CECS 277
LAB ASSIGNMENT #3
Assigned date:2/18
Due date: 2/25
35 points

Part I [20 points]

1. [3 points] For the following expressions. what is the order of the growth of each?

1. n³  - 1000n² + 10⁹
2.  n + log(n)
3. n²  + n log(n)
4. 2ⁿ  + n²

2. [3 points] Suppose algorithm A takes 5 seconds to handle a data set of 1,000 records. Fill in the following tables, which shows approximate growth of the excution times depending on the complexity of the algorithm.

For example, because 3000² / 1000² = 9, the algorithm would take 9 times long or 45 seconds, to handle a data set of 3000 records.

3. [3 points] What is the growth rate of the standard algorithm to find the minimum value of an arrary? Of finding both the minimum and the maximum.

4. [4 points] Your task is to remove all duplicates from an array. For example, if the array has the values

  4  7  11  4  9  5  11  7  3  5

Then the array should change to

4  7  11  9  5  3

Here is a simple algorithm. Look at a[i]. Count how many time it occurs in a. If the count is larger than 1, remove it. What is the growth rate of the time required for this algorithm?

5. [3 points] Given two arrays of n integers each, describe a O(n log(n)) algorithm for determining whether they have an element in common.

6. [4 points] Sort an array list of strings by increasing length. Hint: Use a Comparator.

Part II. [15 points]

Implement a binanry search program with the following requirements:

• Create a generic class called BinarySearcher for executing binary searches through an array. Finds a value in a sorted array, using the binary search algorithm.  The binary search method has one parameter (the value to search) and returns the index at which the value occurs, or -1 if it does not occur in the array. The class BinarySearcher has a private data member as an array, a constructor, and the binary search method.
• Create a class called InsertionSort. The class has a static method that will sort the passing array as an argument using a insertion sort algorithm. The sort method should be able to sort any objects in ascending or descending order.
• Write a test driver to search the following:
  • An faculty object. Initialize an array of faculty objects.
  • An integer number. A set of integer number is entered from the user.

Grading

• A printout of answers on problems 1 to 7.
• A printout of source codes: binarySearcher, SelectionSort, and test driver.