CSE 30 Fall 2021 – Homework 5 以下是描述，需要答案请联系微信scratch8。专业承接大中小学生Python作业培训与辅导。

Instructions

Please disregard the YOUR NAME and COLLABORATORS above. They are put there atomatically by the grading tool. You can find instructions on how to work on a homework on Canvas. Here is a short summary:

Submitting your work

To submit your work:

First, click on “Runtime > Restart and run all”, and check that you get no errors. This enables you to catch any error you might have introduced, and not noticed, due to your running cells out of order.

Second, download the notebook in .ipynb format (File > Download .ipynb) and upload the

.ipynb file to this form.

You can submit multiple times; the last submission before the deadline is the one that counts.

Homework format

For each question in this notebook, there is:

A text description of the problem.

One or more places where you have to insert your solution. You need to complete every place marked:

# YOUR CODE HERE

and you should not modify any other place.

One or more test cells. Each cell is worth some number of points, marked at the top. You should not modify these tests cells. The tests pass if no error is printed out: when there is a statement that says, for instance:

assert x == 2

then the test passes if x has value 2, and fails otherwise. You can insert a print(x) (for this case!) somewhere if you want to debug your work; it is up to you.

Notes:

Your code will be tested both according to the tests you can see (the assert statements you can see), *and *additional tests. This prevents you from hard-coding the answer to the particular questions posed. Your code should solve the *general *intended case, not hard-code the particular answer for the values used in the tests.

你的代码将会被你看到的语句进行测试及额外的测试。这阻止你进行硬编码。

请不要删除或添加单元。

**Please do not delete or add cells! **The test is autograded, and if you modify the test by adding or deleting cells, even if you re-add cells you delete, you may not receive credit.

**Please do not import modules that are not part of the standard library. **You do not need any, and they will likely not available in the grading environment, leading your code to fail.

**If you are inactive too long, your notebook might get disconnected from the back-end. **Your work is never lost, but you have to re-run all the cells before you continue.

You can write out print statements in your code, to help you test/debug it. But remember: the code is graded on the basis of what it outputs or returns, not on the basis of what it prints.

**TAs and tutors have access to this notebook, **so if you let them know you need their help, they can look at your work and give you advice.

Grading

Each cell where there are tests is worth a certain number of points. You get the points allocated to a cell only if you pass *all *the tests in the cell.

The tests in a cell include both the tests you can see, and other, similar, tests that are used for grading only. Therefore, you cannot hard-code the solutions: you really have to solve the essence of the problem, to receive the points in a cell.

Code of Conduct

Work on the test yourself, alone.

You can search documentation on the web, on sites such as the Python documentation sites, Stackoverflow, and similar, and you can use the results.

You cannot share your work with others or solicit their help.

We have seen in the chapter on classes how to implement complex numbers: 下面是一个复数类：

import math

class Complex(object):

def init (self, r, i): self.r = r # Real part

self.i = i # Imaginary part

def add (self, other):

return Complex(self.r + other.r, self.i + other.i)

def sub (self, other):

return Complex(self.r – other.r, self.i – other.i)

def mul (self, other):

return Complex((self.r * other.r – self.i * other.i), (self.r * other.i + self.i * other.r))

@property

def modulus_square(self):

return self.r * self.r + self.i * self.i

@property

def modulus(self):

return math.sqrt(self.modulus_square)

def inverse(self):

m = self.modulus_square # to cache it return Complex(self.r / m, – self.i / m)

def truediv (self, other): return self * other.inverse()

def repr (self):

“””This defines how to print a complex number.””” if self.i < 0:

return “{}-{}i”.format(self.r, -self.i)

return “{}+{}i”.format(self.r, self.i)

def eq (self, other):

“””We even define equality”””

return self.r == other.r and self.i == other.i

There are several ideas above:

To implement the mathematical operations + , – , * , / , between complex numbers, we implement the methods add__ __, sub__ __, mul__ __, truediv__ __. You can find more information in the documentation for the P ython data model.

Similarly, to define equality we define eq__ __, and to define < we define lt__ __.

We will now do something similar to define fractions.

Problem 1: Implement Fractions 作业就是模仿上面的复数类，定义一个分数类，它能表示一个分数。 要有分数的加减乘除和判断相等以及小于。

We want to define a class Fraction to represent a fraction, with integers as numerator and denominator.

Similarly to the Complex class above, you need to implement the methods necessary to define + , – ,

* , / among fractions, as well as equality.

You will represent fractions in *normal form*, such that:

numerator and denumerator which do not have common factors (common divisors), except for 1 (of course),

the denominator is positive.

For example, when you create a fraction via:

r = Fraction(8, 6)

and then ask for the denominator,

r.numerator

the result will be 4, and

r.denominator

will be 3.

