Computer Science 320SC – (2024)
Programming Assignment 5
Academic Integrity
Before attempting to solve the assignment, please read the message below very carefully. As described on https://academicintegrity.cs.auckland.ac.nz/, you must NOT

Use all or part of another student’s solution to the assignment. Changing variable names or substituting words in a sentence does not make it your solution.

Allow someone else to complete all or part of the assignment for you.

Solicit answers for the assignment on contractcheating websites such as Chegg.com and
Bartleby.com.

Use code from Internet sources such as StackOverflow or generativeAI tools such as Chat
GPT. You are encouraged to learn from Internet sources and tools, but you need to come up
with your own implementation of the code to show your learning.

Allow another student to copy all or part of your solution to the assignment.

Do all or part of an assignment for someone else.

Share code that can lead to the solution of an assignment.

Post the assignment anywhere online or share it with anyone else. The assignment material
is copyrighted and sharing or posting them online violates our copyright.

Post your solution online on public websites. Your online solutions will encourage other students to copy your solution. Private GitHub repositories and other private online stor age drives are acceptable, and you can also share your solution privately with prospective
employers.

Reuse your own work unless discussed otherwise with the lecturer.

Leave your computers, devices, and belongings unattended — you must secure these at all
times to prevent anyone having access to your assessments or solutions.
Last year, out of 218 students, there were 11 misconducted cases found on A5  Task 1. We kept the submissions from the last few years to run MOSS at https://theory.stanford.edu/~aiken/moss/.
I hope that there will be no cases this year!
1
Requirements
This 5th assignment lets you get familiar with dynamic programming design and development. It is worth 5% of your total course marks. We would like you to implement efficient dynamic programming algorithms for two tasks: Task 1: Finding partner and Task 2: Killing enemies.
An excessive number of submissions (over 10) for a particular problem will accrue a 20% penalty per that problem if you eventually solve it. Therefore, please write a bruteforce algorithm and test your dynamic programming version with your own generated inputs at scale before submitting to the automated marker.
We only accept Python programs that use builtin packages (i.e. packages that do not require pip install).
1 Task 1: Meet your partner at skyscraper 1.1 Problem description
You are standing at the ground floor and your partner is waiting at the top floor of a s`kyscraper. You will have to use an algorithmically designed lift L to reach your partner. The lift L is designed in the manner that if you use the lift at the floor i, you are able to reach any floor from i+1 to i+L[i] where L[i] is a positive integer that presents the capacity of the lift at the ith floor. Each time you use the lift costs $1.
Assume that the skyscraper has n floors and you are at the floor 0. Your partner is at the floor n − 1 and waiting for you to see the sky view. The lift information L[i] for 0 ≤ i < n is available at the ground floor. Write a function to return the minimum cost, i.e. the number of time using the lift, to reach your partner.
O(n) solutions are preferred since we have set the running time limit on the automarker. 1.2 Test case description
Your input will be a sequence of n integers, each value per line corresponding to the lift information L[i] (e.g. the capacity of the lift) on the ith floor. The first line is for the 0th floor. The last line is for the (n − 1)th floor, which is a redundant information :). Your output will be an integer.
There are 4 test cases.
1. Atrialtestcaseofn=10hasnomark.
2. A test case of n = 100,000 and has 1 mark.
3. A test case of n = 1000, 000 and has 2 marks.
2
Sample Input 1:
8 1 3 1 3
Sample Output 1:
1
You only need to use the lift once since L[0] = 8 is sufficient to get you to the 4th floor. Sample Input 2:
2 5 1 4 8
Sample Output 2:
2
You only need to use the lift twice. The first one with L[0] = 2 to the 1st floor, and L[1] = 5 is sufficient to get you to the 4th floor.
3
2 Task 2: Arrange tanks to eliminate enemies 2.1 Problem description
You have a queue of n tanks hidden in a forest. Due to the UAV of enemies, only 1 tank is used per day, and the used tank can only be taken from the front or rear of the queue for some security reasons. Each tank has a number indicating the number of potential units the tank can eliminate. Since tanks are hurrily queued up during the night, you cannot organize the tank in the good order to use. Instead, you have a queue of n values, each reflects the number of potential eliminated units for each tank in the queue.
Since the war is more and more severe, the number of potential eliminated units dramatically increases daybyday. Let the labels of the number of eliminated units from n tanks in the queue be t1, t2, . . . , tn. In the ith day, the used tank k will eliminate i ∗ tk units.
As a commander, for each day, your task is to give an order 1 or 0 corresponding to whether the front or the rear tank in the queue is used. Write a program to compute the best order of using n tanks for n days to eliminate maximum number of enemies’ units.
Since there might be several orderings that output the same number of eliminated units, you would need to output the maximum number of eliminated units only.
You might see that the best solution runs in O(n2) time asymptotically. However, a program with low memory usage (e.g. O(n)) is preferred since the automarker has limited resources, and we have set the running time limit on the automarker.
2.2 Test case description
Your input will be a sequence of n integers, each value per line i corresponding to the amount of elimi nated units of the tank ti. The first and last lines correspond to the front and rear tanks, respectively. Your output is an integer in range [0..231] corresponding to the maximum number of eliminated units.
There are 2 test cases.
1. Atrialtestcaseofn=10hasnomark. 2. A test case of n = 10,000 has 2 marks.
4
Sample Input 1:
4 8 12 4 10
Sample Output 1:
128
The order is {1,0,0,1,1}, and the maximum number of detroyed units is 4 * 1 + 10 * 2 + 4 * 3 + 8 * 4+12*5=128. Notethatforthelasttank(#3),anyorderof1or0doesnotmatter.
Sample Input 2:
1 9 1 9 8 8 7 7
Sample Output 2:
261
The maximum number of detroyed units is 261 and the order is {1, 1, 1, 0, 0, 0, 0, 1}. Note that for the last tank (#4), any order of 1 or 0 does not matter.