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COMS 311: Homework 4

Total Points: 200
Late submission policy. If you submit by Oct 31, 11:59PM, there will be 20% penalty. That
is, if your score is x points, then your final score for this homework after the penalty will be
0.8 × x. Submission after Oct 31, 11:59PM will not be graded without explicit permission from the
instructors.
Points. Total points for this homework assignment is 200pts. There will be extra credit test
cases worth 40pts.
Learning outcomes.
Design, implement and evaluate algorithms following specifications.
0 Preamble
Description of a programming assignment is not a linear narrative and may require multiple readings
before things start to click. You are encouraged to consult instructor/Teaching Assistants for any
questions/clarifications regarding the assignment. Your programs must be in Java.
1 Problem Description
You are given a 2-D rectangular grid in which a robot is supposed to move from one location to
another. The grid contains n rows and m columns, with row values in the range [0, n − 1] and
column values in the range [0, m − 1]. Each location in the grid is defined by the value of row and
column. For instance, the row-column pair (5, 2) is the address of the location with row value 5
and with column value 2. The top-left corner of the grid has the location (0, 0). Locations outside
the range of the row and column values do not exist.
The grid includes certain locations that are marked to include obstacles.
The robot at location (i, j) can make direct moves in 4 possible directions: north (n) to a
location (i − 1, j) (if the location exists and does not contain obstacle); south (s) to a location
(i + 1, j) (if the location exists and does not contain obstacle); west (w) to a location (i, j − 1) (if
the location exists and does not contain obstacle); east (e) to a location (i, j + 1) (if the location
exists and does not contain obstacle). The robot can make one or more direct moves to go from
one location to another.
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You are also given two specific locations: the start location S and the destination location D.
An illustration of the grid is as follows (locations with obstacles are presented as *, start location
is S, destination location is D, all other locations are marked 0):
0 0 0 * 0 0 0 0 0 0
0 0 S * 0 0 0 0 0 0
0 * * 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 0 D 0 0
0 0 0 0 0 0 0 0 0 0
A plan is a sequence of moves, which can be used to move the robot from S to D (avoiding the
obstacles). Your objective is to identify such a plan or plans. For instance, for the above grid, a
possible plan can be illustrated as:
0 0 0 * 0 0 0 0 0 0
s w S * 0 0 0 0 0 0
s * * 0 0 0 0 0 0 0
e e e e e e e s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 0 D 0 0
0 0 0 0 0 0 0 0 0 0
It states that starting from S, the robot can move to a location with non-zero value (other than
obstacle) and at each location, it can follow the direction of move to eventually reach D. In the
above illustration, from S (location (1, 2)), the robot moves to location (1, 1), from where it needs
to move west (w). By moving west, the robot comes to location (1, 0), from where it needs to move
south (s).
There are many different plans that can move the robot from S to D.
2 Encoding Description
You are required to write a Java program that takes as input the 2-D grid information, as presented
above, and outputs plan(s), if one exists. The input will be provided in a file; the file will be present
in the same folder (working directory if you use eclipse IDE) as your program’s executable and the
name of the file will be an input argument for your executable. The file will contain information
about the number of rows and columns in the grid, the start and the destination locations of the
robot and the obstacle locations. For instance, the above grid will be encoded as
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nrows 10 ncols 10
start 1 2
dest 8 7
obstacles
2 2
1 3
0 3
2 1
4 6
6 6
5 6
7 6
(Each element in the text file is separated by a single space.)
You are required to write the following:
1. A class RobotPath. You can decide what attributes/properties should be part of the class.
2. A method in RobotPath with signature
public void readInput(String FileName) throws IOException
The objective of the method is to read the input problem instance (grid information, start/destination
and obstacle information) and populate the class-attributes.
3. A method in RobotPath with signature
public void planShortest()
The objective of this method is to use the input grid and identify all possible shortest plans.
The length of a plan is defined by the number of moves made the Robot. A plan with minimal
length is a shortest plan. Note that, there may be more than one shortest plan.
