莫纳什大学 FIT1045 assignment2课业解析

题意：

使用python解决两个task，锻炼使用算法解决问题的能力

解析：

task1-partA：找到列表数字的峰值（峰值定义为大于其邻居的数字。一个峰值可能是列表中的第一个或最后一个数字，在这种情况下，它必须大于其唯一的邻居），首先判断列表首尾是否为峰值，lst[0]与lst[1]大小以及lst[n-2]和lst[n-1]的大小，其次判断中间数字和邻居数字的大小关系是否为峰值。

task1-partB：写一个函数power（n，p），它接受一个数和一个幂，并返回提升到给定幂的数。由于不能使用幂运算符，可将n连乘p次的结果，x=x*n，return x

task2-partA：根据嵌套列表作为邻接矩阵的图来显示路径大小，可根据路径列表先构造路线再根据邻接矩阵找到对应路径长度求和即可

task2-partB：寻找快速路径，根据路线矩阵返回路线图，路线图首尾为0，根据邻接矩阵图从0开始，选取最短路径，返回节点即可

涉及知识点：

列表，图的邻接矩阵，贪心算法

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FIT1045 Algorithms and programming in Python, S2-2019
Assignment 2 (value 10%)
Due: Sunday 22nd September 2019, 11:55 pm.
Objectives
The objectives of this assignment are:
• To demonstrate the ability to implement algorithms using basic data structures and operations on them.
• To gain experience in designing an algorithm for a given problem description and implementing that
algorithm in Python.
• To demonstrate an understanding of complexity, and to the ability to implement algorithms of a given
complexity.
Submission Procedure

