Algorithms

Communication 1

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Communication 2

Exam sessions dates (informal):

• 23 January 2018

• 26 February 2018

• 10 May 2018

• 22 June 2018

• 25 September 2018

• 23 October 2018

Any question about the previous lecture?

Historic hero: Ada Lovelace

English mathematicians

English translator of the first article about Babbage's Analytical Engine, written by Luigi Federico Menabrea in French

She enriched the English translation of the article with several annotations

Original article: ~8000 words

Notes by Ada: additional ~19000 words

Ada's heritage

First mechanical computer programmer: in the article notes, there is a description of how to use the Analytical Engine to calculate the Bernoulli numbers

The operating mechanism can even be thrown into action independently of any object to operate upon (although of course no result could then be developed). Again, it might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine. Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

Science of Operations = Computer Science

Common features

What do recipes and instructions for assembling objects have in common?

Shared abstract notion: step-by-step procedure for producing something starting from some initial material we have = algorithm

Algorithm

The word algorithm is a combination of the Latin word algorismus (that is the Latinization of the name Al-Khwarizmi, who was a great mathematician from Persia in the 8th century) and the Greek word arithmos, meaning number

Each algorithm is written in a specific language which is functional to communicate its instruction to a computer

Computer programmer: anyone that creates algorithms that can be interpreted by any computer

Pseudocode

A pseudocode in an informal language that could be interpreted easily by any computer

It is used by Computer Scientists for sketching an algorithm before to implement it in a particular programming language

Checking if an algorithm can be interpretable by a computer: provide a colleague with the pseudocode of the algorithm and ask her to execute it using a particular input, writing down all the passages of the execution on a piece of paper

ThyMopani

It is a pseudocode enough expressive for allowing one to describe any kind of algorithm that can be implemented in any programming language

Our first algorithm: taking in input three different strings, i.e. two words and a bibliographic entry of a published paper, return 2 if both the words are contained in the bibliographic entry, 1 if at least one of the words is contained in the bibliographic entry, and 0 otherwise

E.g.: input "Berners-Lee", "web" and "Tim Berners-Lee: Designing the web for an open society. WWW 2011: 3-4"; output 2.

Defining an algorithm

def <algorithm_name>(<parameter_1>, <parameter_2>, ...)

<algorithm_name> and <parameter_i> cannot contain spaces and cannot start with a number

def contains_word(first_word, second_word, bibliographic_entry):
    ...
    ...
    ...

A first step

Partial algorithm: if the first input word is contained in the bibliographic entry, then the number 1 is returned, otherwise 0 is returned

We need:

• a mechanism to return a particular value if a specific condition is true

• a way for checking if the input word is contained in the bibliographic reference

• a command for returning the result

Conditional block

It allows one to execute a particular instruction if a condition is true (the if statement), while an alternative set of instructions is executed instead if the condition specified is false (the else statement)

if <condition>:
    ...
    ...
else:
    ...
    ...

Specify the condition

The command in ise used to check if a certain string is contained in another one

<string1> in <string2> would be true if the value <string1> is contained in <string2>

A string is a particular type of value that records a sequence of characters, and it is usually defined by using the quotes – e.g. "Berners-Lee"

Return statement

return <value_to_return>

The execution of a return statement finishes the whole execution of an algorithm, and all the instructions that follow that statement are not processed anymore

E.g.: return 1

A number is defined by writing it down as it is – e.g. 42 and -42 for positive/negative integers, 1.625 and -1.625 for positive/negative decimals

"42" is different from 42

Partial algorithm

def contains_word(first_word, second_word, bibliographic_entry):
    if first_word in bibliographic_entry: 
        return 1
    else:
        return 0

Boolean values

The description of the algorithm says to return 2 if both the input words are contained in the bibliographic entry

A boolean can be assigned to one out of two distinct and disjoint values, True and False

E.g.: first_word in bibliographic_entry returns a boolean value

Logical operations

<operator> <B1>, where <operator> can be only not

<B1> <operator> <B2>, where <operator> can be either or or and

Comparisons

Strings: <S1> <operator> <S2>

Numbers: <N1> <operator> <N2>

Complete algorithm

def contains_word(first_word, second_word, bibliographic_entry):
    if first_word in bibligraphic_entry and 
       second_word in bibliographic_entry:
        return 2
    else:
        if first_word in bibliographic_entry or 
           second_word in bibliographic_entry:
            return 1
        else:
            return 0

Avoiding repetitions

first_word in bibliographic_entry and second_word in bibliographic_entry used and evaluated twice

It can be avoided defining new variables: <variable_name> = <variable_value>

For instance:

• contains_first_word = first_word in bibliographic_entry

• contains_second_word = second_word in bibliographic_entry

Collapsing else-if blocks

It is possible to collapse occurrences of else statements when these contain an if statement as their first instruction.

In this case, the else-if pair can be safely replaced by an elif statement

if <condition1>:
    ...
else:
    if <condition2>:
        ...
    else:
        ...

if <condition1>:
    ...
elif <condition2>:
    ...
else:
    ...

Final algorithm

def contains_word(first_word, second_word, bibliographic_entry):
    contains_first_word = first_word in bibliographic_entry 
    contains_second_word = second_word in bibliographic_entry 
    
    if contains_first_word and contains_second_word: 
        return 2
    elif contains_first_word or contains_second_word: 
        return 1
    else: 
        return 0