mirror of
https://github.com/jackyzha0/quartz.git
synced 2025-12-24 05:14:06 -06:00
115 lines
5.5 KiB
Markdown
115 lines
5.5 KiB
Markdown
---
|
||
title: assignment 1
|
||
---
|
||
# COSC201 Assignment 1: Counting the seas
|
||
|
||
## 1 Due : 11:59 p.m. Friday, April 1, 2022
|
||
[9474308Hughes](None)
|
||
## 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.
|
||
|
||
|
||
|
||
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:
|
||
|
||
|
||
|
||
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?
|
||
|
||
|