CS 314 - Specification 1: Designing and Implementing Algorithms
Assignment 1: Individual Assignment. You must complete this assignment on your own. You may not acquire from any source (e.g. another student, an internet site, generative AI / chatbot such as chatGPT) a partial or complete solution to a problem or project that has been assigned. You may not show another student your solution to the assignment. You may not have another person (current student, former student, tutor, friend, anyone) “walk you through” how to solve an assignment. You may get help from the instructional staff. You may discuss general ideas and approaches with other students but you may not develop or debug code together. Review the class policy on collaboration from the syllabus.
The purposes of this assignment are:
Provided Files: CodeCamp.java contains 6 method shells. CodeCampTester.java contains a main method used for testing. CodeCamp.html is the documentation for the program.
Note, just because you pass all the provided tests in CodeCampTester.java, does NOT mean your program is correct and will pass all tests. We have hundred of other test cases used for grading. None of these test cases violate the preconditions of the method or overflow the primitive data types, but they do test some corner and edge cases that students do not consider.
Assignment Restrictions: This assignment evaluates your ability to design and implement algorithms using Strings, arrays, and two dimensional arrays. I don't want to know how well you know the Java standard library or how well you can use search engine.
Therefore the following restriction apply to this assignment: The only methods and classes from the Java standard library you may use in your final solutions are:
mostVowels question you may use any methods from
the String classAlso, for this assignment, do not look up algorithms on the web or from textbooks. I want YOU to design and implement the algorithms for this assignment. I assume you know how to search the web. What I really need to know is if you can design and implement algorithms.
Note: All the methods require that the parameter not be altered in any way. You can, of course, create local copies of the parameters and alter the copies.
Getting Help: Start the assignment early in order to get help. Recall, you must complete this assignment on your own. You are not to copy code from other students in the class, current or previous, and you are not to copy code from the web. There are still ways to get help.
Assignments in CS314: If you took CS312, one difference
in programming assignments is you will not always write complete programs. You will often, but not always, be given a partial program and
have to complete it. You will do a lot of coding to "spec", that is coding
to specification; the program will have already been designed and you must
implement it, given the design. You will have to develop algorithms on your
own, but the specification of methods are already complete.
Many of the methods you write
won't ask the user for input or do any output. The "input" to the
methods will be via parameters and the "output " will be the return value.
Of course you can add user input and output to the methods that call the
specified methods to provide a way of interactively testing the methods you
write. And you can add temporary output statements to the methods you are
writing to assist in debugging issues.
Complete the six methods in the program named hammingDistance,
isPermutation, mostVowels, sharedBirthdays, queensAreSafe,
and getValueOfMostValuablePlot.
See the method descriptions below.
Note, you are encouraged to add private "helper" methods to remove
redundancy and / or provide structure to your solution.
Complete the required experiments. Place your experiment
code in CodeCamp.java. You may NOT share your experiment code with other
students.
Add at least 2 tests per method, 12 tests total to
CodeCampTester. You may copy the structure of the provided tests, but
change the data and expected results. You must write your own test cases to turn in, but you can
share test cases on Piazza to help test each others programs. In the version of CodeCampTester.java that you
turn in delete the original tests. Tests shall not violate the
preconditions of the method.
Ensure your two classes are part of the default package.
No package statement in your Java
classes for CS314..
Fill in the header for CodeCamp.java. Replace
<NAME> with your name. You are stating, on your honor, that you did
the assignment on your own, as required and did not share your code with
anyone else. If you copy code from someone else,
have the code generated by an LLM, or give your code to someone
else, the case shall be submitted to the Office of the Dean of Students.
Academic penalties up to and including an F in the course are likely. Fill in the header at the top of CodeCampTetser.java.
Submit your CodeCamp.java and CodeCampTester.java file to assignment 1 on Gradescope. Access Gradescope via Canvas. See this howto guide for more details.