4. A method in RobotPath with signature
public void quickPlan()
The term “quick” in quickPlan refers to quickly finding a plan (not necessarily the shortest
plan). The objective of this method is to use the input grid and identify a plan using the
following strategy:
(a) No Back-paddling. the plan must not include directives that will make the Robot to go
through the same location more than ones.
(b) Predictive Selection. Recall that, from each location l, the Robot can make multiple
direct moves leading to (at most four) different locations. Let us refer to these locations
as C, the set of choices. The quickPlan algorithm proceeds by considering a choice in C
and if by using that choice, the algorithm can find a path leading to destination, then the
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algorithm outputs the plan; otherwise, it considers a different choice in C (until there is
no more choices to consider).
The quickPlan algorithm considers these choices in specific order, such that any choice
that is closer to the D is considered before any choice that is further from D. The
closeness of measured using Euclidean distance1 between the choice and the D.
If there are two choices at same distance from D, then the choice with smaller value for
the row will be considered to be closer D.
For instance, in our running example, if for the location (3, 3), there are 4 possible moves
(e, w, n, s) leading to choices C = {(3, 4),(3, 2),(2, 3),(4, 3)}. The choice (4, 3) is closest
to D = (8.7) and the next choice closest to D is (3.4), and so on. Hence, the algorithm
will first consider the move to south from (3, 3) to look for a plan; if no plan is found
using that choice, then the algorithm will consider the move to east from (3, 3) to look
for a plan; and after than will consider the move to west and finally, the move to north.
(c) Quick Stop. The search for a plan must terminate as soon as a plan is found.
5. A method in RobotPath with signature
public void output()
The objective of this method is to output the plans generated by either planShortest or
quickPlan methods. In other words, you can assume that this method will be only invoked
after planShortest or quickPlan. For instance, for the above example,
planShortest();
output();
will produce the following output.
0 0 0 * 0 0 0 0 0 0
s w S * 0 0 0 0 0 0
s * * 0 0 0 0 0 0 0
se se se se se se e s 0 0
se se se se se s * s 0 0
se se se se se s * s 0 0
se se se se se s * s 0 0
se se se se se s * s 0 0
e e e e e e e D 0 0
0 0 0 0 0 0 0 0 0 0
Note that, some of the grid locations have more than one directive for the Robot plan.
For instance, location (3, 0) has the directive that the Robot can move south or east—each
directive is part of some shortest plan. In the event, there are multiple directives at a location,
the order in which the directives will be presented is s n w e. In the above example, we see
multiple directives se. If there was a location with multiple directives leading to n and e,
then the output for that location should be ne (not en).
On the other hand, in our running example, the output after
1Distance between two locations: (i, j) and (i
0
, j0
) is p
(i − i
0)
2 + (j − j
0)
2.
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quickPlan();
output();
0 0 0 * 0 0 0 0 0 0
s w S * 0 0 0 0 0 0
s * * 0 0 0 0 0 0 0
e e e s 0 0 0 0 0 0
0 0 0 e s 0 * 0 0 0
0 0 0 0 e s * 0 0 0
0 0 0 0 0 s * 0 0 0
0 0 0 0 0 s * 0 0 0
0 0 0 0 0 e e D 0 0
0 0 0 0 0 0 0 0 0 0
The methods planShortest or quickPlan may not find any plan due to the presence of
obstacles in the input grid. In such scenario, the output should just produce the input grid.
