XJTLU Entrepreneur College (Taicang) Cover Sheet
Module code and Title DTS203TC Design and Analysis of Algorithms
School Title School of AI and Advanced Computing
Assignment Title Coursework
Submission Deadline Sunday, May 11th 23:59 (UTC+8 Beijing), 2025
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DTS203TC Design and Analysis of Algorithms
Coursework
Deadline: Sunday, May 11th 23:59 (UTC+8 Beijing), 2025
Percentage in final mark: 40%
Learning outcomes assessed:
A. Describe the different classes of algorithms and design principles associated with them;
Illustrate these classes by examples from classical algorithmic areas, current research and
applications.
B. Identify the design principles used in a given algorithm, and apply design principles to produce
efficient algorithmic solutions to a given problem.
C. Have fluency in using 代写XJTLU Entrepreneur Collegebasic data structures in conjunction with classical algorithmic problems.
Late policy: 5% of the total marks available for the assessment shall be deducted from the
assessment mark for each working day after the submission date, up to a maximum of five working
days
Risks:
• Please read the coursework instructions and requirements carefully. Not following these
instructions and requirements may result in loss of marks.
• The assignment must be submitted via Learning Mall to the correct drop box. Only electronic
submission is accepted and no hard copy submission.
• All students must download their file and check that it is viewable after submission.
Documents may become corrupted during the uploading process (e.g. due to slow internet
connections). However, students themselves are responsible for submitting a functional and
correct file for assessments.
• Academic Integrity Policy is strictly followed.
Overview
In this coursework, you are expected to design and implement algorithms to produce solutions to
four given problems (Tasks 1-4) in Python. For Tasks 1-4, you should have function(s) to receive
task input as parameters, implement your algorithm design and return results. You also need to
write a short report answering a list of questions in Task 5 that are related to the given four
problems.
Task 1 (15 marks)
Implement 5 sorting algorithms: Insertion sort, selection sort, merge sort, quick sort and heap
sort. After implementing these algorithms, test their performance under various conditions and
record the running times in a table. The conditions to evaluate: 1) sorting random arrays of integers
of different sizes, such as 10, 100, 1000, 10000, etc. 2) the input array is already sorted in ascending
order, 3) the input array is reverse sorted in descending order, 4) the input array contains only a
few unique values, where the number of unique values 𝑘 is significantly smaller than the array size
𝑛.
Task 2 (15 marks)
Given an array representation of a Binary Search Tree (BST) without duplicate keys, update the
array such that each key is replaced by the sum of all keys in the BST that are greater than it.
Example:
Input: bst = [6, 5, 8, None, None, 7, 9]
Output: [24, 30, 9, None, None, 17, 0]
Explanation: To represent a binary tree of height ‘h’, we need an array of size 2
h+1
-1 with None
indicating locations without a tree node. The binary search tree corresponding to the input [6, 5, 8,
None, None, 7, 9] is shown in the figure, where the height of the tree is 2 and the length of the
input array is 7. Keys 7, 8 and 9 are larger than 6, therefore, the root 6 is updated to 7+8+9 = 24.
You should create a function named BSTSum that takes a list which represents a BST and return
a list show the updated values for each key. Please consider the time complexity when you design
your algorithm. A naïve approach will result in loss of marks.
Task 3 (15 marks)
Suppose there are n projects P= [p1, p2 …pi …pn] that you need to finish for your clients. Each
project pi= [timei, duedatei] need timei days to complete and must be delivered before or on
duedatei. You can work on only one project at a time and must finish the current project before
starting a new one. Assuming you start on day 1, design an efficient algorithm to find the maximum
number of projects you can complete.
Example:
Input: P = [[1,2], [3,4], [1,3], [5,7]]
Output: 3
Explanation: take 1st project and complete it on the 1st day, take 3rd project and complete it on the
2
nd day, take 4th project and complete it on the 7th day. You can at most complete 3 projects.
You should have a function named maxProjects to receive the information of n projects P
(List[List[int]]) and return the maximum number of projects could be completed (int). Please
consider the time complexity when you design your algorithm. A naïve approach will result in
loss of marks.
Task 4 (15 marks)
You’re planning a road trip across a country represented by an 𝑚 × 𝑛 grid. You begin at your
home located at the top-left corner (0, 0) and aim to reach your destination at the bottom-right
corner (m-1, n-1). You can travel up, down, left or right to an adjacent city. Assume you’re starting
with an initial budget of k dollars, and travel through a city where grid[i][j] = 1 will cost 1 dollar
for toll roads. Design an efficient algorithm that check if you can reach your destination without
going into debt (budget >=0).
Example:
Input: graph = [[0,0,0],
[1,1,0],
[0,0,0],
[0,1,1],
[0,0,0]], budget = 0
Output: true
Explanation: the bottom right cell can be reached by travelling along the green cells.
You should have a function named findPath to receive the receive the grid (List[List[int]]) and the
budget (int) and return the whether the path exists (boolean). Please consider the time complexity
when you design your algorithm. A naïve approach will result in loss of marks.
Task 5 (40 marks)
Answer the following questions in your report. (Clarity and brevity are valued over length).
T5-1: For Task 1, once the data is collected, discuss your observations. Provide explanations for
the observed performance, focusing on the factors influencing the performance of algorithms under
the different conditions. Finally, suggest possible improvements or optimizations to the sorting
algorithms for specific scenarios, if applicable.
T5-2: For Task 2, what is the time and space complexity of your algorithm? Now assume that the
BST can store duplicate keys as its right child. Will your algorithm still work in this case? If so,
justify your answer; otherwise, explain how you would modify the algorithm to handle this
scenario.
T5-3: For Task 3, explain the design, prove the correctness, and analyse the time and space
complexity of your algorithm.
T5-4: For Task 4, describe an algorithm that find the shortest path (measured by the minimum
number of cities visited) to the destination while satisfying the given constraint. Analyse the time
and space complexity of the algorithm.
Submission
Electronic submission on Learning Mall is mandatory. You need to submit a zip file (named
DTS203TC-CW-YOUR_NAME.zip) containing the following documents.
- Cover letter with your student ID.
- Your source code for Tasks 1-4: Solutions.ipynb
- A pdf file contains all the source code (should be the same as the submitted ipynb file)
and your report (task 5). You can also write the report in jupyter notebook and export as a
pdf file. WX：codinghelp
