Exam - Tue 02, July 2019

Scientific Programming - Data Science Master @ University of Trento

Download exercises and solution


  • Taking part to this exam erases any vote you had before


  • Correct implementations: Correct implementations with the required complexity grant you full grade.

  • Partial implementations: Partial implementations might still give you a few points. If you just can’t solve an exercise, try to solve it at least for some subcase (i.e. array of fixed size 2) commenting why you did so.

  • Bonus point: One bonus point can be earned by writing stylish code. You got style if you:

    • do not infringe the Commandments

    • write pythonic code

    • avoid convoluted code like i.e.

      if x > 5:
          return True
          return False

      when you could write just

      return x > 5

Valid code



For example, if you are given to implement:

def f(x):
    raise Exception("TODO implement me")

and you ship this code:

def my_f(x):
    # a super fast, correct and stylish implementation

def f(x):
    raise Exception("TODO implement me")

We will assess only the latter one f(x), and conclude it doesn’t work at all :P !!!!!!!

Helper functions

Still, you are allowed to define any extra helper function you might need. If your f(x) implementation calls some other function you defined like my_f here, it is ok:

# Not called by f, will get ignored:
def my_g(x):
    # bla

# Called by f, will be graded:
def my_f(y,z):
    # bla

def f(x):

How to edit and run

To edit the files, you can use any editor of your choice, you can find them under Applications->Programming:

  • Visual Studio Code

  • Editra is easy to use, you can find it under Applications->Programming->Editra.

  • Others could be GEdit (simpler), or PyCharm (more complex).

To run the tests, use the Terminal which can be found in Accessories -> Terminal

IMPORTANT: Pay close attention to the comments of the functions.

WARNING: DON’T modify function signatures! Just provide the implementation.

WARNING: DON’T change the existing test methods, just add new ones !!! You can add as many as you want.

WARNING: DON’T create other files. If you still do it, they won’t be evaluated.


If you need to print some debugging information, you are allowed to put extra print statements in the function bodies.

WARNING: even if print statements are allowed, be careful with prints that might break your function!

For example, avoid stuff like this:

x = 0

What to do

  1. Download sciprog-ds-2019-07-02-exam.zip and extract it on your desktop. Folder content should be like this:

  1. Rename sciprog-ds-2019-07-02-FIRSTNAME-LASTNAME-ID folder: put your name, lastname an id number, like sciprog-ds-2019-07-02-john-doe-432432

From now on, you will be editing the files in that folder. At the end of the exam, that is what will be evaluated.

  1. Edit the files following the instructions in this worksheet for each exercise.

  2. When done:

  • if you have unitn login: zip and send to examina.icts.unitn.it/studente

  • If you don’t have unitn login: tell instructors and we will download your work manually

Part A

Open Jupyter and start editing this notebook exam-2019-07-02.ipynb

A1 Botteghe storiche

NOTICE: this part of the exam was ported to softpython website

There you can find a more curated version (notice it may be longer than here)

You will work on the dataset of Botteghe storiche del Trentino (small shops, workshops of Trentino)

Data provider: Provincia Autonoma di Trento - dati.trentino.it

A function load_botteghe is given to load the dataset (you don’t need to implement it):

def load_botteghe():
    """Loads file data and RETURN a list of dictionaries with the botteghe dati

    import csv
    with open('data/botteghe.csv', newline='',  encoding='utf-8',) as csvfile:
        reader = csv.DictReader(csvfile,  delimiter=',')
        lst = []
        for d in reader:
    return lst

botteghe = load_botteghe()

IMPORTANT: look at the dataset !

Here we show only first 5 rows, but to get a clear picture of the dataset you should explore it further.

[OrderedDict([('Numero', '1'),
              ('Insegna', 'BAZZANELLA RENATA'),
              ('Indirizzo', 'Via del Lagorai'),
              ('Civico', '30'),
              ('Comune', 'Sover'),
              ('Cap', '38068'),
              ('Frazione/Località', 'Piscine di Sover'),
              ('Note', 'generi misti, bar - ristorante')]),
 OrderedDict([('Numero', '2'),
              ('Insegna', 'CONFEZIONI MONTIBELLER S.R.L.'),
              ('Indirizzo', 'Corso Ausugum'),
              ('Civico', '48'),
              ('Comune', 'Borgo Valsugana'),
              ('Cap', '38051'),
              ('Frazione/Località', ''),
              ('Note', 'esercizio commerciale')]),
 OrderedDict([('Numero', '3'),
              ('Insegna', 'FOTOGRAFICA TRINTINAGLIA UMBERTO S.N.C.'),
              ('Indirizzo', 'Largo Dordi'),
              ('Civico', '8'),
              ('Comune', 'Borgo Valsugana'),
              ('Cap', '38051'),
              ('Frazione/Località', ''),
              ('Note', 'esercizio commerciale, attività artigianale')]),
 OrderedDict([('Numero', '4'),
              ('Insegna', 'BAR SERAFINI DI MINATI RENZO'),
              ('Indirizzo', ''),
              ('Civico', '24'),
              ('Comune', 'Grigno'),
              ('Cap', '38055'),
              ('Frazione/Località', 'Serafini'),
              ('Note', 'esercizio commerciale')]),
 OrderedDict([('Numero', '6'),
              ('Insegna', 'SEMBENINI GINO & FIGLI S.R.L.'),
              ('Indirizzo', 'Via S. Francesco'),
              ('Civico', '35'),
              ('Comune', 'Riva del Garda'),
              ('Cap', '38066'),
              ('Frazione/Località', ''),
              ('Note', '')])]

