Exam 2 Review Sheet

Recursion

You should be prepared for the following:

• Identify and repair errors in a given recursive algorithm or method.
• Describe the output of a given recursive method.
• Write a recursive method (in pseudocode) to solve a given problem, for example a portion of a lab or project where you previously used iteration.
• Analyze the running time of a recursive method.

Things to remember:

• A recursive method must have a base case.
• Recursive calls must make progress toward the base case.
• Recursive algorithms should never duplicate work.

Algorithm Analysis

You should be prepared to give the running time of a specified method and to write methods that have a specified running time. Remember, most of the methods we've looked at have a running time of O(1) or O(N).

Linked Lists

You should be prepared for the following (for singly and doubly linked lists):

• Identify and repair errors in a LinkedList method.
• Describe the output of a given LinkedList method
• Write a method (in pseudocode) for a LinkedList class.
• Analyze the running time of a given method from a LinkedList class.

Things to remember:

• Always remember to handle special cases such as when your list is empty.
• The order in which you move references is extremely important.

Stacks/Queues

You should be prepared for the following (for both stacks and queues):

• Know how to execute stack/queue methods on data.
• Analyze the running time of stack/queue methods.
• Understand the implementation of a stack/queue using an array and a singly linked list.
• Use stacks/queues to solve other problems.
• Write new stack/queue methods to perform given operations.

Things to remember:

• To achieve O(1) running time for enqueue/dequeue when using an array as the underlying implementation, you must use a circular array.
• Always remember to handle special cases, such as when your stack/queue is full/empty.

Trees

You should be prepared for the following:

• Know how to execute tree methods on data.
• Understand the ordering property of binary search trees.

Things to remember:

• The worst case tree is a linked list.

Practice Problems

These problems are similar to the questions that will appear on the exam.

1. Use a Stack to determine whether the parentheses are balanced in a given Java statement.

2. Sketch the implementation of a class TwoStack. TwoStack behaves as two independent stacks implemented in a single class and provides four methods: pushA, pushB, popA, popB. Use a single array to store data and only throw a StackFullException in the case that the entire array is full.

3. Implement a Stack using two Queues. What is the running time of push/ pop?

4. Give the pseudocode for a method that takes as input the references to the heads of two unsorted singly linked lists and returns a reference to a sorted singly linked list that contains all of the elements of l1 and all of the elements of l2. What is the running time of your algorithm?

Date: 2007-11-19