Data Structures and Algorithms in Python

Classes - Object-Oriented Programming
• Allow to implement abstract data type to provide logical
description of
• What a data object looks like (its state)
• What it can do (its methods)
• To build a class for this, one can take advantage of the
abstraction process while providing necessary details to use
the abstraction in a program
1

Class Definition
• class class_name:
def __init__(self, para_name_1, para_name_2, ...)
statement body
def other_method_name(self, other_para_1, ...)
statement body
• Constructor method is always __init__ function
• self is always 1st parameter, used to refer back to the object itself
• E.g., self.var_name can be used to refer to the object’s internally defined
variable var_name (as part of the object’s state) 2

Fraction Class as an Example
• Recall that a fraction such as
3
5
consists of two parts
• Top value, i.e., numerator, can be any integer
• Bottom value, i.e., denominator, can be any positive integer
• Negative fractions have a negative numerator
• Operations/methods for Fraction type allow a Fraction data
object to behave like any other numeric value
• Such as add, subtract, multiply and divide
• Fraction should be displayed in “slash” form (e.g., 3/5)
• All methods should return results in lowest terms (i.e., most
common forms, e.g., 3/5 rather than 6/10)
3

Implementation of Fraction Class
• Class definition and its constructor
class Fraction:
def __init__(self, top, bottom):
self.num = top
self.den = bottom
• Fraction state data, i.e., numerator and denominator are denoted
by internal data objects self.num and self.den, respectively
• __init__ initializes the internal state by assigning values of the top
and bottom parameters to self.num and self.den, respectively
4

Create Instance of Fraction Class
• To create a Fraction instance, we use the name of the class,
which invokes constructor and passes actual values for the
necessary state
• Note that we never directly invoke __init__
• Note that 1st parameter self is never given
actual parameter value upon invocation
• E.g., my_fraction = Fraction(3, 5)
invokes constructor and creates a
Fraction instance
3
5
as show on the right
5

Display Fraction
• print function requires object convert itself into string so as
to be written to output
• To tell Fraction class how to convert itself into string, we
need to override standard method __str__, i.e., to redefine
its behavior:
def __str__(self):
return str(self.num) + “/” + str(self.den)
• Examples on when this function is invoked
print(my_fraction)
my_fraction.__str__()
str(my_fraction)
6

“Add” Operation for Fraction
• Allow two Fraction objects to be added together using “+”
• For this, we need to override __add__ standard method
• So that f1 + f2 will call f1.__add__(f2), the overridden method
• Recall two fractions must have same denominator to be added
• Easiest solution is to multiply two denominators as common
denominator, i.e., for two fractions
𝑎
𝑏
and
𝑐
𝑑
, we add them as
𝑎
𝑏
+
𝑐
𝑑
=
𝑎𝑑
𝑏𝑑
+
𝑏𝑐
𝑏𝑑
=
𝑎𝑑+𝑏𝑐
𝑏𝑑
7

“Add” Operation for Fraction (cont.)
• “Add” operation implementation:
def __add__ (self, other_fractioin):
new_num = self.num * other_fraction.den +
self.den * other_fraction.num
new_den = self.den * other_fraction.den
return Fraction(new_num, new_den)
• Considering print(Fraction(1, 4)+Fraction(1, 2)), what is the result?
• 6/8 will be returned but 3/4 is supposed to be the best answer
8

Make Result in Lowest Term
• For this, we need a helper function to reduce fraction
• We use this function to calculate the greatest common divisor
(GCD) between numerator and denominator
• We can then divide both numerator and denominator by the GCD
to reduce the result to lowest term
• Best-known algorithm to find GCD is Euclid’s algorithm
• The GCD between m and n is n if n divides m evenly, otherwise it is the
GCD between n and m%n
• This algorithm only works for positive integer n, which is our case
(negative fraction is represented by negative numerator)
9

Make Result in Lowest Term (cont.)
• Implementation of Euclid’s algorithm:
def gcd(m, n):
while m % n != 0:
old_m = m
old_n = n
m = old_n
n = old_m % old_n
return n
10

