Question 1

Which of the following statements about inserting a node into a red-black tree is correct?

Accepted Answer

A) If it is the first node, it must be red. 
B) If the parent of the new node is red, no other actions are required. 
C) Color the new node black. 
D) If a double-red situation results, you must correct this. 
A) If it is the first node, it must be red. 
B) If the parent of the new node is red, no other actions are required. 
C) Color the new node black. 
D) If a double-red situation results, you must correct this.

Question 2

Consider the following tree diagrams:   Which tree represents the arithmetic expression (2 + 5) * 4?

Accepted Answer

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

Question 3

Consider the following tree diagram:   Which arithmetic expression is represented by this tree?

Accepted Answer

A) 2 * 3 + 5 + 4 * 6 - 1 
B) 2 * (3 + 5 + 4) * (6 - 1) 
C) [(2 * 3) + 5 + 4] * (6 - 1) 
D) 2 * 3 + 5 + 4 - 6 - 1 
A) 2 * 3 + 5 + 4 * 6 - 1 
B) 2 * (3 + 5 + 4) * (6 - 1) 
C) [(2 * 3) + 5 + 4] * (6 - 1) 
D) 2 * 3 + 5 + 4 - 6 - 1

Question 4

Which of the following is NOT a property of a red-black tree?

Accepted Answer

A) All paths from root to null have the name number of nodes. 
B) The root is black. 
C) All child nodes of a red node must be black. 
D) All nodes must be red or black. 
A) All paths from root to null have the name number of nodes. 
B) The root is black. 
C) All child nodes of a red node must be black. 
D) All nodes must be red or black.

Question 5

Given the BinarySearchTree and Node classes (partially shown below), select an expression to complete the recursive method smallest in the Node class.The method returns the smallest data value in the binary search tree rooted at a node.

Accepted Answer

A) right.smallest() 
B) left.smallest() 
C) Math.min(left.smallest(), right.smallest()) 
D) data.smallest() 
A) right.smallest() 
B) left.smallest() 
C) Math.min(left.smallest(), right.smallest()) 
D) data.smallest()

Question 6

In a binary search tree, where the root node data value = 45, what do we know about the values of all the descendants in the right subtree of the root?

Accepted Answer

A) some values will be > 45, but there may be a few values  45 
C) the root's right child value > 45, but the left child of the root's right child key is  45 
A) some values will be > 45, but there may be a few values  45 
C) the root's right child value > 45, but the left child of the root's right child key is  45

Question 7

Assuming that the variable t is instantiated to an empty BinarySearchTree, select a statement to complete the following code segment, so that the resulting binary search tree has a height of 4.

Accepted Answer

A) t.add("your"); 
B) t.add("the"); 
C) t.add("his"); 
D) t.add("my"); 
A) t.add("your"); 
B) t.add("the"); 
C) t.add("his"); 
D) t.add("my");

Question 8

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

Accepted Answer

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

Question 9

Which of the following statements about the three tree traversal schemes studied is correct?

Accepted Answer

A) Preorder traversal is used for evaluating arithmetic expression trees on a stack-based calculator. 
B) Postorder traversal is used for evaluating arithmetic expression trees on a stack-based calculator. 
C) Preorder traversal is used for removing file directories by removing subdirectories first. 
D) Postorder traversal is used for copying file directories. 
A) Preorder traversal is used for evaluating arithmetic expression trees on a stack-based calculator. 
B) Postorder traversal is used for evaluating arithmetic expression trees on a stack-based calculator. 
C) Preorder traversal is used for removing file directories by removing subdirectories first. 
D) Postorder traversal is used for copying file directories.

Question 10

What is the efficiency of adding an element to a red-black tree?

Accepted Answer

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

Question 11

Which of the following statements about the heapsort algorithm is correct?

Accepted Answer

A) The heapsort sorts an array that is already sorted in O(n). 
B) The heapsort algorithm is based on inserting elements into a heap and removing them in sorted order. 
C) Each insertion and removal is O(n log(n)). 
D) The heapsort algorithm requires more space than the mergesort. 
A) The heapsort sorts an array that is already sorted in O(n). 
B) The heapsort algorithm is based on inserting elements into a heap and removing them in sorted order. 
C) Each insertion and removal is O(n log(n)). 
D) The heapsort algorithm requires more space than the mergesort.

Question 12

If the child references of a binary tree node are both null, the node is ____.

Accepted Answer

A) a parent node 
B) a leaf node 
C) an interior node 
D) a root node 
A) a parent node 
B) a leaf node 
C) an interior node 
D) a root node

Question 13

You wish to traverse a binary search tree using preorder 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) II, III, I 
B) II, I, III 
C) I, II, III 
D) III, I, II 
A) II, III, I 
B) II, I, III 
C) I, II, III 
D) III, I, II

Question 14

Consider the following binary search tree:   Which of the following sequences correctly represents an inorder traversal of this tree?

Accepted Answer

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

Question 15

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

Accepted Answer

A) C 
B) B 
C) B and H 
D) H 
A) C 
B) B 
C) B and H 
D) H

Question 16

Consider the following binary search tree:   Which of the following sequences correctly represents a preorder traversal of this tree?

Accepted Answer

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

Question 17

When we map a min-heap with n elements to an array with n + 1 elements, we ignore array element 0, and place the root value at which array index?

Accepted Answer

A) 2 
B) n+1 
C) n 
D) 1 
A) 2 
B) n+1 
C) n 
D) 1

Question 18

Which of the following statements about binary trees is correct?

Accepted Answer

A) Each node in a binary tree has at most two child nodes. 
B) If divided down the middle from top to bottom, a binary tree must be symmetrical. 
C) Each node in a binary tree has at least two child nodes. 
D) The number of child nodes for each node in a binary tree is any power of two. 
A) Each node in a binary tree has at most two child nodes. 
B) If divided down the middle from top to bottom, a binary tree must be symmetrical. 
C) Each node in a binary tree has at least two child nodes. 
D) The number of child nodes for each node in a binary tree is any power of two.

Question 19

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 B, calling addNode on the root of the tree?

Accepted Answer

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

Question 20

Consider the following binary search tree:   Which of the following sequences correctly represents a postorder traversal of this tree?

Accepted Answer

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

Exam 17: Tree Structures

Which of the following statements about inserting a node into a red-black tree is correct?

Consider the following tree diagrams: Which tree represents the arithmetic expression (2 + 5) * 4?

Consider the following tree diagram: Which arithmetic expression is represented by this tree?

Which of the following is NOT a property of a red-black tree?

Given the BinarySearchTree and Node classes (partially shown below), select an expression to complete the recursive method smallest in the Node class.The method returns the smallest data value in the binary search tree rooted at a node.

In a binary search tree, where the root node data value = 45, what do we know about the values of all the descendants in the right subtree of the root?

Assuming that the variable t is instantiated to an empty BinarySearchTree, select a statement to complete the following code segment, so that the resulting binary search tree has a height of 4.

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

Which of the following statements about the three tree traversal schemes studied is correct?

What is the efficiency of adding an element to a red-black tree?

Which of the following statements about the heapsort algorithm is correct?

If the child references of a binary tree node are both null, the node is ____.

You wish to traverse a binary search tree using preorder 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

Consider the following binary search tree: Which of the following sequences correctly represents an inorder traversal of this tree?

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

Consider the following binary search tree: Which of the following sequences correctly represents a preorder traversal of this tree?

When we map a min-heap with n elements to an array with n + 1 elements, we ignore array element 0, and place the root value at which array index?

Which of the following statements about binary trees is correct?

Consider the following binary search tree: Which of the following sequences correctly represents a postorder traversal of this tree?

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