For instance,
0 * 0 * 0 0 0 0 0 0
0 * S * 0 0 0 0 0 0
0 0 * 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 * 0 0 0
0 0 0 0 0 0 0 D 0 0
0 0 0 0 0 0 0 0 0 0
Here is another example scenario with the input Grid specification as follows:
nrows 10 ncols 10
start 1 2
dest 8 7
obstacles
2 2
1 3
0 3
2 1
4 6
6 6
5 6
7 6
8 6
9 6
The result of
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planShortest();
output();
will be
0 0 0 * 0 0 0 0 0 0
s w S * 0 0 0 0 0 0
s * * 0 0 0 0 0 0 0
e e e e e e e s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * D 0 0
0 0 0 0 0 0 * 0 0 0
And, the result of
quickPlan();
output();
will be
0 0 0 * 0 0 0 0 0 0
s w S * 0 0 0 0 0 0
s * * 0 0 0 0 0 0 0
e e e s 0 e e s 0 0
0 0 0 e s n * s 0 0
0 0 0 0 e n * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * s 0 0
0 0 0 0 0 0 * D 0 0
0 0 0 0 0 0 * 0 0 0
3 Output Formatting
As the assessment of your submission will be conducted on the output, which has a strict format,
it is necessary to adhere to the format. Submissions that produce incorrectly formatted output are
incorrect. To match the output correctly, use the following directive for all grid-cell outputs (in
addition to appropriate row and column format):
System.out.printf(“%5s”, <string-to-output-in-a-cell>);
4 Submission Requirements
1. You shall use default package (that is, no package at all). Though it is not recommended in
practice, organize your classes as follows:
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(a) Prepare a file RobotPath.java. In this file you will write the specified class and its
methods, and other helper classes. You can have as many helper classes and methods
as you want. For instance,
// import directives
import java.io.IOExceptions;
//
// primary class for this file
public class RobotPath {
// attributes
public void readInput(String filename) throws IOException {
// implementation for reading file with grid information
}
public void planShortest() {
// uses the grid data for finding all shortest plans
}
public void quickPlan() {
// uses the grid data for finding plan as per specs
}
public void output() {
// invoked after planShortest or quickPlan
}
// Any other helper methods
}
class MyClass {
// Any helper class needed
}
(b) Prepare another file with any name suitable for your setup which only contains the
main method and declares the object of type RobotPath and invokes it methods. You
can use the following sample file containing the main method (there is no constraint on
how/what you write in this file as this file will not be part of your submission).
import java.io.IOException;
public class HW4Test {
public static void main(String[] args) throws exception {
RobotPath rPath = new RobotPath();
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rPath.readInput(args[0]);
System.out.println(“\n planShortest:\n”);
rPath.planShortest();
rPath.output();
System.out.println(“\n quickPlan:\n”);
rPath.quickPlan();
rPath.output();
}
}
Assume that the running example is present in a file named Grid.txt, then for a correct implementation of RobotPath, it (javac HW4.java; java HW4 Grid.txt) should
output on the console two grids with plans (a sample file is provided).
You are required to submit the RobotPath.java file and nothing else. (Double check that all
necessary helper classes are present in this file.)
5 Postscript
1. You must follow the given specifications. Method names, classnames, return types, input
types. Any discrepancy may result in lower than expected grade even if “everything works”.
2. In the above problems, there are several data structure/organization that are left for you
to decide. Please do not ask questions related to such data structure/organization. Part of
the exercise to understand and assess a good way to organize data that will allow effective
application of methods/algorithms.
3. You will have to think about how to model the problem into a graph-based problem and
apply your knowledge of graph algorithms to address the original problem. Please do not ask
questions about how to model the problem as a graph-based problem and/or what graph algorithms to use. Part of the exercise is to understand and assess a good way to represent/reduce
a problem to a known problem for which we know an efficient algorithm.
4. Start reading and sketching the strategy for implementation as early as possible. That does
not mean starting to “code” without putting much thought on what to code and how to code
it. This will also help in resolving all doubts about the assignment before it is too late. Early
detection of possible pitfalls and difficulties in the implementation will help in reducing the
endTime-startTime for this assignment.
5. Both correctness and efficiency are important for any algorithm assignment. Writing a highly
efficient incorrect solution will result in low grade. Writing a highly inefficient correct solution
may result in low grade. In most cases, the brute force algorithm is unlikely to be the most
efficient. Use your knowledge from lectures, notes, book-chapters to design and implement
algorithms that are correct and efficient.
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6. Test your code extensively (starting with individual methods). Your submission will be
assessed using test cases that are different from the ones provided as part of this assignment
specification. Your grade will primarily depend on the number of these test cases for which
your submission produces the correct result.
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