OU-iti1120 Assignment 1题意：使用Python编写一些函数
解析：1）编写一个勾股定理的判断函数，输入两个整数a,b如果存在另一个整数c^2=a^2+b^2则返回true，否则返回false；2）编写一个英里/小时转换为公里每小时的函数；3）输入三个数，xs、ys、side，x，y表示正方形左下角的坐标，side表示正方形的边长，函数的作用是判断一个坐标是否在正方形内部，边界也属于内部；4）判断一个数字中是否含有数字9，或者能否被9整除，是则返回true，否则返回false；5）接受三个字符串参数：qu’ote，name，year，然后以此输出一段话；6）编写一个无参数版本的“5)”中的函数；7）编写一个石头剪刀布的游戏，输入相同为平局。 涉及知识点：Python，字符处理更多可加微信讨论微信号：Ssss_970521pdf
ASSIGNMENT 1Read the instructions below carefully. The instructions must be followed. This assignment isworth 4% of your grade. The assignment is due on Monday, 30th of September at 8AM. No lateassignments will be accepted.This is an individual assignment. Please review the Plagiarism and Academic Integrity policypresented in the first class, i.e. read in detail pages 15-18 of course outline (i.e. slides ofLecture 1). You can find that file on Brightspace under Lecture 1. While at it, also reviewCourse Policies on pages 13 and 14.The goal of this assignment is to learn and practice (via programming) the concepts that wehave learned so far: numbers, algebraic expressions, boolean expressions, strings, operationson strings, type conversion, variables, use of Python’s builtin functions including input andoutput functions, designing your own functions, documenting your own functions viadocstrings, and testing your functions. Before you can start this assignment, you need to knowhow to use a (IDLE’s) text editor to edit python modules (i.e. files) as well as how to usepython shell interactively to test your code. If you have no idea how to do these thingswatching video of the 3rd lecture, for example, will help. Submit your assignment by thedeadline via Brightspace (as instructed and practiced in the first lab.) You can make multiplesubmissions, but only the last submission before the deadline will be graded. What needs tobe submitted is explained next.The assignment has 14 programming questions (in Section 1 below). Each question asks you todesign one function. Put all these functions (for all the questions below) in ONE file only,called a1_xxxxxx.py (where xxxxxx is replaced with your student number). Within this file,a1_xxxxxx.py, separate your answers (i.e. code) to each question with a comment that lookslike this:###################################################################
# Question X
###################################################################To have an idea on what this file a1_xxxxxx.py should look like, I included with thisassignment a solution to an nonexistent assignment. You can view this mockup solution byopening the included file called a1_mockup_assignment_solution.pyIn addition to a1_xxxxxx.py you must submit a separate file called a1_xxxxxx.txt. Whatshould be in that file is explained below. Thus for assignment 1 you have to SUBMIT TWOFILES:• a1_xxxxxx.py and• a1_xxxxxx.txt.as instructed in lab 1. Submit your assignment by the deadline via Brightspace (as instructedin the first lab.)Your program must run without syntax errors. In particular, when grading your assignment, TAswill first open your file a1_xxxxxx.py with IDLE and press Run Module. If pressing Run Modulecauses any syntax error, the grade for the whole assignment will be zero.Furthermore, for each of the functions below, I have provided one or two tests to test yourfunctions with. For example, you should test question 2 by making function call mh2kh(5) in thePython shell. To obtain a partial mark your function may not necessarily give the correctanswer on these tests. But if your function gives any kind of python error when run on thetests provided below, that question will be marked with zero points.After reading each of these questions once, go to the Section 2: “Testing your code” belowand see what the output of your function should give. In that section, you can find a couple offunction calls and the required results for each question. Studying these example functioncalls will help you a lot to understand what each individual question requires, or rather whatits function should do.To determine your grade, your functions will be tested both with examples provided inSection 2: “Testing your code” and with some other examples. Thus you too should test yourfunctions with more example than what I provided in Section 2.Each function must be documented with docstrings (as will be explained in Lecture 5 on Sept18). In particular, each function has to have docstrings that specify:
- type contract
