Exam - Mon 24, Aug 2020

Scientific Programming - Data Science @ University of Trento

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Part A - Prezzario

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)

Open Jupyter and start editing this notebook exam-2020-08-24.ipynb

You are going to analyze the dataset EPPAT-2018-new-compact.csv, which is the price list for all products and services the Autonomous Province of Trento may require. Source: dati.trentino.it

DO NOT WASTE TIME LOOKING AT THE WHOLE DATASET!

The dataset is quite complex, please focus on the few examples we provide

We will show examples with pandas, but it is not required to solve the exercises.

import pandas as pd
import numpy as np

pd.set_option('display.max_colwidth', -1)

df = pd.read_csv('EPPAT-2018-new-compact.csv', encoding='latin-1')

The dataset contains several columns, but we will consider the following ones:

df = df[['Codice Prodotto', 'Descrizione Breve Prodotto', 'Categoria', 'Prezzo']]
df[:22]

	Codice Prodotto	Descrizione Breve Prodotto	Categoria	Prezzo
0	A.02.35.0050	ATTREZZATURA PER INFISSIONE PALI PILOTI	NaN	NaN
1	A.02.35.0050.010	Attrezzatura per infissione pali piloti.	Noli e trasporti	109.09
2	A.02.40	ATTREZZATURE SPECIALI	NaN	NaN
3	A.02.40.0010	POMPA COMPLETA DI MOTORE	NaN	NaN
4	A.02.40.0010.010	fino a mm 50.	Noli e trasporti	2.21
5	A.02.40.0010.020	oltre mm 50 fino a mm 100.	Noli e trasporti	3.36
6	A.02.40.0010.030	oltre mm 100 fino a mm 150.	Noli e trasporti	4.42
7	A.02.40.0010.040	oltre mm 150 fino a mm 200.	Noli e trasporti	5.63
8	A.02.40.0010.050	oltre mm 200.	Noli e trasporti	6.84
9	A.02.40.0020	GRUPPO ELETTROGENO	NaN	NaN
10	A.02.40.0020.010	fino a 10 KW	Noli e trasporti	8.77
11	A.02.40.0020.020	oltre 10 fino a 13 KW	Noli e trasporti	9.94
12	A.02.40.0020.030	oltre 13 fino a 20 KW	Noli e trasporti	14.66
13	A.02.40.0020.040	oltre 20 fino a 28 KW	Noli e trasporti	15.62
14	A.02.40.0020.050	oltre 28 fino a 36 KW	Noli e trasporti	16.40
15	A.02.40.0020.060	oltre 36 fino a 56 KW	Noli e trasporti	28.53
16	A.02.40.0020.070	oltre 56 fino a 80 KW	Noli e trasporti	44.06
17	A.02.40.0020.080	oltre 80 fino a 100 KW	Noli e trasporti	50.86
18	A.02.40.0020.090	oltre 100 fino a 120 KW	Noli e trasporti	55.88
19	A.02.40.0020.100	oltre 120 fino a 156 KW	Noli e trasporti	80.47
20	A.02.40.0020.110	oltre 156 fino a 184 KW	Noli e trasporti	94.00
21	A.02.40.0030	NASTRO TRASPORTATORE CON MOTORE AD ARIA COMPRESSA	NaN	NaN

Pompa completa a motore Example

If we look at the dataset, in some cases we can spot a pattern like the following (rows 3 to 8 included):

df[3:12]

	Codice Prodotto	Descrizione Breve Prodotto	Categoria	Prezzo
3	A.02.40.0010	POMPA COMPLETA DI MOTORE	NaN	NaN
4	A.02.40.0010.010	fino a mm 50.	Noli e trasporti	2.21
5	A.02.40.0010.020	oltre mm 50 fino a mm 100.	Noli e trasporti	3.36
6	A.02.40.0010.030	oltre mm 100 fino a mm 150.	Noli e trasporti	4.42
7	A.02.40.0010.040	oltre mm 150 fino a mm 200.	Noli e trasporti	5.63
8	A.02.40.0010.050	oltre mm 200.	Noli e trasporti	6.84
9	A.02.40.0020	GRUPPO ELETTROGENO	NaN	NaN
10	A.02.40.0020.010	fino a 10 KW	Noli e trasporti	8.77
11	A.02.40.0020.020	oltre 10 fino a 13 KW	Noli e trasporti	9.94

We see the first column holds product codes. If two rows share a code prefix, they belong to the same product type. As an example, we can take product A.02.40.0010, which has 'POMPA COMPLETA A MOTORE' as description (‘Descrizione Breve Prodotto’ column). The first row is basically telling us the product type, while the following rows are specifying several products of the same type (notice they all share the A.02.40.0010 prefix code until 'GRUPPO ELETTROGENO' excluded). Each description specifies a range of values for that product: fino a means until to , and oltre means beyond.