We would like to know which different categories of bottega there are, and count them. Unfortunately, there is no specific field for Categoria, so we will need to extract this information from other fields such as Insegna and Note. For example, this Insegna contains the category BAR, while the Note (commercial enterprise) is a bit too generic to be useful:

'Note': 'esercizio commerciale',

while this other Insegna contains just the owner name and Note holds both the categories bar and ristorante:

'Note': 'generi misti, bar - ristorante',

As you see, data is non uniform:

  • sometimes the category is in the Insegna

  • sometimes is in the Note

  • sometimes is in both

  • sometimes is lowercase

  • sometimes is uppercase

  • sometimes is single

  • sometimes is multiple (bar - ristorante)

First we want to extract all categories we can find, and rank them according their frequency, from most frequent to least frequent.

To do so, you need to

  • count all words you can find in both Insegna and Note fields, and sort them. Note you need to normalize the uppercase.

  • consider a category relevant if it is present at least 11 times in the dataset.

  • filter non relevant words: some words like prepositions, type of company ('S.N.C', S.R.L., ..), etc will appear a lot, and will need to be ignored. To detect them, you are given a list called stopwords.

NOTE: the rules above do not actually extract all the categories, for the sake of the exercise we only keep the most frequent ones.

A1.1 rank_categories

Show solution
def rank_categories(db, stopwords):
    raise Exception('TODO IMPLEMENT ME !')

stopwords = ['',
             'S.N.C.', 'SNC','S.A.S.', 'S.R.L.', 'S.C.A.R.L.', 'SCARL','S.A.S', 'COMMERCIALE','FAMIGLIA','COOPERATIVA',
             '-', '&', 'C.', 'ESERCIZIO',
             'IL', 'DE', 'DI','A', 'DA', 'E', 'LA', 'AL',  'DEL', 'ALLA', ]
categories = rank_categories(botteghe, stopwords)

[('BAR', 191),
 ('RISTORANTE', 150),
 ('HOTEL', 67),
 ('ALBERGO', 64),
 ('MACELLERIA', 27),
 ('PANIFICIO', 22),
 ('CALZATURE', 21),
 ('FARMACIA', 21),
 ('ALIMENTARI', 20),
 ('PIZZERIA', 16),
 ('SPORT', 16),
 ('TABACCHI', 12),
 ('FERRAMENTA', 12),
 ('BAZAR', 11)]

A1.2 plot

Now plot the 10 most frequent categories. Please pay attention to plot title, width and height, axis labels. Everything MUST display in a readable way.

# write here

Show solution


A1.3 enrich

Once you found the categories, implement function enrich, which takes the db and previously computed categories, and RETURN a NEW DB where the dictionaries are enriched with a new field Categorie, which holds a list of the categories a particular bottega belongs to.

Show solution
def enrich(db, categories):
    raise Exception('TODO IMPLEMENT ME !')

new_db = enrich(botteghe, rank_categories(botteghe, stopwords))

new_db[:6]   #NOTE here we only show a sample
[{'Numero': '1',
  'Indirizzo': 'Via del Lagorai',
  'Civico': '30',
  'Comune': 'Sover',
  'Cap': '38068',
  'Frazione/Località': 'Piscine di Sover',
  'Note': 'generi misti, bar - ristorante',
  'Categorie': ['BAR', 'RISTORANTE']},
 {'Numero': '2',
  'Indirizzo': 'Corso Ausugum',
  'Civico': '48',
  'Comune': 'Borgo Valsugana',
  'Cap': '38051',
  'Frazione/Località': '',
  'Note': 'esercizio commerciale',
  'Categorie': []},
 {'Numero': '3',
  'Indirizzo': 'Largo Dordi',
  'Civico': '8',
  'Comune': 'Borgo Valsugana',
  'Cap': '38051',
  'Frazione/Località': '',
  'Note': 'esercizio commerciale, attività artigianale',
  'Categorie': []},
 {'Numero': '4',
  'Indirizzo': '',
  'Civico': '24',
  'Comune': 'Grigno',
  'Cap': '38055',
  'Frazione/Località': 'Serafini',
  'Note': 'esercizio commerciale',
  'Categorie': ['BAR']},
 {'Numero': '6',
  'Insegna': 'SEMBENINI GINO & FIGLI S.R.L.',
  'Indirizzo': 'Via S. Francesco',
  'Civico': '35',
  'Comune': 'Riva del Garda',
  'Cap': '38066',
  'Frazione/Località': '',
  'Note': '',
  'Categorie': []},
 {'Numero': '7',
  'Indirizzo': 'Via Nazionale',
  'Civico': '29',
  'Comune': 'Lavis',
  'Cap': '38015',
  'Frazione/Località': 'Nave San Felice',
  'Note': '',
  'Categorie': ['RISTORANTE', 'HOTEL', 'PIZZERIA']}]

