Question 1

When a new item is added to an AVL tree

Accepted Answer

A)  the tree may become unbalanced in only one way 
B)  the tree may become unbalanced two different ways,but the two imbalances are mirror images of each other 
C)  the tree may become unbalanced in four different ways,but because of mirror images,there are really only two fundamentally different imbalances 
D)  the height of one of the subtrees of the root may become three times the height of the other subtree 
A)  the tree may become unbalanced in only one way 
B)  the tree may become unbalanced two different ways,but the two imbalances are mirror images of each other 
C)  the tree may become unbalanced in four different ways,but because of mirror images,there are really only two fundamentally different imbalances 
D)  the height of one of the subtrees of the root may become three times the height of the other subtree

Question 2

An AVL tree is

Accepted Answer

A)  a binary search tree in which the heights of the subtrees at each node differ by at most one 
B)  a binary tree in which the left and right subtree have heights that differ by at most one 
C)  a priority queue with a balance condition 
D)  a binary tree in which each child is greater than its parent 
A)  a binary search tree in which the heights of the subtrees at each node differ by at most one 
B)  a binary tree in which the left and right subtree have heights that differ by at most one 
C)  a priority queue with a balance condition 
D)  a binary tree in which each child is greater than its parent

Question 3

Assuming a Node class
class Node
{
int element;
Node left,right;
Node(int el,Node left,Node right){
element = el;
this.left = left;
this.right = right;
}
}
Write a method int depth(Node tree)that returns the length of the longest path that begins at the node tree and ends at any leaf of the binary tree.

Accepted Answer

int depth(Node tree)
{
if (tre

Question 4

A binary tree with just one node has height

Accepted Answer

A)  -1 
B)  0 
C)  1 
D)  None of the above 
A)  -1 
B)  0 
C)  1 
D)  None of the above

Question 5

A binary tree stores items that have a natural order in such a way that at each node X,all items stored in the left subtree of X are less than the item stored at X,and all items stored in the right subtree are greater than the item stored at X.Such a binary tree is called

Accepted Answer

A)  an ordered binary tree 
B)  a binary search tree 
C)  an AVL tree 
D)  a priority queue 
A)  an ordered binary tree 
B)  a binary search tree 
C)  an AVL tree 
D)  a priority queue

Question 6

A binary tree is a collection of nodes in which

Accepted Answer

A)  each node has at most one predecessor and at most one successor 
B)  each node has at most one predecessor and exactly two successors 
C)  each node has at most one predecessor and at most two successors 
D)  each node has at least one predecessor and at most two successors 
A)  each node has at most one predecessor and at most one successor 
B)  each node has at most one predecessor and exactly two successors 
C)  each node has at most one predecessor and at most two successors 
D)  each node has at least one predecessor and at most two successors

Question 7

Binary trees have been used

Accepted Answer

A)  in compilers and interpreters to represent expressions 
B)  in computer hardware to model branching patterns of electronic signals 
C)  in the Java Collections Framework to internally implement the Vector class 
D)  None of the above 
A)  in compilers and interpreters to represent expressions 
B)  in computer hardware to model branching patterns of electronic signals 
C)  in the Java Collections Framework to internally implement the Vector class 
D)  None of the above

Question 8

Let X be a node in a binary tree.Any node on the path from X to a leaf is called

Accepted Answer

A)  a descendant of X 
B)  an ancestor of X 
C)  a relative of X 
D)  a subordinate of X 
A)  a descendant of X 
B)  an ancestor of X 
C)  a relative of X 
D)  a subordinate of X

Question 9

Consider the operation of deleting the root of a binary search tree.If the root has two children,then

Accepted Answer

A)  the root node should be removed,then the least node in the right subtree should be deleted and used to replace the root 
B)  the rood node should be removed,and the deepest rightmost leaf should be used to replace the root 
C)  the rood node should be removed,the deepest rightmost leaf should be used to replace the root,and then a sift down should be performed to take the root replacement to its proper place 
D)  the operation should be recursively performed on the two subtrees of the root. 
A)  the root node should be removed,then the least node in the right subtree should be deleted and used to replace the root 
B)  the rood node should be removed,and the deepest rightmost leaf should be used to replace the root 
C)  the rood node should be removed,the deepest rightmost leaf should be used to replace the root,and then a sift down should be performed to take the root replacement to its proper place 
D)  the operation should be recursively performed on the two subtrees of the root.