Notice that:

• first row has only one number

• intermediate rows have two numbers

• last row of the product series (row 8) has only one number and contains the word oltre ( beyond ) (in some other cases, last row of product series may have two numbers)

A1 extract_bounds

Write a function that given a Descrizione Breve Prodotto as a single string extracts the range contained within as a tuple.

If the string contains only one number n:

• if it contains UNTIL ( ‘fino’ ) it is considered a first row with bounds (0,n)

• if it contains BEYOND ( ‘oltre’ ) it is considered a last row with bounds (n, math.inf)

DO NOT use constants like measure units ‘mm’, ‘KW’, etc in the code

Show solution

import math


#use this list to rmeove unneeded stuff
PUNCTUATION=[',','-','.','%']
UNTIL = 'fino'
BEYOND = 'oltre'

def extract_bounds(text):



    fixed_text = text
    for pun in PUNCTUATION:
        fixed_text = fixed_text.replace(pun, ' ')
    words = fixed_text.split()
    i = 0
    left = None
    right = None

    while i < len(words) and (not left or not right):

        if words[i].isdigit():
            if not left:
                left = int(words[i])
            elif not right:
                right = int(words[i])
        i += 1

    if not right:
        if BEYOND in text:
            right = math.inf
        else:
            right = left
            left = 0

    return (left,right)


assert extract_bounds('fino a mm 50.') == (0,50)
assert extract_bounds('oltre mm 50 fino a mm 100.') == (50,100)
assert extract_bounds('oltre mm 200.') == (200, math.inf)
assert extract_bounds('da diametro 63 mm a diametro 127 mm') == (63, 127)
assert extract_bounds('fino a 10 KW') ==  (0,10)
assert extract_bounds('oltre 156 fino a 184 KW') ==  (156,184)
assert extract_bounds('fino a 170 A, avviamento elettrico') == (0,170)
assert extract_bounds('oltre 170 A fino a 250 A, avviamento elettrico') == (170, 250)
assert extract_bounds('oltre 300 A, avviamento elettrico')  == (300, math.inf)
assert extract_bounds('tetti piani o con bassa pendenza - fino al 10%') == (0,10)
assert extract_bounds('tetti a media pendenza - oltre al 10% e fino al 45%') == (10,45)
assert extract_bounds('tetti ad alta pendenza - oltre al 45%') == (45, math.inf)

import math


#use this list to rmeove unneeded stuff
PUNCTUATION=[',','-','.','%']
UNTIL = 'fino'
BEYOND = 'oltre'

def extract_bounds(text):
    raise Exception('TODO IMPLEMENT ME !')

assert extract_bounds('fino a mm 50.') == (0,50)
assert extract_bounds('oltre mm 50 fino a mm 100.') == (50,100)
assert extract_bounds('oltre mm 200.') == (200, math.inf)
assert extract_bounds('da diametro 63 mm a diametro 127 mm') == (63, 127)
assert extract_bounds('fino a 10 KW') ==  (0,10)
assert extract_bounds('oltre 156 fino a 184 KW') ==  (156,184)
assert extract_bounds('fino a 170 A, avviamento elettrico') == (0,170)
assert extract_bounds('oltre 170 A fino a 250 A, avviamento elettrico') == (170, 250)
assert extract_bounds('oltre 300 A, avviamento elettrico')  == (300, math.inf)
assert extract_bounds('tetti piani o con bassa pendenza - fino al 10%') == (0,10)
assert extract_bounds('tetti a media pendenza - oltre al 10% e fino al 45%') == (10,45)
assert extract_bounds('tetti ad alta pendenza - oltre al 45%') == (45, math.inf)

A2 extract_product

Write a function that given a filename, a code and a unit, parses the csv until it finds the corresponding code and RETURNS one dictionary with relevant information for that product

• Prezzo ( price ) must be converted to float

• implement the parsing with a csv.DictReader, see example

• as encoding, use latin-1

# Suppose we want to get all info about A.02.40.0010 prefix:
df[3:12]

	Codice Prodotto	Descrizione Breve Prodotto	Categoria	Prezzo
3	A.02.40.0010	POMPA COMPLETA DI MOTORE	NaN	NaN
4	A.02.40.0010.010	fino a mm 50.	Noli e trasporti	2.21
5	A.02.40.0010.020	oltre mm 50 fino a mm 100.	Noli e trasporti	3.36
6	A.02.40.0010.030	oltre mm 100 fino a mm 150.	Noli e trasporti	4.42
7	A.02.40.0010.040	oltre mm 150 fino a mm 200.	Noli e trasporti	5.63
8	A.02.40.0010.050	oltre mm 200.	Noli e trasporti	6.84
9	A.02.40.0020	GRUPPO ELETTROGENO	NaN	NaN
10	A.02.40.0020.010	fino a 10 KW	Noli e trasporti	8.77
11	A.02.40.0020.020	oltre 10 fino a 13 KW	Noli e trasporti	9.94

