Exam - Tue 14, Jan 2021

Scientific Programming - Data Science Master @ University of Trento

Part A - Witchcraft

The early sixteenth century saw a dramatic rise in awareness and terror of witchcraft in the troubled lands of early modern Scotland: thousands of people were executed, imprisoned, tortured, banished, and had lands and possessions confiscated. Persecution took place in courts of law: you shall analyze the evidence gathered during those dark days.

Data source: Julian Goodare, Lauren Martin, Joyce Miller and Louise Yeoman, ‘The Survey of Scottish Witchcraft’ http://www.shca.ed.ac.uk/witches/ (archived January 2003, accessed ’11/1/2016’).

In particular, we took WDB_Case.csv as published on data.world, which contains cases brought against suspected witches, along with annotations by researchers, mostly as boolean fields.

The dataset has lots of columns, we show here only the relevant ones Case_date, CaseCommonName, Suspects_text and an excerpt of the many boolean columns:

[1]:
import pandas as pd
case_df = pd.read_csv('WDB_Case.csv', encoding='UTF-8')
[2]:
sel_case_df = case_df[['Case_date', 'CaseCommonName', 'Suspects_text', 'Demonic_p', 'Demonic_s', 'Maleficium_p','Maleficium_s', 'WitchesMeeting']]
sel_case_df[1986:1994]
[2]:
Case_date CaseCommonName Suspects_text Demonic_p Demonic_s Maleficium_p Maleficium_s WitchesMeeting
1986 29/6/1649 3 unnamed witches 3.0 0 0 0 0 0
1987 19/8/1590 Leslie,William NaN 0 0 0 1 0
1988 1679 McGuffock,Margaret NaN 0 0 0 1 0
1989 1679 Rae,Grissell NaN 0 0 0 0 0
1990 1679 Howat,Jonet NaN 0 0 0 0 0
1991 15/10/1673 McNicol,Janet NaN 1 1 0 1 1
1992 4/6/1674 Clerk,Margaret NaN 0 0 0 0 0
1993 29/7/1675 Hendrie,Agnes NaN 0 1 0 0 1

A1 parse_bool_cols

Open Jupyter and start editing this notebook exam-2021-01-14.ipynb

Since boolean columns are so many, as a first step you will build a recognizer for them.

  • Consider a column as boolean if all of its values are either 0 or 1.

  • Parse with CSV DictReader

Show solution
[3]:
def get_bool_cols(filename):
    """RETURN a sorted list of all the names of boolean columns"""
    raise Exception('TODO IMPLEMENT ME !')

bool_cols = get_bool_cols('WDB_Case.csv')
print('Found', len(bool_cols), 'cols.', 'EXCERPT: ',)
print( ' '.join(bool_cols[:17]), '...')

from expected_bool_cols import expected_bool_cols
assert bool_cols == expected_bool_cols
Found 77 cols. EXCERPT:
AdmitLesserCharge AggravatingDisease AnimalDeath AnimalIllness ClaimedBewitched ClaimedNaturalCauses ClaimedPossessed CommunalSex Consulting_p Consulting_s Cursing Dancing DemonicPact Demonic_p Demonic_possess_p Demonic_possess_s Demonic_s ...

A2 fix_date

Implement fix_date, which takes a possibly partial date as a string m/d/yyyy and RETURN a string formatted as dd/mm/yyyy. If data is missing, omits it in the output as well, see examples.

Show solution
[4]:
def fix_date(d):
    raise Exception('TODO IMPLEMENT ME !')

assert fix_date('2/8/1649') == '08/02/1649'
assert fix_date('25/4/1627') == '04/25/1627'
assert fix_date('6/11/1629') == '11/06/1629'
assert fix_date('12/1649') == '12/1649'
assert fix_date('7/1652') == '07/1652'
assert fix_date('1560') == '1560'
assert fix_date('') == ''

A3 parse_db

Given a CSV of cases, outputs a list of dictionaries, each representing a case with these fields:

  • name: the isolated name of the witch taken from CaseCommonName column if parseable, otherwise the full cell content

  • surname: the isolated surname of the witch taken from CaseCommonName column if parseable, otherwise empty string

  • case_date: Case_date column corrected with fix_date

  • suspects: number of suspects as integer, to be taken from the column Suspects_text. If column is empty, use 1

primary, secondary and tags fields are to be filled with names of boolean columns for which the corresponding cell is marked with '1' according to these criteria:

  • primary: if a column ending with _p is marked '1', this field contains that column name without the '_p'. If column name is 'NotEnoughInfo_p' or in other cases, use None.