A2 dump

The multinational ToxiCorp wants to hire you for devising an automated truck driver which will deposit highly contaminated waste in the illegal dumps they own worldwide. You find it ethically questionable, but they pay well, so you accept.

A dump is modelled as a rectangular region of dimensions nrow and ncol, implemented as a list of lists matrix. Every cell i, j contains the tons of waste present, and can contain at most 7 tons of waste.

The dumpster truck will transport q tons of waste, and try to fill the dump by depositing waste in the first row, filling each cell up to 7 tons. When the first row is filled, it will proceed to the second one from the left , then to the third one again from the left until there is no waste to dispose of.

Function dump(m, q) takes as input the dump mat and the number of tons q to dispose of, and RETURN a NEW list representing a plan with the sequence of tons to dispose. If waste to dispose exceeds dump capacity, raises ValueError.

NOTE: the function does not modify the matrix


m = [

dump(m, 22)

[2, 3, 1, 3, 0, 6, 4, 3]

For first row we dispose of 2,3,1 tons in three cells, for second row we dispose of 3,0,6 tons in three cells, for third row we only dispose 4, 3 tons in two cells as limit q=22 is reached.

Show solution
def dump(mat, q):
    raise Exception('TODO IMPLEMENT ME !')

m1 = [

assert dump(m1,0) == []  # nothing to dump

m2 = [

assert dump(m2,2) == [2]

m3 = [

assert dump(m3,3) == [2, 1]

m3 = [

assert dump(m3,3) == [2, 0, 1]

m5 = [
    [2,5],   # 5 2
    [4,3]    # 3 1


assert dump(m5,11) == [5,2,3,1]

m6 = [         # tons to dump in each cell
    [5,4,6],   # 2 3 1
    [4,7,1],   # 3 0 6
    [3,2,6],   # 4 3 0
    [3,6,2],   # 0 0 0

assert dump(m6, 22) == [2,3,1,3,0,6,4,3]

    dump ([[5]], 10)
    raise Exception("Should have failed !")
except ValueError:

Part B

B1 Theory

Write the solution in separate ``theory.txt`` file

Let L1 and L2 be two lists containing n lists, each of them of size n. Compute the computational complexity of function fun() with respect to n.

def fun(L1,L2):
    for r1 in L1:
        for val in r1:
            for r2 in L2:
                if val = sum(r2):
Show answer

B2 Linked List sorting

Open a text editor and edit file linked_sort.py

B2.1 bubble_sort

You will implement bubble sort on a LinkedList.

def bubble_sort(self):
    """ Sorts in-place this linked list using the method of bubble sort

        - MUST execute in O(n^2) where n is the length of the linked list

Testing: python3 -m unittest linked_sort_test.BubbleSortTest

As a reference, you can look at this example_bubble implementation below that operates on regular python lists. Basically, you will have to translate the for cycles into two suitable while and use node pointers.

NOTE: this version of the algorithm is inefficient as we do not use j in the inner loop: your linked list implementation can have this inefficiency as well.

def example_bubble(plist):
    for j in range(len(plist)):
        for i in range(len(plist)):
            if i + 1 < len(plist) and plist[i]>plist[i+1]:
                temp = plist[i]
                plist[i] = plist[i+1]
                plist[i+1] = temp

my_list = [23, 34, 55, 32, 7777, 98, 3, 2, 1]

[1, 2, 3, 23, 32, 34, 55, 98, 7777]

B2.2 merge

Implement this method:

def merge(self,l2):
    """ Assumes this linkedlist and l2 linkedlist contain integer numbers
        sorted in ASCENDING order, and  RETURN a NEW LinkedList with
        all the numbers from this and l2 sorted in DESCENDING order

        IMPORTANT 1: *MUST* EXECUTE IN O(n1+n2) TIME where n1 and n2 are
                     the sizes of this and l2 linked_list, respectively

        IMPORTANT 2: *DO NOT* attempt to convert linked lists to
                     python lists!