A call to

pprint(extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm'))

Must produce:

{'category': 'Noli e trasporti',
 'code': 'A.02.40.0010',
 'description': 'POMPA COMPLETA DI MOTORE',
 'measure_unit': 'mm',
 'models': [{'bounds': (0, 50),        'price': 2.21, 'subcode': '010'},
            {'bounds': (50, 100),      'price': 3.36, 'subcode': '020'},
            {'bounds': (100, 150),     'price': 4.42, 'subcode': '030'},
            {'bounds': (150, 200),     'price': 5.63, 'subcode': '040'},
            {'bounds': (200, math.inf),'price': 6.84, 'subcode': '050'}]}

Notice that if we append subcode to code (with a dot) we obtain the full product code.

Show solution

import csv
from pprint import pprint

def extract_product(filename, code, measure_unit):


    c = 0
    with open(filename, encoding='latin-1', newline='') as f:
        my_reader = csv.DictReader(f, delimiter=',')   # Notice we now used DictReader
        for d in my_reader:

            if d['Codice Prodotto'] == code:
                ret = {}
                ret['description'] = d['Descrizione Breve Prodotto']
                ret['code'] = code
                ret['measure_unit'] = measure_unit
                ret['models'] = []

            if d['Codice Prodotto'].startswith(code + '.'):
                ret['category'] = d['Categoria']
                subdiz = {}
                subdiz['price'] = float(d['Prezzo'])
                subdiz['subcode'] = d['Codice Prodotto'][len(code)+1:]
                subdiz['bounds'] = extract_bounds(d['Descrizione Breve Prodotto'])
                ret['models'].append(subdiz)

    return ret


pprint(extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm'))
assert extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm') == \
    {'category': 'Noli e trasporti',
     'code': 'A.02.40.0010',
     'description': 'POMPA COMPLETA DI MOTORE',
     'measure_unit': 'mm',
     'models': [{'bounds': (0, 50),        'price': 2.21, 'subcode': '010'},
                {'bounds': (50, 100),      'price': 3.36, 'subcode': '020'},
                {'bounds': (100, 150),     'price': 4.42, 'subcode': '030'},
                {'bounds': (150, 200),     'price': 5.63, 'subcode': '040'},
                {'bounds': (200, math.inf),'price': 6.84, 'subcode': '050'}]}

#pprint(extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0020', 'KW'))
#pprint(extract_product('EPPAT-2018-new-compact.csv', 'B.02.10.0042', 'mm'))
#pprint(extract_product('EPPAT-2018-new-compact.csv','B.30.10.0010', '%'))

{'category': 'Noli e trasporti',
 'code': 'A.02.40.0010',
 'description': 'POMPA COMPLETA DI MOTORE',
 'measure_unit': 'mm',
 'models': [{'bounds': (0, 50), 'price': 2.21, 'subcode': '010'},
            {'bounds': (50, 100), 'price': 3.36, 'subcode': '020'},
            {'bounds': (100, 150), 'price': 4.42, 'subcode': '030'},
            {'bounds': (150, 200), 'price': 5.63, 'subcode': '040'},
            {'bounds': (200, inf), 'price': 6.84, 'subcode': '050'}]}

import csv
from pprint import pprint

def extract_product(filename, code, measure_unit):
    raise Exception('TODO IMPLEMENT ME !')

pprint(extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm'))
assert extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm') == \
    {'category': 'Noli e trasporti',
     'code': 'A.02.40.0010',
     'description': 'POMPA COMPLETA DI MOTORE',
     'measure_unit': 'mm',
     'models': [{'bounds': (0, 50),        'price': 2.21, 'subcode': '010'},
                {'bounds': (50, 100),      'price': 3.36, 'subcode': '020'},
                {'bounds': (100, 150),     'price': 4.42, 'subcode': '030'},
                {'bounds': (150, 200),     'price': 5.63, 'subcode': '040'},
                {'bounds': (200, math.inf),'price': 6.84, 'subcode': '050'}]}

#pprint(extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0020', 'KW'))
#pprint(extract_product('EPPAT-2018-new-compact.csv', 'B.02.10.0042', 'mm'))
#pprint(extract_product('EPPAT-2018-new-compact.csv','B.30.10.0010', '%'))

{'category': 'Noli e trasporti',
 'code': 'A.02.40.0010',
 'description': 'POMPA COMPLETA DI MOTORE',
 'measure_unit': 'mm',
 'models': [{'bounds': (0, 50), 'price': 2.21, 'subcode': '010'},
            {'bounds': (50, 100), 'price': 3.36, 'subcode': '020'},
            {'bounds': (100, 150), 'price': 4.42, 'subcode': '030'},
            {'bounds': (150, 200), 'price': 5.63, 'subcode': '040'},
            {'bounds': (200, inf), 'price': 6.84, 'subcode': '050'}]}

A3 plot_product

Implement following function that takes a dictionary as output by previous extract_product and shows its price ranges.

