# T5-bak

```CS 5302 Data Structures and Algorithm
Tutorial 5 Tree
Written Exercise
1.
Give an O(n) algorithm for computing the depth of all the nodes of a tree T,
where n is the number of nodes of T.
2.
For a tree T, let NI denote the number of internal nodes, and let NE denote the
number of its external nodes. Show that if every internal node in T has exactly 3
children, then NE = 2NI + 1.
Programming Exercise
3
Design and implement two ADT for binary tree respectively with (a) linked
methods listed below. Some source codes can be found in pages 283-287.
Analyze the running time of each method.

Create and return a new node r storing element e and make r the root. An
error occurs if the tree is not empty.

insertLeft(v,e)
Create and return a new node w storing element e, and w as the left child of
v and return w. An error occurs if v already has a left child.

insertRight(v,e)
Create and return a new node z storing element e, add z as the right child of
v and return z. An error occurs if v already has a right child

preorderTraverse()
Perform preorder traversal of the binary tree.
```