Answer all four (4) questions.
You have 110 minutes to complete the exam.
This is an open-book exam. All written material is allowed.
No electronic devices other than a flash drive and the lab PC may be used during the exam.
No communication with others (electronic, verbal, written or otherwise) is allowed during the exam. Violations will result in a mark of zero and disciplinary action.
Add the Python code described below in the cells provided.
Test your code using the menu item Cell ► Run All
The message "Solution to question N may be correct." at the bottom of the notebook means that your answer to question N may be correct.
When the exam time is over, save the notebook (the .ipynb file) and upload it to the appropriate dropbox on the course web site.
Create a list y1 with 30 elements where the value of the i'th
element is the sum of all integers from 0 to i. For example,
the first four values are 0, 1, 3, 6, .... Hint: sum()
returns the sum of its argument.
y1=[sum(range(i+1)) for i in range(30)]
The following code sets the variable a to a list of strings and
the variable b to a list of integers. Write Python code that
creates a dictionary d where each entry's key is an element of a
repeated the number of times given by the corresponding value of b
and that entry's value is the corresponding value in b. For
example, if a is ['aa', 'b', 'c'] and b is [2, 3, 5] then d
should contain { 'aaaa':2, 'bbb':3, 'ccccc':5 }. Hint: using the
multiplication operator on a string repeats it that number of
times (for example, 'a'3 gives 'aaa')*
from random import randrange as rr
a=[''.join([chr(rr(97,123)) for j in range(rr(1,4))]) for i in range(rr(3,7))]
b=[rr(1,4) for i in range(len(a))]
print(a,b)
d={k*v:v for k,v in zip(a,b)}
print(d,len(d.keys()),len(a))
Write a function called minel(l) that takes a an argument l
that is a list of 2-element tuples and returns a list consisting
of the smallest element in each tuple. For example, if l=[
(1,2), (3,-1), (1,0)] the function would return [1, -1, 0].
def minel(l):
return [min(t) for t in l]
A set of linear equations expressed in matrix form: y=Ax can be
solved by computing x=inv(A)*y where inv() represents a
matrix inverse and means matrix multiplication. The code below
defines the matrix A and the vector y. Compute x. Hint: the function numpy.linalg.inv(a) returns the inverse of a.*
import numpy as np
A=np.random.random((3,3))
y=np.random.random((3,1))
x=np.linalg.inv(A).dot(y)
print(A,y,x)
# exam validation code; do not modify
def examcheck():
try:
if all(i==a-b for i,a,b in zip(range(1,31),y1[1:],y1[0:-1])):
print("Solution to question 1 may be correct.")
except:
pass
try:
if len(d) == len(a) and all([k[0:(len(k)//v)] in a for k,v in d.items()]):
print("Solution to question 2 may be correct.")
except:
pass
try:
import random
l1=random.choices(range(10),k=10)
l2=random.choices(range(10),k=10)
if all(v<=l1[i] and v<=l2[i] for i,v in enumerate(minel(zip(l1,l2)))):
print("Solution to question 3 may be correct.")
except:
pass
try:
import numpy as np
if np.allclose(A.dot(x),y):
print("Solution to question 4 may be correct.")
except:
pass
examcheck()