Testing: python3 -m unittest linked_sort_test.MergeTest

B3 Stacktris

Open a text editor and edit file stacktris.py

A Stacktris is a data structure that operates like the famous game Tetris, with some restrictions:

  • Falling pieces can be either of length 1 or 2. We call them 1-block and 2-block respectively

  • The pit has a fixed width of 3 columns

  • 2-blocks can only be in horizontal

We print a Stacktris like this:

\ j 012
4  | 11|    # two 1-block
3  | 22|    # one 2-block
2  | 1 |    # one 1-block
1  |22 |    # one 2-block
0  |1 1|    # on the ground there are two 1-block

In Python, we model the Stacktris as a class holding in the variable _stack a list of lists of integers, which models the pit:

class Stacktris:

    def __init__(self):
        """ Creates a Stacktris
        self._stack = []

So in the situation above the _stack variable would look like this (notice row order is inverted with respect to the print)


The class has three methods of interest which you will implement, drop1(j) , drop2h(j) and _shorten


Let’s see an example:

from stacktris_sol import *

st = Stacktris()

At the beginning the pit is empty:


We can start by dropping from the ceiling a block of dimension 1 into the last column at index j=2. By doing so, a new row will be created, and will be a list containing the numbers [0,0,1]

IMPORTANT: zeroes are not displayed

DEBUG:  Stacktris:
        |  1|


Now we drop an horizontal block of dimension 2 (a 2-block) having the leftmost block at column j=1. Since below in the pit there is already the 1 block we previosly put, the new block will fall and stay upon it. Internally, we will add a new row as a python list containing the numbers [0,2,2]

DEBUG:  Stacktris:
        | 22|
        |  1|


We see the zeroth column is empty, so if we drop there a 1-block it will fall to the ground. Internally, the zeroth list will become [1,0,1]:

DEBUG:  Stacktris:
        | 22|
        |1 1|


Now we drop again a 2-block at column j=2, on top of the previously laid one. This will add a new row as list [0,2,2].

DEBUG:  Stacktris:
        | 22|
        | 22|
        |1 1|


In the game Tetris, when a row becomes completely filled it disappears. So if we drop a 1-block to the leftmost column, the mid line should be removed.

NOTE: The messages on the console are just debug print, the function drop1 only returns the extracted line [1,2,2]:

DEBUG:  Stacktris:
        | 22|
        |1 1|

DEBUG:  POPPING [1, 2, 2]
DEBUG:  Stacktris:
        | 22|
        |1 1|

[1, 2, 2]

Now we insert another 2-block starting at j=0. It will fall upon the previously laid one:

DEBUG:  Stacktris:
        |22 |
        | 22|
        |1 1|


We can complete teh topmost row by dropping a 1-block to the rightmost column. As a result, the row will be removed from the stack and the row will be returned by the call to drop1:

DEBUG:  Stacktris:
        | 22|
        |1 1|

DEBUG:  POPPING [2, 2, 1]
DEBUG:  Stacktris:
        | 22|
        |1 1|

[2, 2, 1]

Another line completion with a drop1 at column j=0:

DEBUG:  Stacktris:
        |1 1|

DEBUG:  POPPING [1, 2, 2]
DEBUG:  Stacktris:
        |1 1|

[1, 2, 2]

We can finally empty the Stacktris by dropping a 1-block in the mod column:

DEBUG:  Stacktris:

DEBUG:  POPPING [1, 1, 1]
DEBUG:  Stacktris:
[1, 1, 1]

B3.1 _shorten

Start by implementing this private method:

def _shorten(self):
    """ Scans the Stacktris from top to bottom searching for a completely filled line:
        - if found, remove it from the Stacktris and return it as a list.
        - if not found, return an empty list.

If you wish, you can add debug prints but they are not mandatory

Testing: python3 -m unittest stacktris_test.ShortenTest

B3.2 drop1

Once you are done with the previous function, implement drop1 method:

NOTE: In the implementation, feel free to call the previously implemented _shorten method.

def drop1(self, j):
    """ Drops a 1-block on column j.

         - If another block is found,  place the 1-block on top of that block,
           otherwise place it on the ground.

        - If, after the 1-block is placed, a row results completely filled, removes
          the row and RETURN it. Otherwise, RETURN an empty list.

        - if index `j` is outside bounds, raises ValueError

Testing: python3 -m unittest stacktris_test.Drop1Test

B3.3 drop2h

Once you are done with the previous function, implement drop2 method:

def drop2h(self, j):
    """ Drops a 2-block horizontally with left block on column j,

         - If another block is found,  place the 2-block on top of that block,
           otherwise place it on the ground.

        - If, after the 2-block is placed, a row results completely filled,
          removes the row and RETURN it. Otherwise, RETURN an empty list.

        - if index `j` is outside bounds, raises ValueError

Testing: python3 -m unittest stacktris_test.Drop2hTest

Show solution
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