1. DATA STRUCTURES AND ALGORITHMS
LAB 9
Bianca Tesila
FILS, April 2014

2. OBJECTIVES
 Binary Trees
 Binary Search Trees

3. BINARY TREES & BINARY SEARCH TREES
 What is a tree? How can we check if a graph is a
tree?
 What binary tree traversals do you know? How
do they work?
 What’s the difference between a binary tree and a
binary search tree?
 What traversal should we use in order to get the
values of the nodes in ascending order?
 What happens when we delete a node from a
binary search tree?

4. BINARY TREES APPLICATIONS
!! Exercise:
Write a function that displays the values of
the nodes located on a given level (sent as a parameter).
Hint:
 What happens when the given level greater than the
tree’s height?
 Make a recursive function in which you decrement
level by 1 as you advance to the next level. When level
equals 0, you’ve reached the given level.
Display (T,level):
if(level==0) then print(T.data)
else Display (T.left, level-1); Display (T.right,
level-1);

5. BINARY TREES APPLICATIONS
!! Exercise:
Given a binary tree, compute its "maximumHeight"
-- the number of nodes along the longest path from
the root node down to the farthest leaf node.
Hint:
The maximum height of a tree is the maximum of the
heights of its children

6. BINARY TREES APPLICATIONS
!! Exercise:
Write a function that returns, for the root node, the difference
between the height of the left sub-tree and the height of the right
sub-tree.
Hint:
 you should take into consideration the maximum heights of the sub-trees.
 use the previous exercise
int difHeight() {
if(this == NULL) { return - 1;}
return abs(left_son->maxHeight()-right_son-
>maxHeight());
}

7. BINARY SEARCH TREES APPLICATIONS
!! Exercise:
Write a function which finds the lowest value in a
binary search tree.
Hint:
 traverse the node from root to left, recursively, until
left is NULL
 the node whose left is NULL is the node with minimum
value

8. BINARY SEARCH TREES APPLICATIONS
!! Exercise:
Write a function that displays the nodes which
have values greater than x and smaller than
y, where x and y are given as parameters.
Hint:
Take the value of the root into account in order to decide
on which way to go to find the corresponding nodes.

9. BINARY SEARCH TREES APPLICATIONS

10. BINARY SEARCH TREES APPLICATIONS
!! Exercise:
Write a function that rotates a binary search tree
that is given as a parameter. It shouldn’t change
the results of the inorder traversal.

11. BINARY SEARCH TREES APPLICATIONS
Hint:
 if the height of the right subtree is smaller than
the height of the left subtree, it should be right-
rotated.
 if the height of the left subtree is smaller than
the height of the right subtree, it should be left-
rotated.
 if the tree is balanced, nothing happens

12. HOMEWORK
Finish all the lab assignments.