Question 1: Non-recursive In-order traverse of a binary tree

Using Stack is the obvious way to traverse tree without recursion. Below is an algorithm for traversing binary tree using stack. See this for step wise step execution of the algorithm.

1) Create an empty stack S.

2) Initialize current node as root

3) Push the current node to S and set current = current->left until current is NULL

4) If current is NULL and stack is not empty then

a) Pop the top item from stack.

b) Print the popped item, set current = popped_item->right

c) Go to step 3.

5) If current is NULL and stack is empty then we are done.

Let us consider the below tree for example

1

/ \\

2 3

/ \\

4 5

Step 1 Creates an empty stack: S = NULL

Step 2 sets current as address of root: current -> 1

Step 3 Pushes the current node and set current = current->left until current is NULL

current -> 1

push 1: Stack S -> 1

current -> 2

push 2: Stack S -> 2, 1

current -> 4

push 4: Stack S -> 4, 2, 1

current = NULL

Step 4 pops from S

a) Pop 4: Stack S -> 2, 1

b) print \"4\"

c) current = NULL /*right of 4 */ and go to step 3

Since current is NULL step 3 doesn't do anything.

Step 4 pops again.

a) Pop 2: Stack S -> 1

b) print \"2\"

c) current -> 5/*right of 2 */ and go to step 3

Step 3 pushes 5 to stack and makes current NULL

Stack S -> 5, 1

current = NULL

Step 4 pops from S

a) Pop 5: Stack S -> 1

b) print \"5\"

c) current = NULL /*right of 5 */ and go to step 3

Since current is NULL step 3 doesn't do anything

Step 4 pops again.

a) Pop 1: Stack S -> NULL

b) print \"1\"

c) current -> 3 /*right of 5 */

Step 3 pushes 3 to stack and makes current NULL

Stack S -> 3

current = NULL

Step 4 pops from S

a) Pop 3: Stack S -> NULL

b) print \"3\"

c) current = NULL /*right of 3 */

Traversal is done now as stack S is empty and current is NULL.

Write a non-recursive application for the in-order traverse for a binary tree.

Question 2: Level order traverse of a binary tree (breadth first traversal)

Level order traversal of the above tree is 1 2 3 4 5.

We can use a FIFO queue to implement the level order tranversal of a binary tree.

For each node, first the node is visited and then its child nodes are put in a FIFO queue.

Step 1: Create an empty queue

Step 2: Start from the root, enqueue the root

Step 3 Loop whenever the queue is not empty

a) dequeue a node from the front of the queue and print the data

b) Enqueue the node's children (first left then right children) to the queue

Write a method to implement the level order traversal of a binary tree.

Notes: For both questions, you can use the Binary Tree class and the Node class defined in the book, you can also define your own Node class and Binary Tree class.