  • secondary: sorted column names ending with _s. If col name is 'NotEnoughInfo_s' or it’s already present as primary, it’s discarded. Remove trailing _s from values in the list.

  • tags: sorted column names which are not primary nor secondary

Parse with CSV DictReader

Show solution
[5]:
import csv

def parse_db(filename):
    raise Exception('TODO IMPLEMENT ME !')

cases_db = parse_db('WDB_Case.csv')

Example (full output is in expected_cases_db.py):

[7]:
cases_db[1992:1994]
[7]:
[{'primary': None,
  'secondary': [],
  'tags': [],
  'name': 'Margaret',
  'surname': 'Clerk',
  'suspects': 1,
  'case_date': '06/04/1674'},
 {'primary': None,
  'secondary': ['Demonic'],
  'tags': ['Dancing', 'DevilPresent', 'Singing', 'WitchesMeeting'],
  'name': 'Agnes',
  'surname': 'Hendrie',
  'suspects': 1,
  'case_date': '07/29/1675'}]
[8]:
assert cases_db[0]['primary'] == None
assert cases_db[0]['secondary'] == []
assert cases_db[0]['name'] == '3 unnamed witches'
assert cases_db[0]['surname'] == ''
assert cases_db[0]['suspects'] == 3  # int !
assert cases_db[0]['case_date'] == '08/02/1649'

assert cases_db[1]['primary'] == None
assert cases_db[1]['secondary'] ==  ['ImplicatedByAnother']
assert cases_db[1]['tags'] ==  []
assert cases_db[1]['name'] ==  'Cristine'
assert cases_db[1]['surname'] ==  'Kerington'
assert cases_db[1]['suspects'] ==  1    # Suspects_text is '', we put 1
assert cases_db[1]['case_date'] == '05/08/1591'

assert cases_db[1991]['primary'] == 'Demonic'
#NOTE: since 'Demonic' is already 'primary', we removed it from 'secondary'
assert cases_db[1991]['secondary'] == ['ImplicatedByAnother', 'Maleficium', 'UNorthodoxRelPract']
assert cases_db[1991]['tags'] == ['DevilPresent', 'UnorthodoxReligiousPractice', 'WitchesMeeting']
assert cases_db[1991]['name'] == 'Janet'
assert cases_db[1991]['surname'] == 'McNicol'
assert cases_db[1991]['suspects'] == 1    #  Suspects_text is '', we put 1
assert cases_db[1991]['case_date'] == '10/15/1673'

assert cases_db[0]['case_date'] == '08/02/1649'  # 2/8/1649
assert cases_db[1143]['case_date'] == '1560'     # 1560
assert cases_db[924]['case_date'] ==  '07/1652'  # 7/1652
assert cases_db[491]['suspects'] == 15           # 15

from expected_cases_db import expected_cases_db
assert cases_db == expected_cases_db

A4 plot_cases

Given the previously computed db, plot the number of cases per year.

  • plot the ticks with 10 years intervals, according to the actual data (DO NOT use constants like 1560 !!)

  • careful some cases have no year

Show solution
[9]:

def plot_cases(db):
    raise Exception('TODO IMPLEMENT ME !')

#plot_cases(cases_db)
[10]:
plot_cases(cases_db)
../../../_images/exams_2021-01-14_solutions_exam-2021-01-14-sol_28_0.png

Part B

B1.1 Theory - Complexity

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

  1. 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)
        if n <= 1:
            return 1
        else:
            L1 = L[0:n//2]
            L2 = L[n//2:]
            a = my_fun(L1) + min(L1)
            b = my_fun(L2) + min(L2)
            return max(a, b)

B1.2 Theory - Graph

Briefly describe what a BFS visit of a graph is. Please provide the order of visited nodes of a possible BFS visit on the following graph (starting from node ‘a’):

bfs

B2 Bank

A bank stores all its transactions in a log: possible types of transactions are opening an account, transfering some amount of money, withdrawal, etc. For simplicity, we represent each transaction type with a character, and in the log which is a Python list we put only such characters (we don’t care about their meaning).

