Question 1

Given the Node class (partially shown below), select an expression to complete the isLeaf method, which is designed to return true if the node is a leaf, false otherwise.

Accepted Answer

A)  children.size()  == 0
B)  children.get(0)  == null
C)  data == null
D)  root == null A

Question 2

What is the efficiency of locating an element in a red-black tree?

Accepted Answer

A)  O(n) 
B)  O(n2) 
C)  O(1) 
D)  O(log (n) )  D

Question 3

Consider the following binary search tree diagram:  Consider the following addNode method for inserting a newNode into a binary search tree:
public void addNode(Node newNode)
{
int comp = newnode.data.compareTo(data);
if (comp < 0)
{
if (left == null) {left = newNode;}
else { left.addNode(newNode); }
}
else
{
if (right == null) {right = newNode;}
else { right.addNode(newNode); }
}
}
Which of the following trees represents the correct result after inserting element T, calling addNode on the root of the tree?

Accepted Answer

A)  II
B)  I
C)  IV
D)  III A

Question 4

Consider the following tree diagrams:  Which are binary search trees?

Accepted Answer

A)  Neither I nor II
B)  I only
C)  Both I and II
D)  II only

Question 5

What are the differences between preorder, postorder, and inorder traversals?

Accepted Answer

A)  Postorder only visits the right subtree.
B)  The order of the root visit.
C)  Preorder only visits the left subtree.
D)  The order in which we visit the left and right subtrees.

Question 6

What is the efficiency of the heapsort algorithm?

Accepted Answer

A)  O(1) 
B)  O(n2) 
C)  O(n log (n) ) 
D)  O(log (n) )

Question 7

Consider the following binary search tree:  Which of the following sequences correctly represents breadth-first traversal of this tree?

Accepted Answer

A)  A, C, H, G, E, N, P, M, J
B)  A, C, E, G, H, J, M, N, P
C)  J, E, M, C, G, P, A, H, N
D)  J, E, C, A, G, H, M, P, N

Question 8

Consider the following tree diagram:  Which of the following statements is NOT correct?

Accepted Answer

A)  Nodes H, M, and X form a subtree
B)  Nodes D and K form a subtree
C)  Nodes R and N form a subtree
D)  Nodes L and T form a subtree

Question 9

A binary tree of height h can have up to ____ nodes.

Accepted Answer

A)  2h + 1
B)  2h + 1.
C)  2h - 1
D)  2h- 1.

Question 10

What is the efficiency of removing an element from a red-black tree?

Accepted Answer

A)  O(log (n) ) 
B)  O(n2) 
C)  O(1) 
D)  O(n)

Question 11

Which of the following statements about a heap is NOT correct?

Accepted Answer

A)  A heap is a form of binary tree.
B)  The shape of a heap is very regular.
C)  A heap is always completely filled at all levels.
D)  In a heap, both the right and left subtrees of any node store elements that are at least as large as the node value.

Question 12

Consider the following tree diagram:  What is the size of the subtree with root R?

Accepted Answer

A)  2
B)  4
C)  3
D)  6

Question 13

Removing an element from a balanced binary search tree takes ____ time.

Accepted Answer

A)  O(1) 
B)  O(log (n) ) 
C)  O(n2) 
D)  O(n)

Question 14

Consider the following tree diagram:  Which of the following nodes are interior nodes?

Accepted Answer

A)  C, N, and P
B)  B
C)  C and P
D)  N

Question 15

The height of a tree can be obtained by recursively computing the heights of its subtrees, while keeping track of the height of the deepest subtree.Given the Node class (partially shown below), select an expression to complete the recursive method height, which is designed to return the height of the tree rooted at a node.

Accepted Answer

A)  maxChildHeight + 1
B)  maxChildHeight + 2
C)  maxChildHeight
D)  maxChildHeight + height()

Question 16

Adding an element to a balanced binary search tree takes ____ time.

Accepted Answer

A)  O(log (n) ) 
B)  O(1) 
C)  O(n2) 
D)  O(n)

Question 17

You wish to traverse a binary search tree using postorder traversal.Arrange the following actions in the correct order to accomplish this.
i.Print the right subtree recursively
II.Print the root
III.Print the left subtree recursively

Accepted Answer

A)  III, II, I
B)  I, III, II
C)  III, I, II
D)  I, II, III

Question 18

Locating an element in an unbalanced binary search tree takes ____ time.

Accepted Answer

A)  O(n) 
B)  O(n2) 
C)  O(1) 
D)  O(log (n) )

Question 19

Consider the following tree diagram:  Which of the following statements is NOT correct?

Accepted Answer

A)  C is an ancestor of N
B)  R is an ancestor of N
C)  D is an ancestor of P
D)  H is an ancestor of M

Question 20

Which of the following is a correct statement about red-black trees?

Accepted Answer

A)  It is a balanced binary search tree that rebalances itself after each insertion or removal.
B)  The root is red.
C)  All child nodes of a black node must be red.
D)  All paths from root to null have the name number of red nodes.

Exam 17: Tree Structures

Given the Node class (partially shown below) , select an expression to complete the isLeaf method, which is designed to return true if the node is a leaf, false otherwise.

What is the efficiency of locating an element in a red-black tree?

Consider the following tree diagrams: Which are binary search trees?

What are the differences between preorder, postorder, and inorder traversals?

What is the efficiency of the heapsort algorithm?

Consider the following binary search tree: Which of the following sequences correctly represents breadth-first traversal of this tree?

Consider the following tree diagram: Which of the following statements is NOT correct?