Introduction to Computer Science I

Final exam practice questions

Implement in finalPractice.py the functions described below.

1.    Write a function innerProduct() that that takes as input two lists (of same length) of integers and then computes and returns the inner product of the two lists of integers. The inner product of two lists x = [x1, x2, ..., xn] and y = [y1, y2, ..., yn] is the value x1 y1 +  x2 y2  +  ...  +  xn yn .

Usage:
>>> innerProduct([2,3,4], [1,0,2])
10


2.    Write a function digitsum() that takes a positive integer n as input and returns the sum of the digits of n.
Usage:
>>> digitsum(34)
7
>>> digitsum(934)
16
>>> digitsum(9314)
17

3.    Write a function wordcount() that takes the name of a text file as input and prints the number of occurrences of every word in the file. You function should be case-insensitive so 'Hello' and 'hello' are treated as the same word. You should ignore words of length 2 or less. Test your implementation on file frankenstein.txt.
Usage:
>>> wordcount('frankenstein.txt')
artifice            1
resting             2
compact             1
service             3
sixth               1
lulling             1
radiance            2
offices             1
tree                5
incline             1
treasures           3
unravel             1
oblivion            2
god                 20
malignity           7
promontory          4
acknowledged        1
refinement          1
proceedings         1
surviving           1
inroads             1
arguments           7
pursuits            4
quit                17
...
...

4.    Write a function called frequencies() that takes a table (i.e., a two dimensional list) of numbers as input and returns a dictionary that maps each number that appears in the table to its frequency (i.e., number of times it appears in the table)
>>> t = [[2,0,4,1], [3,1,3,3], [0,4,5,1]]
>>> frequencies(t)
{0: 2, 1: 3, 2: 1, 3: 3, 4: 2, 5: 1}

5.    Write a function named lottery() that takes an integer n as input and that prints 6 different numbers in the range from 1 to 60, chosen uniformly at random, as shown below:
>>> lottery(60)
27
10
58
28
60
2
>>> lottery(60)
6
33
21
55
16
1

6.    Function fileLength(), given to you, takes the name of a file as input and returns the length of the file:
>>> fileLength('finalPractice.py')
125
>>> fileLength('finl.py')
Traceback (most recent call last):
  File "<pyshell#3>", line 1, in <module>
    fileLength('finl.py')
  File "/Users/me/final.py", line 2, in fileLength
    infile = open(filename)
FileNotFoundError: [Errno 2] No such file or directory: 'finl.py'
As shown above, if the file cannot be found by the interpreter or if it cannot be read as a text file, an exception will be raised. Modify function fileLength() so that a friendly message is printed instead:
>>> fileLength('finalPractice.py')
224
>>> fileLength('finl.py')
File finl.py not found.

7.    The constant Pi is an irrational number with value approximately 3.1415928... The precise value of Pi is equal to this infinite sum:
Pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11+ ...
We can get a good approximation of Pi by computing the sum of the first few terms. Write a function approxPi() that takes as input a float-value error and approximates constant Pi within error by computing the above sum, term by term, until the difference between the current sum and the previous sum (with one less term) is no greater than error. The function should return the new sum.
>>> approxPi(0.01)
3.1465677471829556
>>> approxPi(0.0000001)
3.1415927035898146