Ensure you are turning in the version of CodeCamp.java that has your completed methods and the version of CodeCampTester.java with your extra tests added and the original tests deleted. You may have more than one version of the files on your system. Do not turn in the .class file; turn in the Java source code. If you turn in the wrong file you will get a zero on the assignment.
Ensure you have not imported any non standard java classes. If you have an import that starts with something besides java. or javax. your code will not compile when we test it and you will lose all correctness points.
Ensure you files are named CodeCamp.java and CodeCampTester.java. Failure to do so will result in losing all correctness points.
Ensure CodeCamp.java and CodeCampTester are part of the default package. Do not
add a package statement to the either file.
Ensure you submit the assignment under Programming Assignment 1 in Gradescope via Canvas.
Checklist: Did you remember to:
1. Hamming Distance: "The Hamming distance between two strings of equal length is the number of positions for which the corresponding symbols are different. Put another way, it measures the number of substitutions required to change one into the other, or the number of errors that transformed one string into the other." From the Wikipedia article on Hamming Distance. For this problem you will be working with arrays of ints instead of String objects.
/* Determine the Hamming distance between two arrays of ints.
pre: aData != null, bData != null, aData.length == bData.length
post: return the Hamming Distance between the two arrays of ints.
Neither the parameter aList or bList are altered as a result of this method.
*/
public static int hammingDistance(int[] aData, int[] bData){
For example given the array {1, 2, 3, 4, 5, 4, 3, 2, 1} and the array {1, 2, 8, 4, 5, 4, 3, 5, 1} the Hamming distance is 2.
2. isPermutation: This method determines if one int array is a permutation of another int array.
"A permutation, also called an "arrangement number" or "order " is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself." [mathworld.wolfram.com] For example the list {1, 2} has the following permutations; {1, 2} and {2, 1}.
Note the elements of listA and listB are lists, not sets, so duplicate items could appear. So for example given the list {1, 2, 2} the unique permutations are {1, 2, 2}, {2, 1, 2}, and {2, 2, 1}. {2, 1} is not a permutation of {1, 2, 2}., Another example of lists that are not permutations of each other: {2, 1, 1} is not a permutation of {2, 2, 1}.
/* Determine if aData is a
permutation of bData.
pre: aData != null, bData != null
post: return true if aData is a permutation of bData, false
otherwise.
Neither aData or bData are altered as a result of this method.
*/
public static boolean isPermutation(int[] aData, int[] bData)
Hint: Do not try to solve the problem by taking one of the arrays and generating all the permutations of that array and then check to see if the other array is one of those permutations. That is too inefficient except for arrays of a trivial length. One of the simplest solutions is to simply check the frequency of each element in the first array and verify the frequency of that value is the same in the second array. If not, return false right away.
3. mostVowels: On method mostVowels you can
use any and all parts of the String class and native arrays.
The mostVowels methods takes in an array of Strings as a
parameter and determines which String has the most vowels.
For this method vowels are the characters 'A', 'a', 'E', 'e', 'I', 'i', 'O', 'o', 'U', and 'u'. The method is not trying to determine which String has the largest number of distinct vowels. Thus "aaaaaa" has more vowels that "aeiou". The String "aaaaaa" has 6 vowels while the String "aeiou" only has 5 vowels. You can use whatever String methods you want when completing this method.
/* Determine the index of the String that has the largest number of vowels.
Vowels are defined as 'A', 'a', 'E', 'e', 'I', 'i', 'O', 'o', 'U',
and 'u'.
The parameter arrayOfStringsis not altered as a result of this method.
pre: arrayOfStrings!= null, arrayOfStrings.length > 0, there is an
least 1 non null element in arrayOfStrings
post: return the index of the non-null element in arrayOfStringsthat has the largest number of characters that
vowels. If there is a tie return the index closest to zero.
The empty String, "", has zero vowels. It is possible for the maximum number of vowels to be 0.