Question 10

A complete binary tree with N nodes may be stored in an array A of length N by storing the root at A[0],and then storing in successive array locations the nodes of the tree in increasing order of the level of nodes.If nodes in the same level are stored in left to right order,then the node stored at A[k] will be a leaf if and only if

Accepted Answer

A)  2k+1 ≥ N 
B)  2k+1 > N 
C)  k/2 > N 
D)  None of the above 
A)  2k+1 ≥ N 
B)  2k+1 > N 
C)  k/2 > N 
D)  None of the above

Question 11

The predecessor of a node in a binary tree is called its

Accepted Answer

A)  progenitor 
B)  ancestor 
C)  parent 
D)  precursor 
A)  progenitor 
B)  ancestor 
C)  parent 
D)  precursor

Question 12

A complete binary tree with N nodes has depth approximately equal to

Accepted Answer

A)  2N 
B)  log N 
C)  N2 
D)  N 
A)  2N 
B)  log N 
C)  N2 
D)  N

Question 13

To add a new element X to a binary search tree:

Accepted Answer

A)  if the tree is empty,make X the root of a new tree;otherwise,compare X to the root,if X is less,put it in the left subtree,if it is greater,put in the right subtree 
B)  First add X in the position of the root.If X is a leaf,or is less than its children,stop.Otherwise,repeatedly swap X with the smaller of its two children until X becomes a leaf,or becomes less than its children. 
C)  Add X as a leaf,taking care to preserve the completeness of the heap.If X is now the root,or is greater than its parent,stop.Otherwise,repeatedly swap X with its parent until X becomes the root,or becomes greater than its parent. 
D)  insert X using the same algorithm for insertion in a binary search tree.If the tree remains balanced,stop.Otherwise,execute a rebalancing operation. 
A)  if the tree is empty,make X the root of a new tree;otherwise,compare X to the root,if X is less,put it in the left subtree,if it is greater,put in the right subtree 
B)  First add X in the position of the root.If X is a leaf,or is less than its children,stop.Otherwise,repeatedly swap X with the smaller of its two children until X becomes a leaf,or becomes less than its children. 
C)  Add X as a leaf,taking care to preserve the completeness of the heap.If X is now the root,or is greater than its parent,stop.Otherwise,repeatedly swap X with its parent until X becomes the root,or becomes greater than its parent. 
D)  insert X using the same algorithm for insertion in a binary search tree.If the tree remains balanced,stop.Otherwise,execute a rebalancing operation.

Question 14

A binary tree with height 1 must have

Accepted Answer

A)  exactly two nodes 
B)  two or three nodes 
C)  exactly three nodes 
D)  one or two nodes 
A)  exactly two nodes 
B)  two or three nodes 
C)  exactly three nodes 
D)  one or two nodes

Question 15

A node in a binary tree that has no children is called

Accepted Answer

A)  a leaf 
B)  a single node 
C)  barren 
D)  a twig 
A)  a leaf 
B)  a single node 
C)  barren 
D)  a twig

Question 16

A binary tree traversal method that visits the root first,and then recursively traverses the left and right subtrees is called

Accepted Answer

A)  top down traversal 
B)  priority order traversal 
C)  preorder traversal 
D)  postorder traversal 
A)  top down traversal 
B)  priority order traversal 
C)  preorder traversal 
D)  postorder traversal

Question 17

To find the minimum node in a binary search tree

Accepted Answer

A)  you should start at the root,and then keep passing from each node to its left child until you come to a node with no left child 
B)  you should start at the root,and then keep passing from each node to its right child until you come to a node with no right child 
C)  you should look at the root of the binary tree 
D)  you need to examine every node,and then pick the one with the least value 
A)  you should start at the root,and then keep passing from each node to its left child until you come to a node with no left child 
B)  you should start at the root,and then keep passing from each node to its right child until you come to a node with no right child 
C)  you should look at the root of the binary tree 
D)  you need to examine every node,and then pick the one with the least value

Question 18

A ternary tree is like a binary tree,except each node may have up to three successors.Write a TNode class that can be used to represent a ternary tree.Define a notion of preorder and postorder traversal for ternary trees,and write methods void postorder(TNode tree)and void preorder(TNode tree)that implements your notion of those traversals.

