Question 1

What is the complexity of adding an element to a heap?

Accepted Answer

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

Question 2

Which of the following statements about balanced trees is NOT correct?

Accepted Answer

A) For a given height, a balanced tree can hold more nodes than an unbalanced tree. 
B) In a balanced binary tree, each subtree has approximately the same number of nodes. 
C) In a balanced tree, all paths from the root to the leaves have approximately the same length. 
D) The efficiency of algorithms for balanced trees is better expressed using the size of the tree than the height of the tree. 
A) For a given height, a balanced tree can hold more nodes than an unbalanced tree. 
B) In a balanced binary tree, each subtree has approximately the same number of nodes. 
C) In a balanced tree, all paths from the root to the leaves have approximately the same length. 
D) The efficiency of algorithms for balanced trees is better expressed using the size of the tree than the height of the tree.

Question 3

Consider the following Huffman encoding tree:   The letter H will be encoded as ____.

Accepted Answer

A) 010 
B) 001 
C) 011 
D) 000 
A) 010 
B) 001 
C) 011 
D) 000

Question 4

Given the BinaryTree class (partially shown below), select an expression to complete the static recursive helper method countLeaves, which returns the number of leaf nodes in the binary tree rooted at node n.

Accepted Answer

A) n.right == null 
B) n.left == null || n.right == null 
C) n.left == null 
D) n.left == null && n.right == null 
A) n.right == null 
B) n.left == null || n.right == null 
C) n.left == null 
D) n.left == null && n.right == null

Question 5

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

Accepted Answer

A) R 
B) N 
C) M 
D) B 
A) R 
B) N 
C) M 
D) B

Question 6

Consider the following tree diagram:   Which of the following is a path in the tree?

Accepted Answer

A) R, H, X 
B) K, D, P 
C) C, R, N, X 
D) T, L, P, C 
A) R, H, X 
B) K, D, P 
C) C, R, N, X 
D) T, L, P, C

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

What is the complexity of removing an element from a heap?

Accepted Answer

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

Question 10

Given the Node class (partially shown below), select a statement to complete the recursive method descendants, which is designed to return the number of descendants of a node.

Accepted Answer

A) num = num + child.descendants(); 
B) num = num + child.descendants() + 1; 
C) num = child.descendants(); 
D) num = num + child.children.size(); 
A) num = num + child.descendants(); 
B) num = num + child.descendants() + 1; 
C) num = child.descendants(); 
D) num = num + child.children.size();

Question 11

Consider the following tree diagram:   Which of the following is NOT a path starting with the node P in the tree?

Accepted Answer

A) P, L, T 
B) P, K, D 
C) P 
D) P, B 
A) P, L, T 
B) P, K, D 
C) P 
D) P, B

Question 12

Consider the following tree diagrams:   Which of these trees is considered to be unbalanced?

Accepted Answer

A) II only 
B) III only 
C) II and III only 
D) I only 
A) II only 
B) III only 
C) II and III only 
D) I only

Question 13

If a min-heap has 14 nodes, what is known for certain when we add a new node?
i.every level of the tree will be fully occupied
II.the tree does not grow a new level
III.the root contains the smallest element

Accepted Answer

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

Question 14

Given the BinaryTree class (partially shown below), select an expression to complete the static recursive helper method rightMostValue, which is designed to return the data value in the rightmost node of the tree rooted at node n.

Accepted Answer

A) rightMostValue(n.left) 
B) rightMostValue(root.right) 
C) rightMostValue(n) 
D) rightMostValue(n.right) 
A) rightMostValue(n.left) 
B) rightMostValue(root.right) 
C) rightMostValue(n) 
D) rightMostValue(n.right)

Question 15

You wish to traverse a binary search tree in sorted order.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) I, II, III 
B) II, III, I 
C) III, I, II 
D) III, II, I 
A) I, II, III 
B) II, III, I 
C) III, I, II 
D) III, II, I

Question 16

Consider the following addNode method for inserting a newNode into a binary search tree:   Which of the following sequences of insertions will result in a balanced tree? In each sequence, the first node inserted becomes the root of the tree on which the addNode method is called for the subsequent insertions.
i.12, 7, 25, 6, 9, 13, 44
II.12, 7, 25, 44, 13, 6, 9
III.12, 25, 44, 13, 6, 9, 7

Accepted Answer

A) I and II only 
B) I only 
C) II only 
D) I and III only 
A) I and II only 
B) I only 
C) II only 
D) I and III only

Question 17

Locating an element in a balanced binary search tree takes ____ time.

Accepted Answer

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

Question 18

Consider the following tree diagram:   What is the height of this tree?

Accepted Answer

A) 5 
B) 7 
C) 3 
D) 4 
A) 5 
B) 7 
C) 3 
D) 4

Question 19

Which of the following statements about removing a node from a red-black tree is correct?

Accepted Answer

A) Before removing a node in a red-black tree, turn it red and fix any double-black and double-red violations. 
B) If the node to be removed has a child, the child must be black. 
C) If the parent of the removed node is red, no other actions are required. 
D) If the node to be removed is a black leaf, just remove it. 
A) Before removing a node in a red-black tree, turn it red and fix any double-black and double-red violations. 
B) If the node to be removed has a child, the child must be black. 
C) If the parent of the removed node is red, no other actions are required. 
D) If the node to be removed is a black leaf, just remove it.

Question 20

The height h of a completely filled binary tree with n nodes is ____.

Accepted Answer

A) h= log2(n + 1) 
B) h = log2(n) + 1 
C) h = log2(n) - 1 
D) h = log2(n - 1) 
A) h= log2(n + 1) 
B) h = log2(n) + 1 
C) h = log2(n) - 1 
D) h = log2(n - 1)

Exam 17: Tree Structures

What is the complexity of adding an element to a heap?

Which of the following statements about balanced trees is NOT correct?

Consider the following Huffman encoding tree: The letter H will be encoded as ____.

Given the BinaryTree class (partially shown below), select an expression to complete the static recursive helper method countLeaves, which returns the number of leaf nodes in the binary tree rooted at node n.

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

Consider the following tree diagram: Which of the following is a path in the tree?

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

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

What is the complexity of removing an element from a heap?

Given the Node class (partially shown below), select a statement to complete the recursive method descendants, which is designed to return the number of descendants of a node.

Consider the following tree diagram: Which of the following is NOT a path starting with the node P in the tree?

Consider the following tree diagrams: Which of these trees is considered to be unbalanced?

If a min-heap has 14 nodes, what is known for certain when we add a new node? i.every level of the tree will be fully occupied II.the tree does not grow a new level III.the root contains the smallest element

Given the BinaryTree class (partially shown below), select an expression to complete the static recursive helper method rightMostValue, which is designed to return the data value in the rightmost node of the tree rooted at node n.

You wish to traverse a binary search tree in sorted order.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

Locating an element in a balanced binary search tree takes ____ time.

Consider the following tree diagram: What is the height of this tree?

Which of the following statements about removing a node from a red-black tree is correct?

The height h of a completely filled binary tree with n nodes is ____.

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