Before you turn this problem in, make sure everything runs as expected. This is a combination of restarting the kernel and then running all cells (in the menubar, select Kernel$\rightarrow$Restart And Run All).
Make sure you fill in any place that says YOUR CODE HERE or "YOUR ANSWER HERE".
import os
import os.path
import io
import sys
import string
import math
from contextlib import redirect_stdout
datadir = "publicdata"
The following set of questions involve the sorted() built-in Python function and the list of tuples:
students = [('bob', 'B', 19), ('chris', 'B', 18),
('chris', 'A', 18), ('alice', 'A', 19)]
Documentation for sorted() may be found at
students = [('bob', 'B', 19), ('chris', 'B', 18), ('chris', 'A', 18), ('alice', 'A', 19)]
Q1 What is returned when sorted() is invoked on the students list? In this case, we are sorting a list whose elements are tuples. Describe how the algorithm used by sorted() works in the case that two elements are equal in their first element.
YOUR ANSWER HERE
Q2 Look at the documentation for sorted(). If we wanted to sort the students list based on the second element of the tuple (the grade), we want a function that is used to extract the "key" from a list element (tuple) to retrieve that second element. Write a function
getGrade(record)
that, given a student record that consists of a 3-tuple, accesses and returns the middle element of the record/tuple. You are welcome to define getGrade as a lambda function. With this getGrade function object passed as the key parameter, call sorted() and assign the result to the variable gradeSorted.
# Solution cell
# YOUR CODE HERE
raise NotImplementedError()
print(gradeSorted)
# Testing cell
assert getGrade(('alice', 'A', 18)) == 'A'
assert getGrade(('chris', 'B', 18)) == 'B'
assert isinstance(gradeSorted, list)
assert gradeSorted[0] == ('chris', 'A', 18)
Q3 Consider your result: when there are ties in the "key", do you get the elements involved in the tie in the same order as in the original list, or in different orders?
YOUR ANSWER HERE
Q4 Write a function
whichIsBigger(f1,f2,n)
which computes f1(n) and f2(n), and returns whichever function (f1 or f2) results in the larger value when an integer n is passed as a parameter. In case of a tie, return f1. Test with f1(x) defined as $x^3$ and f2(x) defined as $5x^2+4$ and using $n=2$. Test again with $n=100$.
# Solution cell
def whichIsBigger(f1,f2,n):
# YOUR CODE HERE
raise NotImplementedError()
def f1(x):
return x**3
def f2(x):
return 5*x*x + 4
print(whichIsBigger(f1,f2,2))
print(whichIsBigger(f1,f2,100))
# Testing cell
def f1(x):
return x**3 - 7
def f2(x):
return 5*x*x + 4*x + 2
assert whichIsBigger(f1,f2,0) == f2
assert whichIsBigger(f1,f2,-10) == f2
assert whichIsBigger(f1,f2,2) == f2
assert whichIsBigger(f1,f2,50) == f1
Q5 Write a lambda expression and assign it to the variable evensquared such that it squares the value of its single argument if the argument is even, and cubes the argument if it is odd.
Afterward, for example, expression evensquared(5) should yield 125, while evensquared(4) should yield 16.
Hint: We need an expression to handle an if type condition
# Solution cell
# YOUR CODE HERE
raise NotImplementedError()
# Testing cell
assert(evensquared(1)==1)
assert(evensquared(2)==4)
assert(evensquared(3)==27)
assert(evensquared(4)==16)
assert(evensquared(0)==0)
Q6 Write a lambda function that takes three parameters and multiplies them together. Assign the lambda function expression to mult3.
# Solution cell
# YOUR CODE HERE
raise NotImplementedError()
mult3(10,12, 9)
assert mult3(10, 12, 9) == 1080
Q7 The formula for the volume of a barrel is as follows:
$$ V={\pi}h(2D^2+d^2)/12 $$Where $h$=height, $D$=middle radius, and $d$=top or bottom radius.
Write a lambda expression assigned to vol so that the resulting function, vol(h,D,d) computes the volume of a barrel. Use math.pi in your computations, not a hard-coded value for $\pi$. Be careful that your Python precedence follows the precedence of the mathematical formula.
# Solution cell
import math
# YOUR CODE HERE
raise NotImplementedError()
# Testing cell
assert(238.5<vol(8,7,4)<239)
assert(2285.4<vol(10,18,15)<2285.6)
assert(785.3<vol(10,10,10)<785.5)
assert(9691.8<vol(15,28,30)<9691.9)
Mapping Functions
Python has a built-in function map()
whose parameters are a function object followed by one or more iterables. If there are only two arguments, the provided first argument function (which should take a single argument) is invoked over the elements of the second argument. This gives us a built-in way to apply a unary function element-wise over a list or other sequence.
If we pass, as arguments to map(), a function followed by two iterables, then the function is expected to have two parameters, and the function is called for each pair of elements coming from the first and second iterable. This gives us a built-in way to apply a binary function element-wise over two lists/vectors/sequences.
Note that, for efficiency reasons, map() actually returns an iterator that, like range(), can be used as the sequence in a for statement, and waits to compute elements until needed. If we want a list instead of an iterator, we must pass the iterator as the argument to the list() function.
Q8 Write a function
incrementAge(record)
that, given a 3-tuple, record, of a student, composed of a name, a grade, and an age, increments the age component and returns a tuple with the same name and age and the incremented age. Implement this function as a lambda function
# Solution cell
# YOUR CODE HERE
raise NotImplementedError()
# Testing cell
assert incrementAge(('chris', 'A', 18)) == ('chris', 'A', 19)
Q9 Use map() to apply the incrementAge() function to the students list, and create a list assigned to variable students2.
# Solution cell
# YOUR CODE HERE
raise NotImplementedError()
# Testing cell
assert isinstance(students2, list)
assert len(students2) == 4
assert students2[-1] == ('alice', 'A', 20)
Q10 Write a function
vector_mult(L1, L2)
that performs element-wise multiplication between the elements in L1 and L2. You may assume that L1 and L2 are the same length. You must use map() in the vector_mult function, although you may write a helper function. Use lambda functions where you can (i.e. where the function can be formed as an expression).
# Solution cell
# YOUR CODE HERE
raise NotImplementedError()
# Testing cell
A = [5, 3, 1, 2]
B = [2, 1, 4, 3]
assert vector_mult(A, B) == [10, 3, 4, 6]