*/
public static int mostVowels(String[] arrayOfStrings)
4. sharedBirthdays: The birthday problem is a question where most people's intuition is proved
incorrect
by mathematics. The problem is: Given a group of N people, how large must N be
so that there is a 50% chance that at least 2 of the N people have the same
birthday?
Write a method with two parameters, the number of people in a group and the number of days in the year. The method will generate random birthdays for the number of people and then determine how many pairs of people have the same birthday. You don't have to generate actual days of the year for the birthdays. You can simply use ints.
Here are two ways to generate random ints in Java. One uses an object of type
Random and the other uses the random method from the
Math class.
// fist approach
Random r = new Random();
int max = 10;
int x = r.nextInt(max);
// x will now hold a value between 0 and 9 inclusive.
// The distribution of values in uniform.
// second approach
int max = 10;
int x = (int) (Math.random() * max);
// x will now hold a value between 0 and 9 inclusive.
// The distribution of values in uniform.
If three people (Olivia, Kelly, Isabelle) share the same birthday, that is 3 pairs of people:
/* Perform an experiment simulating the birthday problem.
Pick random birthdays for the given number of people.
Return the number of pairs of people that share the same birthday.
pre: numPeople > 0, numDaysInYear > 0
post: The number of pairs of people that share a birthday after
randomly assigning birthdays.
*/
public static int sharedBirthdays(int numPeople, int numDaysInYear) {
After completing the method run the following experiments:
Perform 1,000,000 experiments with 365 days per year and 182 people per experiment . What is the average number of pairs of people with shared birthdays? (Write a method to automate this experiment and put the code in CodeCamp.java.). Include your answer in a comment at the top of your CodeCampTester.java program.
How many people do you think it takes so there is a 50% chance that at least 2 of the people have a shared birthday in a 365 day year?
Perform 50,000 experiments with 365 days per year and vary the number of people from 2 to 100. 50,000 runs with 365 days, and 2 people, 50,000 runs with 365 days and 3 people, ... 50,000 runs with 365 days and 100 people. Total of 4,950,000 runs, 50,000 runs per experiments * 99 experiments = 4,950,000 runs. For each of the given number of people determine the percentage of experiments where at least one pair of people shared a birthday. At what number of people (between 2 and 100) does the percentage first exceed 50%? Does the answer surprise you? How did it compare to your predicted answer?
Include a table in a comment in your CodeCampTester.java program with the results of this experiment using the following format:
Num people: 2, number of experiments with one or more shared
birthday: 120, percentage: 0.24
.....
Num people: 100, number of experiments with one or more shared birthday: 50000,
percentage: 100.00
At the top of the table state how many people it requires to have a 50% chance of there being at least 1 shared birthday, given a 365 day year.
Note, in the version of the program you turn in, list your results in a comment, but do not include any code that calls your methods that perform these experiments.
5. queensAreSafe: The eight queens problem is a chess and programming problem with the goal is to place eight queens on a chess board so that none of them may attack any other queen. That is, no two queens are in the same row, column, or diagonal. In chess, a queen may move any number of spaces straight up, down, left, right, or along any of the 4 diagonals. In the method you are completing the board is square (same number of rows as columns) but is not necessarily 8 by 8.
Consider the following board:
A queen's position is designated with the Q. The red arrows show the squares that queen can attack. Thus if there were a queen in any of those squares this would be an unsafe board. Text based version of this board. Q is the queen, asterisks (*) mark cells that are unsafe, and hyphons (-) mark the safe cells.
*--*--*-
-*-*-*--
--***---
***Q****
--***---
-*-*-*--
*--*--*-
---*---*
are unsafe cells, and So the following set up is unsafe.
*--*--*-
-*-*-*--
--***---
***Q****
--***---
-*-*-*--
*--*--Q-
---*---*
The following set up is safe, but the number of other safe squares is going down fast.
..