1. Save your files into a zip file called yourStudentID yourFirstName yourLastName.zip
2. Submit your zip file containing your solution to Moodle.
3. Your assignment will not be accepted unless it is a readable zip file.
   Important Note: Please ensure that you have read and understood the university’s policies on plagiarism
   and collusion available at http://www.monash.edu.au/students/policies/academic-integrity.html. You
   will be required to agree to these policies when you submit your assignment.
   A common mistake students make is to use Google to find solutions to the questions. Once you have seen a
   solution it is often difficult to come up with your own version. The best way to avoid making this mistake is
   to avoid using Google. You have been given all the tools you need in workshops. If you find you are stuck, feel
   free to ask for assistance on Moodle, ensuring that you do not post your code.
   Marks: This assignment will be marked both by the correctness of your code and by an interview with
   your lab demonstrator, to assess your understanding. This means that although the quality of your code
   (commenting, decomposition, good variable names etc.) will not be marked directly, it will help to write clean
   code so that it is easier for you to understand and explain.
   This assignment has a total of 10 marks and contributes to 10% of your final mark. For each day an assignment
   is late, the maximum achievable mark is reduced by 10% of the total. For example, if the assignment is late by
   3 days (including weekends), the highest achievable mark is 70% of 10, which is 7. Assignments submitted 7
   days after the due date will normally not be accepted.
   Detailed marking guides can be found at the end of each task. Marks are subtracted when you are unable to
   explain your code via a code walk-through in the assessment interview. Readable code is the basis of a
   convincing code walk-through.
   Task 1: Complexity (4 Marks)
   Create a Python module called complexity.py. Within this module implement the following task. For this
   module you may not use the Python built-in function pow(x) and you may not use the power operator **.
   You may not import any other libraries or modules.
   Part A: Peaks (2 Marks)
   Sometimes in life we care more about finding peaks than we care about finding the maximum. For example,
   during semester you know that the week containing the maximum amount of assessment is (probably) during
   exam block. But you will also have weeks in which that particular week contains more assessment than the
   week directly before it, or directly after it. As such, if you are planning on going to the movies with friends,
   you should probably do it in a week that is not an assessment peak.
   Write a function local peak(lst) that takes in a list of numbers, and returns the index of a local peak.
   Input: a list lst containing two or more numbers, where no number is the same as its neighbour.
   Output: an integer indicating the index of a local peak. If there is more than one peak in the given list, the
   index of any peak may be returned. A peak is defined as a number that is greater than its neighbours. A
   peak may be the first or last number in the list, in which case it must be greater than its only neighbour.
   For full marks, this function must have a complexity of O(log(N)), where N is the length of lst. Be aware
   that some Python functions have a higher complexity than you might think. One example is slicing, which has
   a complexity of O(k) where k is the length of the slice.
   Examples
   a) Calling local peak([0,2,4,6,5,2]) returns 3.
   b) Calling local peak([-7,-6,-2,-10,-5,-11]) returns either 2 or 4.
   c) Calling local peak([8.8,8.6,8.1,8.2,8.1,8.01]) returns either 0 or 3.
   Part B: Powers (2 Marks)
   Write a function power(n, p) that takes a number and a power and returns the number raised to the given
   power.
   Input: a number n and a non-negative integer p.
   Output: a number that is the evaluation of np
   For full marks, this function must have a complexity of O(log§).
   Examples
   a) Calling power(2,8) returns 256.
   Marking Guide (total 4 marks)
   Marks are given for the correct behavior of the different functions:
   (a) 1 mark for the correct behaviour of local peak, and 1 mark for implementing the function with a complexity
   of O(log(N)). You must be able to explain why the function has a complexity of O(log(N)) to receive the
   full mark.
   (b) 1 mark for the correct behaviour of power, and 1 mark for implementing the function with a complexity
   of O(log§). You must be able to explain why the function has a complexity of O(log§) to receive the
   full mark.
   Note: marks will be deducted for including in submitted module function calls that are outside of function
   definitions, or print statements.
   Task 2: Birthday Card (6 Marks)
   Your good friend, Xanthe, who also lives in Melbourne, is turning 21 in a few weeks. To celebrate the occassion
   you would like to give Xanthe a birthday card that has been signed by all of her friends. The only problem is
   Xanthe is incredibly well travelled, and has friends all through the country and the world.
   To figure out the best way to get the card to all of these friends before Xanthe’s birthday, you have turned
   to graph theory. Every city and town in which a friend of Xanthe lives has been allocated a number between
   1 and the number of friends (minus one), and Melbourne has been allocated the number 0. You have recorded
   postage times between locations as edge weights. You have found that all pairs of locations are such that the
   postage time from A to B is the same as the postage time from B to A, so your graph is undirected. You have
   also found that there is a postage connection between every pair of locations, so your graph is connected and
   complete. You have implemented this graph as an adjacency matrix, where each cell represents the weight of
   an edge. All postage times are given in integers, representing how many days the card would take to travel
   between the two locations. (I.e. an edge weight of 2 between A and B means it would take two days to get the
   card between location A and location B.)
   Create a Python module called card.py. Within this module implement the following three tasks. You are
   encouraged to decompose the given tasks into additional functions. You may not import any other libraries or
   modules.
   Part A: Time (1 Mark)
   Write a function post time(graph, path) that returns how long it will take Xanthe’s card to travel the given
   path.
   Input: a nested list graph that represents a graph as an adjacency matrix, that models the postage routes
   and times between Xanthe’s friends; and a list of integers path that represents a proposed path in the
   graph. You may assume the given path exists in the graph.
   Output: an integer that is the number of days it would take Xanthe’s card to travel the given path.
   Examples
   postage1 =
   [ [0,1,1,3,2],
   [1,0,4,5,1],
   [1,4,0,1,3],
   [3,5,1,0,1],
   [2,1,3,1,0] ]
   postage2 =
   [ [0,2,2,1,2],
   [2,0,1,1,2],
   [2,1,0,1,4],
   [1,1,1,0,1],
   [2,2,4,1,0] ]
   The example graphs postage1 and postage2 are provided for illustrative purpose. Your implemented function
   must be able to handle arbitrary graphs in matrix form.
   a) Calling post time(postage1, [0,1,4,3,2,0]) returns 5.
   b) Calling post time(postage1, [0,3,1,2,3]) returns 13.
   Part B: Where to post? (2.5 Marks)
   Write a function post route(graph) that uses a greedy approach to find a fast (but not necessarily the fastest)
   route by which to send the card. The metric for the greedy approach is: send the card to the location that takes
   the shortest time to get to that the card has not yet been visited; or, if all locations have been visited, send the
   card back to Melbourne. If there are multiple locations to chose from, all with the same distance, choose the
   location that has been allocated the smaller number.
   Input: a nested list graph that represents a graph as an adjacency matrix, that models the postage routes
   and times between Xanthe’s friends.
   Output: a list of integers, where each integer is a location, ordered such that visiting each location in the
   order given creates a cycle that begins and ends in Melbourne. The only number that can appear twice is

Examples
a) Calling post route(postage1) returns [0,1,4,3,2,0].
b) Calling post route(postage2) returns [0,3,1,2,4,0].
Part C: Can it be done? (2.5 Marks)
Write a function on time(graph,days) that determines whether there exists a postage route that can be
completed before Xanthe’s birthday.
Input: a nested list graph that represents a graph as an adjacency matrix, that models the postage routes
and times between Xanthe’s friends; and a non-negative integer days, which is the number of days until
Xanthe’s birthday.
Output: a boolean, True if there exists a cycle beginning and ending at Melbourne, that visits every location,
and that has a weight equal or less than days; otherwise False.
You must cite any lecture code you use.
Examples
a) Calling on time(postage1,5) returns True, because there is a cycle in graph postage1 with weight ≤ 5
that fits the criteria: [0,1,4,3,2,0].
b) Calling on time(postage2,8) returns True, because there is a cycle in graph postage2 with weight ≤ 8
that fits the criteria: [0,1,2,3,4,0].
c) Calling on time(postage2,5) returns False, because there is no cycle in graph postage2 with weight ≤ 5
that fits the criteria.
Marking Guide (total 6 marks)
Marks are given for the correct behavior of the different functions:
(a) 1 mark for post time.
(b) 2.5 marks for post route.
© 2.5 marks for on time.
Note: marks will be deducted for including in submitted module function calls that are outside of function
definitions, or print statements.