Write a C++ program that creates a tree from given input, and prints the height of the tree using the level-order traversal, where the height of a tree is defined as the maximum level number for any node in the tree.

The following is how we define tree nodes:

struct node

{ int item; node *l, *r;

node(int x)

{ item = x; l = 0; r = 0; }

};

typedef node* link;

(Hint: You may want to add a new field to the above definition to store the height of a node)

The trees for this assignment have the following properties:

1) Each node has zero, one, or two children (left child and right child);

2) Each node has a unique key. That is, the item in each node is different from items in all other nodes.

3) Each input item is also unique.

You may find the following function useful. This function visits nodes in a tree in level order starting at the given root h using a QUEUE (you can use any implementation for QUEUE):

void traverse(link root, int n)

{

link h;

QUEUE q(n);

q.put(root);

while (!q.empty())

{

h = q.get(); // get link h at the head of the queue

if (h->l != 0) q.put(h->l);

if (h->r != 0) q.put(h->r);

}

}

Your program will receive the following input and do the following for each input:

C : Create the root node with item r. If the tree is not empty (i.e. the root exists), return an error

L : Find the node with item p. Let u be that node. Create a new node v with item l. Make node v node us left child. If node u has already a left child, return an error

R : Find the node with item p. Let u be that node. Create a new node v with item r. Make node v node us right child. If node u has already a right child, return an error

P: Print the tree height using a level order traversal

See the example dialogue below:

C 5

Root node with item 5 has been created

C 10

Error: Tree is not empty

L 5 3

Node with item 3 has been added

R 5 4

Node with item 4 has been added

P

the tree height is 2 (using the level order traversal of the entire tree)

L 4 7

R 7 8

R 3 9

L 9 11

R 4 12

L 7 13

L 8 14

R 12 15

R 8 16

L 13 17

P

the tree height is 5 (using the level order traversal of the entire tree)

L 14 19

P

the tree height is 6 (using the level order traversal of the entire tree)