*--**-*-
-*-***--
*-***---
***Q****
--***-*-
-*-***--
****Q***
---***-*
Here is an example with 8 queens that are all safe:
----Q---
Q-------
-------Q
---Q----
-Q------
------Q-
--Q-----
-----Q--
Complete the method that checks if a given board represents a safe placement of Queens. Note, the board size may be different that 8 by 8.
Strive to have a single, generalized method that checks directions. Not 4 or 8 methods for checking directions.
/* Determine if the queens on the given board are safe.
pre: board != null, board.length > 0, board is a square matrix. (In other words all rows in
board have
board.length columns.), all elements of board == 'q' or '.'.
'q's
represent queens, '.'s represent open spaces.
post: return true if the configuration of board is safe, that is no queen
can attack any
other queen on the board. Return false otherwise. The parameter board is not altered as a
result of this method.
*/
public static boolean queensAreSafe(char[][] board)
6. getValueOfMostValuablePlot: Again, do
NOT look up solutions or even approaches to this problem on the web. You are to
create a solution yourself, with help from the instructional staff if needed.
There is a video available on the course Canvas page explaining a brute force
O(N6) approach to this problem. For this problem a 2d array of ints
represents the value of each block in a
city. Each element in the array is a city block. The value of a block could be negative indicating the block is a liability to own.
Complete a method that finds the value of the most valuable contiguous sub
rectangle in the city represented by the 2d array. The sub rectangle must be at
least 1 by 1. (If all the values are negative "the most valuable" rectangle
would be the negative value closest to 0.) Note, for this method you may assume
the given 2d array of ints will not cause your method to overflow or underflow
the Java int data type.
Consider the following example. The 2d array of ints has 6 rows and 5 columns per row, representing an area of the city. The cells with the white background and underlined represent the most valuable contiguous sub rectangle in the given array. (Value of 15.)
| 0 | -2 | -7 | 0 | -1 |
| 9 | 2 | -6 | 2 | 0 |
| -4 | 1 | -4 | 1 | 0 |
| -1 | 8 | 0 | -2 | 1 |
| -10 | 1 | 1 | -5 | 6 |
| -15 | -1 | 1 | 5 | -4 |
Here is another example with the almost same 2D array with a single change. The value of the block at row 4, column 2 has been changed from 1 to 6. Given that configuration the most valuable contiguous sub rectangle in the given array has a value of 17 and is the cells with the white background and underlined.
| 0 | -2 | -7 | 0 | -1 |
| 9 | 2 | -6 | 2 | 0 |
| -4 | 1 | -4 | 1 | 0 |
| -1 | 8 | 0 | -2 | 1 |
| -10 | 6 | 1 | -5 | 6 |
| -15 | -1 | 1 | 5 | -4 |
Another example. The whole 2d array is the most valuable sub plot:
| 3 | 2 | 13 | 7 |
| 9 | 2 | 0 | 6 |
| 14 | 1 | 5 | 4 |
Hint: Implement a brute force approach that examines each possible sub matrix independently. The brute force approach is typically O(N6) which is acceptable for this assignment. The brute force approach is still complicated, but use helper methods to break the problem down into smaller, more manageable pieces.
/* Given a 2D array of ints return the value of the most valuable
contiguous sub rectangle
in the 2D array. The sub rectangle must be at lest 1 by 1.
pre: mat != null, mat.length > 0, mat[0].length > 0, mat is a
rectangular matrix.
post: return the value of the most valuable contiguous sub rectangle
in city.
the 2d array city, is not altered as a result of this method call.
*/
public static int getValueOfMostValuablePlot(int[][] city){
Expected length of solutions: My solutions to the problems above added about 210 lines to CodeCamp.java. That includes many blank lines, lines with a single brace, and comments. About 140 actual lines of new code in my solution. This does no include the code for the shared birthdays experiments. Your solution can be larger or smaller than this. I only provide the number of lines of code as a guideline.