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CMT304

Programming Paradigms

Functional Programming

Assignment

Consider a small binary image (or 2D array or matrix) that is represented as a list of lists which contains only the numbers 0 or 1, e.g.,

[[0,0,0,0,1,1],

[1,1,1,1,1,0],

[1,1,0,0,1,0],

[1,1,0,0,1,1],

[1,0,1,1,1,1]]

We wish to find the number of pixels in the largest connected component of such images (there can of course be more than one component with the same largest number). A con- nected component is a cluster of pixels that contain the same value and there is a path from each pixel to each other pixel inside that cluster. A path is formed from a start pixel by mov- ing either horizontally (one element left or right in the same inner list) or vertically (one list up or down in the outer list without changing the position in the inner list) to the next pixel until the end pixel is reached (this is 4-pixel connected, i.e. no diagonal movement). The number of elements in the largest connected component for the value 0 in the above example is 4 (among the 4 components). It is 19 for the value 1 (there is only one component).

Task 1: Write an efficient Haskell function

nlcc l v

that finds the number of elements in the largest connected component of the binary image (list of lists) l for the value v. Note, there are multiple, more or less efficient algorithms to solve this problem – make sure you clearly document your approach. Also note, you must write a function, not a full program (so no main, etc.) and it must have the above name with two arguments (failing to do so may result in 0 marks for this task). Make sure your Haskell code can be compiled/interpreted without errors (otherwise 0 marks may be assigned for this task).

Note that you must write your own code to solve this problem and not just call a library function, or copy code from some other source (independent of plagiarism issues, even if you reference; you only get marks for your own work). You may use the standard libraries listed in the Haskell 2010 language report, but not any other libraries (otherwise the code

will be treated as not compilable/interpretable, which may result in 0 marks for this task). Task 2: Write a short report on functional programming related to the problem:

1. Provide, in up to 300 words, two arguments for and two arguments against using functional programming to solve this problem.

2. Discuss, in up to 300 words, whether the functional programming paradigm is suitable for this problem or whether another paradigm of your choice is more appropriate, based on your previous arguments.

The word limits are an upper limit, not a target length. Text longer than the word limit for each point may be ignored. Clearly mark each argument in your answer of the first point and indicate whether it is for or against. Only provide two arguments for and against; additional arguments will be ignored (this includes multiple arguments passed as one).

Learning Outcomes Assessed

• Explain the conceptual foundations, evaluate and apply various programming paradigms, such as logic, functional, scripting, filter-based programming, pattern matching and quantum computing, to solve practical problems.

• Discuss and contrast the issues, features, design and concepts of a range of program- ming paradigms and languages to be able to select a suitable programming paradigm to solve a problem.

Criteria for assessment

Task 1: maximum 50 marks, assessed according to the following scale:

Fail	0	No code has been submitted.
	1 − 14	Code does not run or does not produce valid output for any valid input; little to no relevant documentation.
	15 − 24	Code is valid without syntax errors and creates a valid output for every valid input (or produces a suitable error message for valid cases it cannot process). The output is not a solution, but a suitable attempt to solve the problem is visible. An attempt to document the code has been made.
Pass	25 − 29	Code is valid without syntax errors and creates a valid output for every valid input (or produces a suitable error message for valid cases it cannot process). A suitable attempt to solve the problem has been made, that will often produce the correct output. The attempt has been reasonably documented, but no consideration has been given to optimise the function’s performance.
Merit	30 − 34	Code is valid without syntax errors and creates a valid output for every valid input (or produces a suitable error message for valid cases it cannot process). A suitable attempt to solve the problem has been made, that will find the correct output. The attempt has been well documented, stating the idea to solve the problem and how it has been implemented.
Distinction	35 − 50	Code is valid without syntax errors and creates a valid output for every valid input. A suitable attempt to solve the problem has been made, that will find the correct output for all problems, with excellent performance. The attempt has been well documented clearly stating the idea to solve the problem and how it has been implemented. It clearly shows an effort to optimise the program’s performance, e.g. by using efficient algorithms, data representations or heuristics.

Task 2: maximum 50 marks, assessed according to the following scale:

Fail	0	No document has been submitted.
	1 − 14	An insufficient number of arguments has been submitted and/or they hardly apply to the functional programming paradigm. At most an incomplete at- tempt to discuss the suitability of the functional paradigm has been made.
	15 − 24	An insufficient number of arguments has been submitted, but they show some understanding of the functional programming paradigm. An attempt has been made to discuss the suitability of the functional paradigm, but it hardly relates to the paradigm.

Pass	25 − 29	The required number of valid arguments has been submitted. They are generally valid for the functional programming paradigm, but they repeat similar issues, do not consider the specific problem or contain mistakes in the details. A attempt has been made to discuss the suitability of the functional paradigm and some understanding of this paradigm is present.
Merit	30 − 34	The required number of valid arguments has been submitted. They show a clear understanding of the functional programming paradigm and it relates to the problem. The discussion of the suitability of the functional paradigm is well-developed, showing a clear understanding of the issues involved, and indicates the differences to the other chosen paradigm.
Distinction	35 − 50	The required number of valid arguments has been submitted. They show a clear understanding of the functional programming paradigm and the under- lying theoretical concepts and/or realisations on programmable machines and how these relate to the problem.