Accepted Answer

class TNode
{
TNode left,middle,right;
S

Question 19

Let X be a node in a binary tree.The collection of all descendants of X

Accepted Answer

A)  form a binary tree called the subtree rooted at X 
B)  form the left subtre of X 
C)  form the right subtree of X 
D)  None of the above 
A)  form a binary tree called the subtree rooted at X 
B)  form the left subtre of X 
C)  form the right subtree of X 
D)  None of the above

Question 20

Traversing a binary search tree in inorder

Accepted Answer

A)  yields the same sequence as a postorder traversal 
B)  yields a sequence in which the minimum element is at the approximate midpoint of the sequence 
C)  will yield a sorted sequence 
D)  is more efficient than traversing the tree in preorder 
A)  yields the same sequence as a postorder traversal 
B)  yields a sequence in which the minimum element is at the approximate midpoint of the sequence 
C)  will yield a sorted sequence 
D)  is more efficient than traversing the tree in preorder

When a new item is added to an AVL tree

An AVL tree is

A binary tree with just one node has height

A binary tree stores items that have a natural order in such a way that at each node X,all items stored in the left subtree of X are less than the item stored at X,and all items stored in the right subtree are greater than the item stored at X.Such a binary tree is called

A binary tree is a collection of nodes in which

Binary trees have been used

Let X be a node in a binary tree.Any node on the path from X to a leaf is called

Consider the operation of deleting the root of a binary search tree.If the root has two children,then

The predecessor of a node in a binary tree is called its

A complete binary tree with N nodes has depth approximately equal to

To add a new element X to a binary search tree:

A binary tree with height 1 must have

A node in a binary tree that has no children is called

A binary tree traversal method that visits the root first,and then recursively traverses the left and right subtrees is called

To find the minimum node in a binary search tree

Let X be a node in a binary tree.The collection of all descendants of X

Traversing a binary search tree in inorder

Introduction to Computers and Java

Java Fundamentals

Decision Structures

Loops and Files

Methods

A First Look at Classes

A First Look at Gui Applications

Arrays and the Arraylist Class

A Second Look at Classes and Objects

Text Processing and More About Wrapper Classes

Inheritance

Exceptions and Advanced File Io

Advanced Gui Applications

Applets and More

Recursion

Sorting, Searching, and Algorithm Analysis

Generics

Collections

Array-Based Lists

Linked Lists

Stacks and Queues

Filters

Exam 22: Binary Trees, Avl Trees, and Priority Queues

When a new item is added to an AVL tree

An AVL tree is

A binary tree with just one node has height

A binary tree stores items that have a natural order in such a way that at each node X,all items stored in the left subtree of X are less than the item stored at X,and all items stored in the right subtree are greater than the item stored at X.Such a binary tree is called

A binary tree is a collection of nodes in which

Binary trees have been used

Let X be a node in a binary tree.Any node on the path from X to a leaf is called

Consider the operation of deleting the root of a binary search tree.If the root has two children,then

The predecessor of a node in a binary tree is called its

A complete binary tree with N nodes has depth approximately equal to

To add a new element X to a binary search tree:

A binary tree with height 1 must have

A node in a binary tree that has no children is called

A binary tree traversal method that visits the root first,and then recursively traverses the left and right subtrees is called

To find the minimum node in a binary search tree

Let X be a node in a binary tree.The collection of all descendants of X

Traversing a binary search tree in inorder

Introduction to Computers and Java

Java Fundamentals

Decision Structures

Loops and Files

Methods

A First Look at Classes

A First Look at Gui Applications

Arrays and the Arraylist Class

A Second Look at Classes and Objects

Text Processing and More About Wrapper Classes

Inheritance

Exceptions and Advanced File Io

Advanced Gui Applications

Applets and More

Recursion

Sorting, Searching, and Algorithm Analysis

Generics

Collections

Array-Based Lists

Linked Lists

Stacks and Queues

Filters