- description about what the function does (while mentioning parameter names)- preconditions, if anyThe purpose of this assignment is to practice concepts that you have seen in the first 2.5weeks of class. Thus this assignment does not require use of loops, if and other branchingstatements, lists … etc, except for question 12 (and Question 10 if you want to be creative).Thus you must solve the questions below without loops, if and other branching statements,lists etc … unless explicitly stated otherwise in the question. Question that break this rulewill receive zero since they suggest that the required understanding of the material coveredin first 2.5 weeks is not attained.In addition to docstrings that will be covered in Lecture 5 on Sept 18, we will also cover ifstatements, in either Lecture 5 or Lecture 6. They will only be needed in question 12.Global variables are not allowed. If you do not know what that means, for now, interpret thisto mean that inside of your file a1_xxxxxx.py variables can only be created (ie. assignedvalue) inside of the bodies of your functions.To avoid confusion, unless otherwise specified in the questions here is what you can use inthis assignment:- comparison operators: <,<=, ==, !=, >, >=- Boolean operators: and, or, not- arithmetic operators: +, -, *, /, **, %, //- the following Python built in functions: print, input, round, len, int, float, str- string operators: +, *- any function from the math module (recall import math, dir(math), and then you can callhelp on any function in math module. eg. help(math.sqrt) )- anything from Turtle module- keywords: def, return- if statements (only in question 12 and possibly question 10)Section 1: Assignment 1 questions1. (2 points) Two numbers a and b are called pythagorean pair if both a and b areintegers and there exists an integer c such that a2 + b2 = c2. Write afunction pythagorean_pair(a,b) that takes two integers a and b as input and returnsTrue if a and b are pythagorean pair and False otherwise.2. (2 points) Write a function mh2kh(s) that given the speed, s, expressed in miles/hourreturns the same speed expressed in kilometres/hour.3. (2 points) Write a function in_out(xs,ys,side) that takes three numbers as input, whereside is non-negative. Here xs and ys represent the x and y coordinates of the bottomleft corner of a square; and side represents the length of the side of the square.(Notice that xs, ys, and side completely define a square and its position in the plane).Your function should first prompt the user to enter two numbers that represent the xand y coordinates of some query point. Your function should print True if the givenquery point is inside of the given square, otherwise it should print False. A point on theboundary of a square is considered to be inside the square.4. (2 points) Write a function safe(n) that takes a non-negative integer n as input where nhas at most 2 digits. The function determines if n is a safe number. A number is notsafe if it contains a 9 as a digit, or if it can be divided by 9. The function should test ifn is safe and return True if n is safe and False otherwise.5. (2 points) Write a function quote_maker(quote, name, year) that returns a sentence,i.e. a string of the following form: In year, a person called name said: “quote”See the next Section 2 below for some examples of how your function must behave.6. (2 points) Write a function quote_displayer() that prompts the user for a quote, name,and year. The function should then print a sentence using the same format as specifiedin the previous question. (To do that, your solution must make a call to quote_makerfunction from the previous question to obtain a string that you then print).7. (2 points) In this question you will write a function that determines the result of arock, paper, scissors game given choices of player 1 and player 2. In particular, write afunction rps_winner() that prompts the user for choice of player 1 and then choice ofplayer 2, and then it displays the result for player 1 as indicated in the examples givenin Section 2. You may assume that the user wil
l only enter words: rock, paper orscissors in lower case. Recall that paper beats rock, that rock beats scissors and thatscissors beat paper. If both players make the same choice, we have a draw.8. (2 points) Write a function fun(x) that takes as input a positive number x and solvesthe following equation for y and returns y. The equation is 104y=x+3.9. (2 points) Write a function ascii_name_plaque(name) that takes as input a stringrepresenting a person’s name and draws (using print function) a name plaque as shownin the examples given in Section 2 below. Recall that you may not use loops nor if/branching statements. (Question 10 and 12 are the only exceptions to that rule.)10. (2 points) Write a function draw_train() that draws, with Turtle graphics, the trainfrom the image below If you are imaginative, you may choose to draw a more complexdrawing of a train or instead of function draw_train() write a functionmy_fun_drawing() that draws something else fun. Whatever you choose it should notbe simpler than the train on the given image. In this questions you can use loops and/or if statements if you want to draw something more complex.11. (2 points) Write a function alogical(n) , that takes as input a number, n, where n isbigger or equal to 1, and returns the minimum number of times that n needs to bedivided by 2 in order to get a number equal or smaller than 1. For example 5.4/2=2.7.Since 2.7 is bigger than 1, dividing 5.4 once by 2 is not enough, so we continue.2.7/2=1.35 thus dividing 5.4 twice by 2 is not enough since 1.35 is bigger than 1. So wecontinue. 