COSC2123/3119: Algorithms and Analysis Assessment

Assessment

Learning Outcomes

This assessment relates to four learning outcomes of the course which are: 

• CLO 1: Compare, contrast, and apply the key algorithmic design paradigms: brute force, divide and conquer, decrease and conquer, transform and conquer, greedy, dynamic programming and iterative improvement; 
• CLO 2: Compare, contrast, and apply key data structures: trees, lists, stacks, queues, hash tables and graph representations; 
• CLO 3: Define, compare, analyse, and solve general algorithmic problem types: sorting, searching, graphs and geometric; 
• CLO 4: Theoretically compare and analyse the time complexities of algorithms and data structures; and 
• CLO 5: Implement, empirically compare, and apply fundamental algorithms and data structures to real-world problems.

Overview

Across multiple tasks in this assignment, you will design and implement data structures that represent mazes as graphs and algorithms to explore these mazes. You will address both fully connected, non-cyclical mazes and mazes with cycles. Some of the components ask you to critically assess your solutions through both theoretical analysis and controlled empirical experiments to encourage reflection on the relationship between algorithm design and real-world performance. The assignment emphasizes on strategic thinking and the ability to communicate solutions clearly and effectively.

Assessment Details

The assignment is broken up into a number of tasks (A, B, C, and D) to help you progressively complete the project. Please note that although completing one task can assist with subsequent tasks, each task can be attempted independently. Moreover, the tasks are designed in a way that even in cases where your implementation does not fully achieve the expected output, you can still discuss and present the theoretical aspects of your algorithmic design through your report.

Marks are broken up into two types: 

• implementation; and
• report 

Implementation marks are given for your code. Your code will be examined using a series of tests. The more tests you pass, the more marks your implementation will be awarded. 3 of your implementation marks are awarded for good software engineering (clean code, good comments, descriptive and small commits, etc), and so 12 marks are strictly for tests.

Tasks

Completing Tasks A, B, C, and D will take you through the stages of completing the above objective for different scenarios, and allow you to assess which methods are the most suitable for different tasks.

Task A: Implement an adjacency list (data structure) for a graph (abstract data type).

Task B: Implement Kruskal’s Algorithm for generating a minimum-spanning tree of a graph and discuss different minimum-spanning tree behaviour.

Task C: Using theoretical and empirical analysis, prove which data structure (matrix vs list) and minimum-spanning tree algorithm (Prim’s vs Kruskal’s) combination is best for this problem (if any).

Task D: Use the minimum-spanning tree to plan an optimal exploration strategy using clones.

Assessment Summary

This assessment is designed to evaluate students’ understanding and practical application of algorithmic design paradigms and data structures through the creation and exploration of mazes represented as graphs. The tasks aim to develop proficiency in implementing algorithms, conducting theoretical and empirical analyses, and understanding performance efficiency in problem-solving contexts.

Key Assessment Requirements:

• Design and implement data structures that represent mazes as graphs.
• Apply algorithmic design paradigms such as brute force, divide and conquer, greedy, and dynamic programming.
• Use and compare key data structures like trees, stacks, queues, lists, hash tables, and graph representations.
• Analyse and compare algorithm performance theoretically (time complexity) and empirically (through controlled experiments).
• Implement minimum-spanning tree algorithms (Kruskal’s and Prim’s) to explore and optimise maze traversal.
• Document and justify each implementation step through a structured report, integrating both conceptual reasoning and coding outcomes.

The assessment is divided into four tasks (A–D):

• Task A: Build an adjacency list to represent the maze as a graph.
• Task B: Implement Kruskal’s algorithm to generate a minimum-spanning tree and analyse its behaviour.
• Task C: Perform theoretical and empirical analysis comparing data structures (matrix vs list) and algorithms (Prim’s vs Kruskal’s).
• Task D: Use the minimum-spanning tree to plan an optimal exploration strategy using clones, showcasing efficiency and design logic.

Mentor’s Guidance and Step-by-Step Approach

The academic mentor guided the student through the assignment using a structured, analytical, and iterative approach to ensure both conceptual clarity and technical accuracy.

Step 1: Understanding the Problem and Requirements

The mentor began by explaining the purpose of the assessmentevaluating algorithmic efficiency and structural design. The student was guided to revisit the course learning outcomes (CLOs) and understand how each task connects to them, particularly focusing on problem-solving using data structures and algorithms.

Step 2: Designing the Graph Structure (Task A)

The mentor helped the student visualise a maze as a graph, explaining the role of nodes (rooms) and edges (paths). Together, they explored how an adjacency list could efficiently represent the maze for traversal and algorithmic exploration. The mentor ensured the student wrote clean, modular, and well-commented code, aligning with good software engineering practices.

Step 3: Implementing Kruskal’s Algorithm (Task B)

The student was guided to implement Kruskal’s Algorithm to create a minimum-spanning tree (MST). The mentor explained the importance of using a disjoint set (union-find) data structure to efficiently manage edges. The focus was on understanding the difference between cyclic and acyclic graph structures and how MSTs help achieve optimal connectivity.

Step 4: Theoretical and Empirical Comparison (Task C)

Here, the mentor guided the student in conducting a comparative analysis between adjacency lists and matrices, as well as Kruskal’s and Prim’s algorithms. The student was taught to calculate time and space complexities, validate results through controlled experiments, and interpret output trends. The mentor emphasised critical thinking and connecting theoretical expectations with real-world performance.

Step 5: Strategy Design and Application (Task D)

Using the results from the MST implementation, the mentor supported the student in developing an exploration strategy. This included using clones (multiple agents) to optimise traversal. The focus was on converting analytical insights into a practical, algorithm-driven solution that maximises efficiency in exploring complex mazes.

Step 6: Report Writing and Reflection

Finally, the mentor guided the student in compiling a clear, structured report that combined implementation details, theoretical insights, and reflective analysis. The student was encouraged to discuss limitations, strengths, and the rationale behind algorithmic choices, thus demonstrating both technical understanding and communication proficiency.

Outcome and Learning Achievements

By completing this assessment under academic mentorship, the student successfully:

• Demonstrated understanding of core algorithmic paradigms and their practical applications.
• Applied graph theory and data structures to solve complex problems.
• Analysed algorithmic performance using both theoretical models and empirical validation.
• Developed professional coding and documentation practices.
• Strengthened problem-solving, analytical reasoning, and communication skills aligned with the course learning outcomes (CLOs 1–5).

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