quartz/content/notes/assignment 1.md

# COSC201 Assignment 1: Counting the seas

## 1 Due : 11:59 p.m. Friday, April 1, 2022
[[9474308Hughes]]
## 2 Introduction

Imagine a square world consisting of cells each of which is either land or water. A
computational cartographer’s paradise if you will. Anyhow, it turns out that a number
of such worlds exist of varying sizes and varying proportions of land to water. Your
continuing mission has been to search out these strange worlds and count how many
distinct bodies of water there are on each of them.

Here’s a world that you discovered recently – its dimensions are 8 × 8 and it has only
14 land cells.

![[Pasted image 20220314221111.png]]

Obviously, in this world there is only one giant sea. On the other hand, another world
with a 10 × 10 grid was also recently discovered:

![[Pasted image 20220314221121.png]]

This world is dominated by land, and there are 10 seas. You may disagree, and think
there are 15 seas, but water cells are considered to be part of the same sea if they meet
along an edge **or** at a corner.

Exploration is a complicated and expensive business and the thoughts of your superiors
have turned to simulation – that is, to creating imaginary worlds of this type in order
to try and understand how the number of seas changes depending on the size of the
underlying grid and the ratio of water to land.

### 2.1 Raw materials

You will be provided with a number of Java classes. These include:

- All the union-find implementations we’ve looked at.
- A classMap.javathat represents maps of the type we’re interested in. This class includes a number of convenience methods for various tasks. For instance:
   - indexing the cells of a map from 0 in the top left corner and then increasing from left to right and top to bottom (so, in the 10 × 10 grid the first row contains cells 0 to 9, the second 10 to 19, the third 20 to 29, and so on);
	- recognising the type of each cell (by index or coordinates);
	- identifying all the neighbours of a given cell (by index).

Using these classes, you are asked to produce some more code and to conduct and
report on some experiments.


### 2.2 Code submission (5 points)

The code you submit for this assignment will be a single class calledMapAnalyser.
Skeleton code for that class will be provided and its Javadoc will specify the require-
ments in detail. However, these and the required underlying algorithms are also dis-
cussed briefly below.

MapAnalyser(Map m)

The constructor for aMapAnalyserrequires aMapinstance. All of its methods refer to
this underlyingMap.

countSeas()

This method returns an integer which is the total number of seas of the underlyingMap.
To compute this number you must be able to identify the seas, i.e., which water cells
belong to the same seas. This is exactly the kind of task that the union-find framework
is designed for.

Specifically, given a map you can initialise aUnionFindinstance whose size is the
total number of cells in the map. Then, you can iterate once over the cells of the map –
whenever you find a water cell, you can do a union operation between it and its water
neighbours. At the end of this process, two water cells belong to the same sea if and
only if they are in same set of the partition (i.e., if and only if they have the samefind
value).

There are a number of options about how to use this idea to count seas (you can do it
as you construct the final state of the union-find instance, or after you have done so).
The choice is up to you.

seaSize(int r, int c)

This method just returns the total number of cells belonging to the same sea as the cell
in rowrand columnc. If this cell is land rather than water it should just return the
value 0.

### 2.3 Written submission (5 points

Please submit the answers to the following questions as a single **PDF** document with
filename of the form314159Pi.pdfwhere 314159 is replaced by your ID number
andPiis replaced by your surname. There are no formal requirements for the format
of your submission, but presentation, spelling and grammar are all important elements
which will account for roughly 40% of the marks for this part of the assignment.

The written answers to questions one and two could be a couple of paragraphs each
(or a bit longer) along with supporting data. A single paragraph (and possibly some
pseudocode) is enough to answer question three.

1. The efficiency of the various union-find instances affects how large a square map
    can be analysed. A reasonable length of time for a single computation might be
    something on the order of a second. Conduct experiments usingUF1,UF2,UF3,
    andUF4to determine rough values for that limit on the hardware you are us-
    ing when the probability of a cell being water is 0. 5. Describe those experiments
    (including the number of repetitions) and report on their results (a table or chart
    would be appropriate). Comment briefly on whether the outcomes match our the-
    oretical discussions of the four different algorithms and how changing the water
    probability might affect their performance.
2. Consider 10 × 10 , 100 × 100 , and 1000 × 1000 maps. Conduct experiments to
    try and determine the proportion of water needed on each so that on average
    there are two or fewer seas. Describe those experiments (including the number of
    repetitions - this should be large enough that you have confidence in the results
    you’re claiming) and report on their results.
3. Suppose that we also wanted to count the islands. How would you do that - and
    what changes to the code might be needed?