)   while x != NULL
(4)      y = x
(5)      if T.element(x) < e
(6)         then x = T.leftChild(x)
(7)         else x = T.rightChild(x)
(8)   if y = NULL
(9)      then T.insertRoot(e)
(10)     else  if T.element(y) < e
(11)          then  T.insertLeftChild(y,e)
(12)          else  T.insertRightChild(y,e)
     
```
- Trace the algorithm by inserting each of the following in order (5, 7, 3, 6, 6).
- Describe what the algorithm is doing in lines (3-7), (8-12).
- Discuss why this algorithm correctly inserts into a binary tree.
- Argue the performance of this algorithm.
- Give an example of the best case and worst case performance of this algorithm.
(10 points) Describe the ADT queue. Discuss how the operations Enqueue, Dequeue and Front work. Describe a C++ structure that would support a queue baised upon dynamic memory. Draw a picture of your queue.