Updated “Add” Operation Implementation
• We update __add__ to use gcd function to reduce result:
def __add__ (self, other_fractioin):
new_num = self.num * other_fraction.den +
self.den * other_fraction.num
new_den = self.den * other_fraction.den
common = gcd(new_num, new_den)
return Fraction(new_num // common, new_den // common)
11

Compare Fractions
• By default, two fractions f1 and f2 are equal (i.e., f1 == f2 is
True) only if f1 and f2 are references to same object, which is
called shallow equality
• What we want is f1 == f2 is True even they are different
objects but with same values (numerator and denominator),
which is called deep equality
12

Equality for Fraction
• Note that our Fraction object now has two
very useful methods as shown in the figures
13

Achieve Deep Equality
• For this, we need to override __eq__ standard method:
def __eq__(self, other):
first_num = self.num * other.den
second_num = other.num * self.den
return first_num == second_num
• Note that there are other operators that can be overridden
• E.g., __le__ (for “<=”), __gt__ (for “>”), __ne__ (for “!=”), __sub__ (for “-”),
__truediv__ (for “/”), etc.
14

Exceptions
• Two types of errors may occur when programming
• Syntax errors
• Mistakes made in the structure of a statement or expression
• Can usually be found by Python interpreter and IDEs
• Runtime errors usually caused by logic errors
• Due to errors in underlying algorithm or in translation/implementation of
that algorithm
• E.g., divide by zero or access item with index out of bound of a list
• Typically called exceptions, and can cause program to terminate
15

Exception Handling
• Provide a way to deal with exceptions that allows programmer to
have some type of intervention
• Use try statement to catch raised exception and use except
statement to handle the caught exception
• E.g., try:
print(math.sqrt(a_number))
except:
print(“Bad value for square root”)
print(“Using absolute value instead”)
print(math.sqrt(abs(a_number)))
16

Exception Handling (cont.)
• Programmers can also create and raise their own exceptions if
they detect a situation in the program execution that warrants it
• E.g., try:
if a_number <0:
raise RuntimeError(“You can’t use a negative number”)
else:
print(math.sqrt(a_number))
except RuntimeError as err_instance:
print(str(err_instance), “nUsing absolute value instead”)
print(math.sqrt(abs(a_number)))
17

List Comprehension
• Allow to easily create a list based on some processing or
selection criteria by using iteration and selection constructs
• a_list = [statement for item in collection if condition]
• If value item takes on from collection makes condition to be True, then the
statement is calculated and the result is added to the a_list being constructed
• It is equivalent to but more concise and efficient than
a_list = []
for item in collection:
if condition:
a_list.append(statement)
18

List Comprehension (cont.)
• E.g., to obtain a list of the squares of the first 10 integers that are odd:
sq_list = [x*x for x in range(1, 11) if x % 2 == 1]
It is equivalent to but more concise and efficient than
sq_list = []
for x in range(1,11):
if x % 2 == 1:
sq_list.append(x*x)
• Another example to build a list from a string
a_list = [ch.upper() for ch in “comprehension” if ch not in “aeiou”]
19

Summary
• Computer science is the study of problem solving and uses
abstraction as a tool for representing both processes and data
• Abstract data types (ADTs) help manage complexity of problem
domain by hiding details of data
• Python is object-oriented, powerful, yet easy-to-use
• Lists, tuples, and strings are built in Python sequential collections
• Dictionaries and sets are nonsequential collections of data
• Classes allow programmers to implement ADTs
• One can override standard methods as well as create new methods
20

Some Useful Links for Python 3
• https://docs.python.org/3/tutorial/, useful Python 3 tutorial to
help quickly get familiar with Python programming
• https://www.tutorialspoint.com/python3/, another good Python
3 tutorial to help quickly get familiar with Python programming
• https://docs.python.org/3/library/index.html, library reference
guide, to find libraries and functions needed for programming
• https://docs.python.org/3/, Python 3 documentation providing
detailed documentation about almost every aspect of Python 3
21

Data Structures and Algorithms in Python

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