The first test will be given in class on Wednesday, October 5. The test will cover everything that we have done from the beginning of the term through class on Friday, September 30. This includes exceptions and the try..catch..finally statement; the analysis of algorithms; recursion; linked lists; the concept of abstract data types; stacks and queues; binary trees, binary sort trees, and expression trees. The reading for this material is Sections 8.3, 8.5, 9.1, 9.2, 9.3, and 9.4. We have also talked about a few things that are not in the textbook, notably Merge Sort, doubly-linked lists, and turtle graphics.
You can expect a variety of questions on the test. There will be some definitions and essay-type questions. There could be one or two questions that ask you to analyze the run time of some code. Some questions will ask you to write code segments or methods or possibly even complete classes. There might also be some questions that ask you to read some code and figure out what it does.
Here are some terms and ideas that you should be familiar with:
exceptions
exceptions are represented in Java by objects in subclasses of Throwable
how exception handling compares to other ways of dealing with errors
handling exceptions: the try..catch statement
the finally clause in a try statement, and why it might be used
throwing exceptions: throw new ExceptionClass(errorMessage);
checked exceptions and mandatory exception handling
questions of efficiency of a program
run-time analysis of algorithms
worst-case analysis, best-case analysis, and average case analysis
log2(n) and how it arises in analysis of some algorithms
"Big Theta" and "Big Oh" notation ( Θ(f(n)) and O(f(n)) )
comparing Θ(n) to Θ(log(n)), or Θ(n2) to Θ(n*log(n))
disregarding "constant multiples" and "lower order terms"
Linear Search versus Binary Search
Selection Sort and Insertion Sort have run time Θ(n2)
Merge Sort (including how to do it by hand)
Merge Sort has run time Θ(n*log(n))
recursion
recursive subroutines
direct recursion and indirect recursion
base case of a recursion, and why base cases are essential
infinite recursion, and why "marking" locations as already visited is important
maze-solving and similar recursions
recursive geometric objects such as the Koch Curve and Sierpinski Triangle
using turtle graphics and recursion to draw pictures of recursive geometric objects
the QuickSort recursive algorithm
the idea of QuickSortStep (but not the detailed code)
the general idea of why QuickSort has average case run time Θ(n*log(n))
the worst case run time of QuickSort
linked data structures
understanding names such as "employee.boss.name" and "node.next.next"
simple linked lists
the head of a list; why you always need to keep a pointer to the head
traversing a linked list; using a "runner" to move down the list
basic linked list processing, such as searching, or adding up items in a list
the meaning of "while (runner != null)" and "runner = runner.next"
adding a node to the head of a list
why working at the head of a list is often a special case
inserting and deleting nodes in a list
using a "tail" pointer in a list; adding a node a the end of a list
doubly-linked lists; next and prev pointers
using a "sentinel node" at the head of a list
Abstract Data Types (ADTs)
an ADT can have more than one implementation
the "Stack" ADT
stack operations: push, pop, isEmpty
how to implement a stack as an array
how to implement a stack as a linked list
the "Queue" ADT
queue operations: enqueue, dequeue, isEmpty
how to implement a queue as a linked list with tail pointer
activation records and how they are used to implement subroutine calls
how recursion is implemented using the stack of activation records
using a stack or a queue instead of recursion
binary trees
left and right subtrees
implementing binary trees using nodes with left and right pointers
root node, leaf node, parent node, child node
recursive processing of trees
inorder, preorder, and postorder traversals of a binary tree
binary sort tree (BST)
inserting items into a binary sort tree
searching for an item in a binary sort tree
balanced binary tree
inserting/searching in a balanced binary sort tree has run time Θ(log(n))
expression trees to represent binary expressions
finding the value represented by an expression tree
postfix expressions
how to use a stack to evaluate a postfix expression
Here are a couple of sample essay-style questions from old exams, just to give you an idea of what kinds of questions might be asked:
1. What is a Binary Sort Tree? What property does a Binary Sort Tree have that a plain binary tree does not have?
2. When your program encounters an error at run time, why is it a good idea to throw an exception rather than, for example, print an error message or terminate the program?
Here are a few practice questions about pointers and linked data structures. These questions use the following classes and variables:
class ListNode { class TreeNode {
String item; int item;
ListNode next; TreeNode left, right;
} }
ListNode head; TreeNode root;
1. Draw the data structure that is created by the following code segment:
ListNode n1, n2;
n1 = new ListNode();
n1.item = "Johnny";
n1.next = new ListNode();
n1.item = "Jane";
n2 = new ListNode();
n2.item = "Jill";
n2.next = n1;
n2.next.next.next = n1;
2. Write a code segment that will find and print the longest string in the list that head points to. (If there are several strings with the same maximal length, output the one that comes first in the list.)
3. Write a method with one parameter of type ListNode and a return type of boolean. The method should test whether the items in the list are already sorted into increasing order.
4. Write a recursive method with one parameter of type TreeNode that finds the number of nodes in the tree in which the item is equal to 17.
5. The height of a binary tree is defined to be the number of nodes on the longest path from the root to any leaf. The height of an empty tree is zero. Figure out how to compute the height of a non-empty tree from the heights of its left and right subtree, and write a recursive method, with a parameter of type TreeNode, to find the height of a binary tree.
6. Draw a binary tree containing at least 12 items, and list the items in the order that they would be visited by a pre-order, by an in-order, and by a post-order traversal.
Here are two practice problems about recursion.
1. Consider this recursive method: | 2. Consider the following recursive
| using turtle graphics:
void guess(int level) { |
if (level == 0) { | void draw(double size, int level) {
System.out.print("*"); | if (level == 0) {
} | turtle.forward(size);
else { | } else {
System.out.print("("); | turtle.forward(size/2);
guess(level - 1); | turtle.turn(90);
System.out.print(("|"); | draw( size/2, level-1 );
guess(level - 1); | turtle.turn(180);
System.out.print(")"); | turtle.forward(size/2);
} | draw( size/2, level-1 );
} | turtle.back(size/2);
| turtle.turn(90);
a) Show the output from guess(1) | }
b) Show the output from guess(2) | }
c) Show the output from guess(3) |
| a) Show the drawing from draw(10, 0)
| b) Show the drawing from draw(10, 1)
| c) Show the drawing from draw(10, 2)
| d) Show the drawing from draw(10, 3)
And here are some practice problems on analysis of algorithms.
Consider the following subroutines. Each subroutine processes an array, A, of integers. In each case, discuss the run time of the code as a function of the array size, N. (The subroutines are not necessarily meant to do anything useful!)
1) static void One(int[] A) {
int sum = 0;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
sum = sum + A[i]*A[j];
}
System.out.println(sum);
}
2) static boolean Two(int[] A) {
int N = A.length;
for (int i = 1; i < N; i++) {
for (int j = 0; j < i; j++) {
if (A[i] == A[j])
return false;
}
}
return true;
}
3) static int Three(int[] A) {
int N = A.length;
int s = 0;
int i = 1;
while (i < N) {
s = s + A[i];
i = 2 * i;
}
return s;
}