BDAT 1004 – Data Programming
Problem Set 1
This problem set is based on lectures 1,2 and 3. For a complete list of topics please
consult page 2 of the course syllabus. Please consult the “Instructions for Problem
Set Submissions” document under course information before submitting your
assignment.
Question 1
What data type is each of the following?
|
5 5.0 5 > 1 '5' 5 * 2 '5' * 2 '5' + '2' 5 / 2 5 // 2 [5, 2, 1] 5 in [1, 4,
6] math.pi |
Question 3
a. Write a function inside(x,y,x1,y1,x2,y2) that returns True or False
depending on whether the point (x,y) lies in the rectangle with lower left
corner (x1,y1) and upper right corner (x2,y2).
>>> inside(1,1,0,0,2,3)
True
>>> inside(-1,-1,0,0,2,3)
False
b. Use function inside() from part a. to write an expression that tests whether
the point (1,1) lies in both of the following rectangles: one with lower left
corner (0.3, 0.5) and upper right corner (1.1, 0.7) and the other with lower
left corner (0.5, 0.2) and upper right corner (1.1, 2).
Question 4
16. You can turn a word into pig-Latin using the following two rules (simplified):
• If the word starts with a consonant, move that letter to the end and append
'ay'. For example, 'happy' becomes 'appyhay' and 'pencil' becomes 'encilpay'.
• If the word starts with a vowel, simply append 'way' to the end of the word.
For example, 'enter' becomes 'enterway' and 'other' becomes 'otherway' . For
our purposes, there are 5 vowels: a, e, i, o, u (so we count y as a consonant).
Write a function pig() that takes a word (i.e., a string) as input and returns its pigLatin form. Your function should still work if the input word contains upper case
characters. Your output should always be lower case however.
>>> pig('happy')
'appyhay
>>> pig('Enter')
'enterway'
Question 5
File bloodtype1.txt records blood-types of patients (A, B, AB, O or OO) at a clinic.
Write a function bldcount() that reads the file with name name and reports (i.e.,
prints) how many patients there are in each bloodtype.
>>> bldcount('bloodtype.txt')
There are 10 patients of blood type A.
There is one patient of blood type B.
There are 10 patients of blood type AB.
There are 12 patients of blood type O.
There are no patients of blood type OO.
Question 6
Write a function curconv() that takes as input:
1. a currency represented using a string (e.g., 'JPY' for the Japanese Yen or
'EUR' for the Euro)
2. an amount
and then converts and returns the amount in US dollars.
>>> curconv('EUR', 100)
122.96544
>>> curconv('JPY', 100)
1.241401
The currency rates you will need are stored in file currencies.txt:
AUD 1.0345157 Australian Dollar
CHF 1.0237414 Swiss Franc
CNY 0.1550176 Chinese Yuan
DKK 0.1651442 Danish Krone
EUR 1.2296544 Euro
GBP 1.5550989 British Pound
HKD 0.1270207 Hong Kong Dollar
INR 0.0177643 Indian Rupee
JPY 0.01241401 Japanese Yen
MXN 0.0751848 Mexican Peso
MYR 0.3145411 Malaysian Ringgit
NOK 0.1677063 Norwegian Krone
NZD 0.8003591 New Zealand Dollar
PHP 0.0233234 Philippine Peso
SEK 0.148269 Swedish Krona
SGD 0.788871 Singapore Dollar
THB 0.0313789 Thai Baht
Question 7
Each of the following will cause an exception (an error). Identify what type of
exception each will cause.
|
Trying to add
incompatible variables, as in adding 6 +
‘a’ Referring to
the 12th item of a list that has only 10 items Using a value
that is out of range for a function’s input, such as calling math.sqrt(-1.0) Using an
undeclared variable, such as print(x) when x has not been defined |
Trying to open a file that does not exist, such as
mistyping the file name or looking in the
wrong
directory.
Question 8
Encryption is the process of hiding the meaning of a text by substituting letters in the
message with other letters, according to some system. If the process is successful, no
one but the intended recipient can understand the encrypted message. Cryptanalysis
refers to attempts to undo the encryption, even if some details of the encryption are
unknown (for example, if an encrypted message has been intercepted). The first step
of cryptanalysis is often to build up a table of letter frequencies in the encrypted text.
Assume that the string letters is already defined as
'abcdefghijklmnopqrstuvwxyz'. Write a function called frequencies()
that takes a string as its only parameter, and returns a list of integers, showing the
number of times each character appears in the text. Your function may ignore any
characters that are not in letters.
>>> frequencies('The quick red fox got bored and went home.')
[1, 1, 1, 3, 5, 1, 1, 2, 1, 0, 1, 0, 1, 2, 4, 0, 1, 2, 0, 2,
1, 0, 1, 1, 0, 0]
>>> frequencies('apple')
Question 9
The Sieve of Erastophenes is an algorithm -- known to ancient Greeks -- that finds
all prime numbers up to a given number n. It does this by first creating a list L from
2 to n and an (initially empty) list primeL. The algorithm then takes the first number
in list L (2) and appends it to list primeL, and then removes 2 and all its multiples
(4,6,8,10,12, ...) from L. The algorithm then takes the new first number in L (3) and
appends it to list primeL, and then removes from L 3 and all its remaining multiples
(9,15,21,...). So, in every iteration, the first number of list L is appended to list
primeL and then it and its multiples are removed from list L. The iterations stop
when list L becomes empty. Write a function sieve() that takes as input a positive
integer n, implements the above algorithm, and returns a list of all prime numbers up
to n.
>>> sieve(56)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53]
>>> sieve(368)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
151, 157, 163, 167, 173, 179, 181, 191, 193, 197,
199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
317, 331, 337, 347, 349, 353, 359, 367]
>>> sieve(32)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
Question 10
Implement function triangleArea(a,b,c) that takes as input the lengths of the 3
sides of a triangle and returns the area of the triangle. By Heron's formula, the area
of a triangle with side lengths a, b, and c is
s(s - a)(s -b)(s -c)
, where
s = (a+b+c)/2.
>>> triangleArea(2,2,2)
1.7320508075688772