• pay attention to display title and axis labels as shown, using input data and not constants.

• in case last range holds a math.inf, show a > sign

• if you don’t have a working extract_product, just copy paste data from previous asserts.

Show solution

%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

def plot_product(product):


    models = product['models']
    xs = np.arange(len(models))
    ys = [ model["price"] for model in models]


    plt.bar(xs, ys, 0.5, align='center')

    plt.title('%s  (%s) SOLUTION' % (product['description'], product['code']) )

    ticks = []
    for model in models:
        bounds = model["bounds"]
        if bounds[1] == math.inf:
            ticks.append('>%s' % bounds[0])
        else:
            ticks.append('%s - %s' % (bounds[0], bounds[1]))

    plt.xticks(xs, ticks)
    plt.gcf().set_size_inches(11,8)
    plt.xlabel(product['measure_unit'])
    plt.ylabel('Price (€)')

    plt.savefig('pompa-a-motore-solution.png')
    plt.show()



product = extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm')
#product = extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0020', 'KW')
#product = extract_product('EPPAT-2018-new-compact.csv', 'B.02.10.0042', 'mm')
#product = extract_product('EPPAT-2018-new-compact.csv','B.30.10.0010', '%')

plot_product(product)

%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

def plot_product(product):
    raise Exception('TODO IMPLEMENT ME !')


product = extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0010', 'mm')
#product = extract_product('EPPAT-2018-new-compact.csv', 'A.02.40.0020', 'KW')
#product = extract_product('EPPAT-2018-new-compact.csv', 'B.02.10.0042', 'mm')
#product = extract_product('EPPAT-2018-new-compact.csv','B.30.10.0010', '%')

plot_product(product)

Part B

B1 Theory

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

B1.1 complexity

Given a list L of n elements, please compute the asymptotic computational complexity of the following function, explaining your reasoning.

def my_fun(L):
    n = len(L)
    tmp = []
    for i in range(int(n)):
        tmp.insert(0,L[i]-L[int(n/3)])
    return sum(tmp)

B1.2 describe

Briefly describe what a graph is and the two classic ways that can be used to represent it as a data structure.

B2 couple_sort

Open a text editor and edit file linked_list.py. Implement this method:

def couple_sort(self):
        """MODIFIES the linked list by considering couples of nodes at *even* indexes
           and their successors: if a node data is lower than its successor data, swaps
           the nodes *data*.

           - ONLY swap *data*, DO NOT change node links.
           - if linked list has odd size, simply ignore the exceeding node.
           - MUST execute in O(n), where n is the size of the list
        """

Testing: python3 -m unittest linked_list_Test.CoupleSortTest

Example:

from linked_list_sol import *
from linked_list_test import to_ll

ll = to_ll([4,3,5,2,6,7,6,3,2,4,5,3,2])

print(ll)

LinkedList: 4,3,5,2,6,7,6,3,2,4,5,3,2

ll.couple_sort()

print(ll)

LinkedList: 3,4,2,5,6,7,3,6,2,4,3,5,2

Notice it sorted each couple at even positions. This particular linked list has odd size (13 items), so last item 2 was not considered.

B3 schedule_rec

Suppose the nodes of a binary tree represent tasks (nodes data is the task label). Each task may have up to two subtasks, represented by its children. To be declared as completed, each task requires first the completion of all of its subtasks.

We want to create a schedule of tasks, so that to declare completed the task at the root of the tree, before all tasks below it must be completed, specifically first the tasks on the left side, and then the tasks on the right side. If you apply this reasoning recursively, you can obtain a schedule of tasks to be executed.

Open bin_tree.py and implement this method:

def schedule_rec(self):
    """ RETURN a list of task labels in the order they will be completed.

        - Implement it with recursive calls.
        - MUST run in O(n) where n is the size of the tree

        NOTE: with big trees a recursive solution would surely
              exceed the call stack, but here we don't mind
    """

Testing: python3 -m unittest bin_tree_test.ScheduleRecTest

Example:

For this tree, it should return the schedule ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']

Here we show code execution with the same tree:

from bin_tree_sol import *
from bin_tree_test import bt

tasks = bt('i',
                bt('d',
                        bt('b',
                                bt('a')),
                        bt('c')),
                bt('h',
                        bt('f',
                                None,
                                bt('e')),
                        bt('g')))

print(tasks)

i
├d
│├b
││├a
││└
│└c
└h
 ├f
 │├
 │└e
 └g

tasks.schedule_rec()

['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']