To remove the common factors from a fraction m/n, simply compute the greatest common divisor d = gcd(m, n) via Euclid’s algorithm (see the chapter on recursion), and reduce the fraction to (m/d)/(n/d).

We advise you to reduce a fraction into normal form directly into the constructor of the class (the

__ ____ __init method).

Here is the code for Fraction ; we leave the interesting bits for you to do.

# Definition of Fraction class

# Here is the gcd function, as it may well be useful to you. def gcd(m, n):

# This is the “without loss of generality” part. m, n = (m, n) if m > n else (n, m)

m, n = abs(m), abs(n)

return m if n == 0 else gcd(m % n, n) class Fraction(object):

def init (self, numerator, denominator): assert isinstance(numerator, int) assert isinstance(denominator, int) assert denominator != 0

# YOUR CODE HERE

def repr (self):

“””Pretty print a fraction.”””

return “{}/{}”.format(self.numerator, self.denominator)

## Here, implement the methods for +, -, *, /, =, and <.

## Done quite at leisure, with spaces and all, this can be done in about

## 25 lines of code.

# YOUR CODE HERE

## Here is an example. Feel free also to use this cell to test your code. Fraction(8, 6)

Here are some tests.

## 5 points: creating a fraction.

## First, let us check that you correctly put the fraction into normal form,

## without common factor between numerator and denominator, and with a

## positive denominator.

f = Fraction(8, 6)

assert f.numerator == 4 and f.denominator == 3

f = Fraction(-8, 6)

assert f.numerator == -4 and f.denominator == 3

f = Fraction(8, -6)

assert f.numerator == -4 and f.denominator == 3

f = Fraction(-8, -6)

assert f.numerator == 4 and f.denominator == 3

f = Fraction(0, 10)

assert f.numerator == 0 and f.denominator == 1

### 5 points: hidden tests for fraction creation.

## 5 points: tests for fraction operations. f = Fraction(8, 6) + Fraction(25, 20)

assert f.numerator == 31 and f.denominator == 12 assert f == Fraction(31, 12)

assert f == Fraction(62, 24)

assert Fraction(6, 4) + Fraction(-8, 6) == Fraction(6, 4) – Fraction(8, 6)

assert not (Fraction(6, 4) + Fraction(-8, 6) == Fraction(6, 5) – Fraction(8, 6))

## 5 points: Hidden tests for fraction operations.

## 5 points: more tests for fractions operations.

assert Fraction(3, 2) * Fraction(2, 3) == Fraction(1, 1)

assert Fraction(3, 2) / Fraction(2, 3) == Fraction(9, 4)

assert Fraction(3, 2) / Fraction(6, 4) == Fraction(1, 1)

assert Fraction(32, 16) == Fraction(2, 1) assert not Fraction(33, 16) == Fraction(4, 2)

## 5 points: More hidden tests for fraction operations.

## 5 points: tests for fraction comparison. assert Fraction(5, 7) < Fraction(5, 6)

assert Fraction(-3, 2) < Fraction(0, 3)

## 5 points: hidden tests for fraction comparisons.

## 10 points: Let’s check you leave things unchanged. a = Fraction(7, 8)

b = Fraction(-4, 5) a + b

a / b

a < b

a * b

assert a == Fraction(7, 8) assert b == Fraction(-4, 5)

## 10 points: And finally, some random tests. import random

for _ in range(1000):

a = Fraction(random.randint(-200, 200), random.randint(1, 100))

b = Fraction(random.randint(-200, 200), random.randint(1, 100))

c = Fraction(random.randint(-200, 200), random.randint(1, 100)) assert Fraction(-1, 1000) < (a – b) * (a – b)

assert (a – b) * (a + b) == a * a – b * b z = Fraction(0, 1) # Zero, as a fraction. if not ((a == z) or (b == z) or (c == z)):

assert (a / b) * b == (a / c) * c

assert (a / b) * (a / c) == (a * a) / (b * c) assert (a / b) / (b / c) == (a * c) / (b * b) assert (a * a * b * c) / (a * c) == a * b

Question 2: An Int class

To define the value 7, you can write Fraction(14, 2) or Fraction(7, 1) (it’s the same), but this is a bit inconvenient. Write a subclass Int of Fraction , so that Int(7) generates a fraction with value 7.

class Int(Fraction):

# YOUR CODE HERE

## You can test your solution here.

And now for some tests.

## 5 points: tests for int class.

assert Int(3) / Int(2) == Fraction(3, 2)

assert Int(3) * Int(4) / (Int(5) + Int(2)) == Fraction(12, 7) assert Int(3) * Int(4) / (Int(5) + Int(1)) == Fraction(2, 1)

这个家庭作业是仿照complex类，即复数类，定义一个Fraction类，即表示分数的类。

以上是作业的描述，需要答案请联系微信scratch8。专业承接大中小学生Python作业培训与辅导。

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