1.35/2=0.675. Since 0.675 is less than 1, the answer is 3. In particular,these calculations determine that 5.4 needs to be divided by 2 three times minimumin order to get a number that is less than or equal to 1. See Section 2 for moreexamples. Recall that you may not use loops nor if/branching statements. (Question 10and 12 are the only exceptions to that rule.)12. (5 points) Write a fancy time formatter, time_format(h,m), that takes a time of day,expressed in hours, h (integer 0 to 23) and minutes, m (integer 0 to 59). The functionfirst rounds the minutes to the nearest 5 minutes, and then returns the time asdescriptive string. In particular, after rounding the minutes, the string has to be suchthat it uses “o’clock” and “half past” for 0 and 30 minutes, respectively. For less than30 minutes, it has to use “past” format and for more than 30 minute it has to use “to”format. See the examples in Section 2 for clarification and examples on how yourfunction must behave. Your code for rounding minutes to the nearest 5 minutes shouldnot take more than ONE line of code. You may use if statements in this question.13. (2 points) Write a function cad_cashier(price,payment) that takes two real nonnegative numbers with two decimal places as input, where payment>=price and wherethe second decimal in payment is 0 or 5. They represent a price and payment inCanadian dollars. The function should return a real number with 2 decimal placesrepresenting the change the customer should get in Canadian dollars. Recall that inCanada, while the prices are expressed in pennies, the change is based on rounding tothe closest 5 cents. See the examples in Section 2 for clarification and examples onhow your function must behave.14. (5 points) Suppose that a cashier in Canada owes a customer some change and that thecashier only has coins ie. toonies, loonies, quarters, dimes, and nickels. Write afunction that determines the minimum number of coins that the cashier can return. Inparticular, write a function min_CAD_coins(price,payment) that returns five numbers(t,l,q,d,n) that represent the smallest number of coins (toonies, loonies, quarters,dimes, and nickels) that add up to the amount owed to the customer (here price andpayment are defined as in the previous question). You program must first callcad_cashier function, from question 13, to determine the amount of change thatneeds to be returned. Then before doing anything else, you may want to convert thisamount entirely to cents (that should be of type int). Once you have the total numberof cents here are some hints on how to find the minimum number of coins.Hints for your solution (algorithm) for question 14:To find the minimum number of coins the, so called, greedy strategy (i.e. greedy algorithm)works for this problem. The greedy strategy tries the maximum possible number of thebiggest-valued coins first, and then the 2nd biggest and so on. For example, if price is $14.22and payment $20, the customer is owed $5.80 (after rounding to closest 5 cents), thus 580cents, the greedy strategy will first figure the maximum number of toonies it can give to thecustomer. In this case, it would be 2 toonies. It cannot be 3 toonies as that equals $6 and thecashier would return too much money. Once the cashier returns 2 toonies, he/she still needsto return 180 cents. The next biggest coin after toonie is a loonie. So the greedy strategywould try loonies next. Only 1 loonie can fit in 180 cents, so the cashier should next return 1loonie. Then there is 80 cents left. The next biggest coin to consider is a quarter … and so on… ending with nickels. (For this example the function should return (2,1,3,0,1) ). Thus for thisquestion, you are asked to implement this strategy to find the optimal solution. See section 2for more examples.Side note: in the Canada (and most other) coin systems, the greedy algorithm of picking thelargest denomination of coin which is not greater than the remaining amount to be made willalways produce the optimal result (i.e. give the smallest number of coins). This is notautomatically the case, though: if the coin denominations were 1, 3 and 4 cents then to make6 cents, the greedy algorithm would choose three coins: one 4-cent coin and two 1-cent coinswhereas the optimal solution is two 3-cent coins.Section 2: Testing your codeWe would like to see evidence that you have tested your functions in python shell, like we didin class. Do this by opening your assignment solution, i.e. opening a1_xxxxxx.py, with IDLEand then test each of your functions individually. Then copy and paste the python shelloutput into a text file called a1_xxxxxx.txt The contents of a1_xxxxxx.txt must havesomething like this in it:>>> # testing Question 1>>>>>> pythagorean_pair(2,2)False>>> pythagorean_pair(6,2)False>>> pythagorean_pair(6,8)True>>> pythagorean_pair(300,-400)True>>>>>> # testing Question 2>>>>>>>>> mh2kh(5)8.0467>>>>>> mh2kh(110.4)177.67113600000002>>>>>>>>> # testing Question 3>>>>>> in_out(0,0,2.5)Enter a number for the x coordinate of a query point: 0Enter a number for the y coordinate of a query point: 1.2True>>> in_out(2.5,1,1)Enter a number for the x coordinate of a query point: -1Enter a number for the y coordinate of a query point: 1.5False>>> in_out(-2.5,1,2.1)Enter a number for the x coordinate of a query point: -1Enter a number for the y coordinate of a query point: 1.5True>>>>>>>>> # testing Question 4>>>>>> safe(93)False>>> safe(82)True>>> safe(29)False>>> safe(36)False>>> safe(9)False>>> safe(7)True>>>>>>>>> # testing Question 5>>>>>> quote_maker(“Everything should be made as simple as possible but not simpler.”, “Albert Einstein”, 1933)’In 1933, a person called Albert Einstein said: “Everything should be made as simple as possible but not simpler.”‘>>>>>> quote_maker(“I would never die for my beliefs because I might be wrong.”, “Bertrand Russell”, 1951)’In 1951, a person called Bertrand Russell said: “I would never die for my beliefs because I might be wrong.”>>>>>>>>> # testing Question 6>>>>>> quote_displayer()Give me a quote: The best lack all conviction while the worst are full of passionate intensity.Who said that? Bertrand RussellWhat year did she/he say that? 1960In 1960, a person called Bertrand Russell said: “The best lack all conviction while the worst are full of passionate intensity.”>>>>>>>>> # testing Question 7>>>>>> rps_winner()What choice did player 1 make?Type one of the following options: rock, paper, scissors: rockWhat choice did player 2 make?Type one of the following options: rock, paper, scissors: paperPlayer
1 wins. That is FalseIt is a tie. That is not True>>> rps_winner()What choice did player 1 make?Type one of the following options: rock, paper, scissors: paperWhat choice did player 2 make?Type one of the following options: rock, paper, scissors: rockPlayer 1 wins. That is TrueIt is a tie. That is not True>>> rps_winner()What choice did player 1 make?Type one of the following options: rock, paper, scissors: scissorsWhat choice did player 2 make?Type one of the following options: rock, paper, scissors: paperPlayer 1 wins. That is TrueIt is a tie. That is not True>>> rps_winner()What choice did player 1 make?Type one of the following options: rock, paper, scissors: paperWhat choice did player 2 make?Type one of the following options: rock, paper, scissors: paperPlayer 1 wins. That is FalseIt is a tie. That is not False>>>>>>>>> # testing Question 8>>>>>> fun(7)0.25>> fun(20)0.3404319590043982>>> fun(999999997)2.25>>> fun(0.1)0.12284042345856817>>>>>>>>> # testing Question 9>>>>>> ascii_name_plaque(“vida”)*************** ** __vida__ ** ***************>>> ascii_name_plaque(“Captain Kara ‘Starbuck’ Thrace”)***************************************** ** __Captain Kara ‘Starbuck’ Thrace__ ** *****************************************>>> ascii_name_plaque(“Seven of Nine”)************************ ** __Seven of Nine__ ** ************************>>>>>>>>> # testing Question 10>>>>>> draw_train()>>>>>>>>> # testing Question 11>>>>>> alogical(5.4)3>>> alogical(4)2>>> alogical(1000)10>>> alogical(4200231)23>>>>>>>>> # testing Question 12>>>>>> time_format(8,0)“8 o’clock”>>> time_format(8,2)”8 o’clock”>>> time_format(8,59)”9 o’clock”>>> time_format(8,8)”10 minutes past 8 o’clock”>>> time_format(8,32)”half past 8 o’clock”>>> time_format(8,48)”10 minutes to 9 o’clock”>>> time_format(17,42)”20 minutes to 18 o’clock”>>> time_format(23,13)”15 minutes past 23 o’clock”>>> time_format(23,42)”20 minutes to 0 o’clock”>>> time_format(0,29)”half past 0 o’clock”>>> time_format(11,59)”12 o’clock”>>> time_format(23,58)”0 o’clock”>>> time_format(0,1)”0 o’clock”>>> time_format(11,1)”11 o’clock”>>>>>>>>> # testing Question 13>>>>>> cad_cashier(10.58,11)0.4>>> cad_cashier(98.87,100)1.15>>> cad_cashier(10.58,15)4.4>>> cad_cashier(10.55,15)4.45>>> cad_cashier(10.54,15)4.45>>> cad_cashier(10.52,15)4.5>>> cad_cashier(10.50,15)4.5>>>>>>>>> # testing Question 14>>>>>> min_CAD_coins(10.58,11)(0, 0, 1, 1, 1)>>> min_CAD_coins(98.87,100)(0, 1, 0, 1, 1)>>> min_CAD_coins(10.58,15)(2, 0, 1, 1, 1)>>> min_CAD_coins(10.55,15)(2, 0, 1, 2, 0)>>> min_CAD_coins(10.54,15)(2, 0, 1, 2, 0)>>> min_CAD_coins(10.52,15)(2, 0, 2, 0, 0)>>> min_CAD_coins(10.50,15)(2, 0, 2, 0, 0)>>> min_CAD_coins(3, 20)(8, 1, 0, 0, 0)