The bank knows some sequences of events are extremely rare, and probably denote suspicious activity. For simplicitly, we assume such sequences only contain two transactions and represent them in tuples called biseqs.

NOTE: a biseq can occur multiple times, but you can consider the number of repetitions negligible with respect to log size.

THESE EXERCISES ARE ABOUT CUSTOM INDEXING, NOT STRINGS: DO NOT convert everything to a string, use regexes, nor use string methods like .index(), .replace(), etc

B2.1 constructor, log and pos

Implement following methods, adding some appropriate indexing data structure.

class Bank:

    def __init__(self):
        """ Initializes an empty bank

            Add a data structure of your choice for indexing the log
        """
        self._trans = []
        raise Exception("TODO IMPLEMENT ME!")

    def log(self, transaction):
        """ Appends transaction to the log

            - REMEMBER to also update the index
            - MUST EXECUTE IN O(1)
        """
def pos(self, biseq):
    """ RETURN a NEW list with all the indeces where the sequence of
        two transactions can be found

        - MUST execute in O(1)
    """

Testing: python3 -m unittest bank_test.LogTest

Example:

[11]:
from bank_sol import *

bank = Bank()
print(bank)
Bank:
[12]:
bank.log('a')
[13]:
print(bank)
Bank: a
[14]:
print(bank.pos( ('a','b') ))  # <-- a biseq is a tuple
[]
[15]:
bank.log('b')
[16]:
print(bank.pos( ('a','b') ))
[0]
[17]:
bank.log('a')
bank.log('a')
bank.log('a')
bank.log('a')
bank.log('b')
print(bank)
Bank: a,b,a,a,a,a,b
[18]:
print(bank.pos(('a','b')))
[0, 5]
[19]:
print(bank.pos(('a','a')))
[2, 3, 4]

B2.2 revert

def revert(self):
    """ Completely eliminates last transaction and RETURN it

        - if bank is empty, raises IndexError

        - REMEMBER to update any index referring to it
        - *MUST* EXECUTE IN O(1)
    """

Testing: python3 -m unittest RevertTest

Example:

[20]:
bank = Bank()
bank.log('a')
bank.log('b')
bank.log('c')
bank.log('a')
bank.log('b')
print(bank.pos(('a','b')))
[0, 3]
[21]:
bank.revert()
[21]:
'b'
[22]:
print(bank)
Bank: a,b,c,a
[23]:
print(bank.pos(('a','b')))
[0]

B2.3 max_interval

Typically, there is a biseq which triggers a period of suspicious activity, and there is another biseq which ends it. So given a start and an end biseq, the bank wants a report of all the transactions that happened in between:

def max_interval(self, bi_start, bi_end):
    """ RETURN a list with all the transactions occurred between
        the *largest* interval among bi-sequences bi_start and bi_end

        - bi_start and bi_end are EXCLUDED
        - if bi_start / bi_end are not found, or if bi_end is before/includes bi_start,
          raise LookupError

        - DO *NOT* MODIFY the data structure
        - MUST EXECUTE IN O(k) where k is the length of the *largest* interval
          you can return
        - consider number of repetitions a negligible size
    """

Testing: python -m unittest bank_test.MaxIntervalTest

Example:

[24]:
bank = Bank()
bank.log('c')
bank.log('d')
bank.log('c')
bank.log('a')
bank.log('b') # <--- b
bank.log('e') #      e
bank.log('f') #      --- f     |
bank.log('a') #          a     |
bank.log('f') #          f     | k
bank.log('c') #          c     |
bank.log('b') #      --- b     |
bank.log('a') # <--- a
bank.log('f') #      f
bank.log('b')
bank.log('e')
bank.log('l')
bank.max_interval( ('b','e'), ('a','f') )
[24]:
['f', 'a', 'f', 'c', 'b']
[ ]: