====== Programming introduction ======
===== 1. Scala introduction =====
**Exercise 1.1.** Write a function ''startStop'' which retrieves the elements of a list from within bounds. Use patterns in your implementation. Define an object ''Main'' as shown below.
Any code within the object can be directly executed. (Hint: use a simply-recursive function)/
object Main extends App {
def startStop[A] (l: List[A] ,start: Int, stop: Int): List[A] = ???
println(startStop(List(1,2,3,4,5,6),1,4))
// = List(2,3,4)
}
**Exercise 1.2.** Write a function which determines the number of occurrences of each character in a string. (Hint: use a tail-recursive function)
def countChars (s:String): Map[Char,Int] = {
def aux(l: List[Char], acc: Map[Char,Int]): Map[Char,Int] = ???
???
}
**Exercise 1.3** Write a function which takes a list of records first name, last name, CNP (encoded as tuples), and returns a list of the last names and ages of all females which are younger than the average of the entire list. E.g. ''List( (“Mary”, “2030694123456”), (“Anne”,“2121092123456”), (“Matei”, “5121202123456”), (“Maggie”, “2121078123456”) )'' yields ''List( (“Mary”,28), (“Anne”,30) )''. Maggie was born in '78, whereas Mary, Anne and Matei were born in '94, '92 and 2002, respectively. (Hint: use combinations of **map** with **filter**)
val example = List(("Mary", "2030694123456"), ("Anne", "2121092123456"), ("Matei", "5121202123456"), ("Maggie", "2121078123456"))
def youngerThanAverage(l: List[(String,String)]): List[(String,Int)] = {
def getAge(s:String):Int = ???
// female gender = True
def getGender(s:String):Boolean = ???
???
}
**Exercise 1.4**
A labelled graph is encoded as a String text where **each line** is an edge '' ''
Example:
0 r 1
0 r 2
0 g 1
1 g 2
1 b 3
1 r 4
4 g 1
3 b 2
2 r 2
2 g 3
* Suppose we encode streets as labelled graphs, where each label 'r', 'g' or 'b' denotes a street color. These colors can be any alphabetical character, not necessarily just rgb.
* Given a **start node** and a **sequence of colors**, find all the destination nodes that can be accessed by traversing streets in that particular color.
* Example: Starting from 0, on the sequence ''rrg'', the destination node are ''1'' (0 red to 1 red to 4 green to 1) and ''3'' (0 red to 2, red to 2, red to 3)
* Hint: use **foldLeft** as well as **for expressions**.
val example = """0 r 1
|0 r 2
|0 g 1
|1 g 2
|1 b 3
|1 r 4
|4 g 1
|3 b 2
|2 r 2
|2 g 3""".stripMargin
type Streets = Map[(Int,Char),Set[Int]]
def readStreets(s: String): Streets = ???
def findDestination(start: Int, colors: String, streets: Streets): Set[Int] = ???
===== 2. Python introduction =====
Python3 is a multi-paradigm language, that combines the **imperative** style with the **functional** style. It also supports Object-Oriented programming, albeit in a limited way.
Python3 offers a few programming constructs that:
* make life real easy for the programmer,
* yield efficient programs,
* sum-up to a programming **style** called **pythonic** (a blend of imperative and functional features).
This lab will introduce some of these constructs.
==== List traversal ====
**Exercise 2.1.** Write a function ''f(l)'' which determines the maximum of a list ''l'' of integers.
Traversing a list using a ''for'' is done as follows:
for elem in collection:
# do something
This idiom can be used for any collection not just lists, as you will discover during the lab.
**Exercise 2.2.** Modify the previous function to ''f(l,start,stop)'' and determine the maximum between positions ''start'' and ''stop''.
When we care about the indices of a list, we can use the function ''range(x,y)'' which returns **a list of integers** starting from ''x'' until ''y-1''.
for i in range(0,len(collection)):
# do something with collection[i]
==== Slicing lists ====
**Exercise 2.3.** Find the **longest** sequence of positive integers from a list. E.g. for the list ''[1,3,-1,2,0,1,5,4,-2,4,5,-3,0,1,2]'' the answer is ''[2,0,1,5,4]''.
Python supports various list slicing operations, as well as "overloaded" indexing:
# the sublist from positions 0 to x of l:
l[0:x]
# the very same list:
l[:x]
# the last element of a list:
l[-1]
# the last three elements of a list:
l[-3:]
# the slice from n-3 to n-1, where n is the number of elements from the list
l[-3:-1]
**Exercise 2.4.** Write a pythonic function to check if a list is palindrome.
===== Other datatypes =====
The most widely used datatypes in Python are lists and dictionaries. Additionally, at LFA, we will also use: **sets**, **stacks**.
==== Stacks ====
In Python, **lists** are also used as stacks:
l = []
l.append(x) # add x at the TOP of the stack (this will be the last element of the list)
l[-1] # this is the top of the stack
x = l.pop() # removes and returns an element from the top of the stack.
**Exercise 2.5.** Write a function which determines (and returns) the **longest** sequence of consecutive integers from a list.
==== Dictionaries ====
Python dictionaries are actually **hash maps** (or **hash tables**). The keys ''k'' are **dispersed** using a hash-function into buckets. Each bucket will hold its respective values. Some examples of dictionary usage:
#create an empty dictionary:
d = {}
#add or modify a key-value:
d[k]=v
#search if a key k is defined in a dictionary d:
if k in d:
# do something
**Exercise 1.6.** Write a function which determines the number of occurrences of each character in a string.
def count(l):
d = {}
for x in l:
if x in d:
d[x] += 1
else:
d[x] = 1
return d
==== Sets ====
Sets are collections where each element is unique. Sets can be traversed and indexed exactly as lists. They are initialised using the constructor ''set'':
# the empty set:
s = set()
# set constructed from a list:
s = set([1,2,3])
# adding a new element to the set:
s.add(4)
**Exercise 1.7.** Determine the list of characters which occur in a string. E.g. for "limbajeformale" we have: "limbajefor". (Hint 1: in Python there is no difference between a character and a singleton string and strings are just lists; Hint 2: to create a list from another object, use ''list()'').
==== Pairs ====
Pairs are very similar to lists and can be substituted by the latter in many cases:
p = (x, y) # a pair where the first element is x and the second is y
t = (x, y, z) # a tuple
fst = p[0]
snd = p[1]
for k in t:
# do something with element k of the tuple
===== The functional style =====
==== Higher-order functions and lambdas ====
The most used higher-order functions in Python are **map** and **reduce**:
from functools import reduce
# adds 1 to each element of a list
def allplus1(l):
return map(lambda x:x+1,l)
# computes the sum of elements of a list
def sum_l (l):
# inner functions are very useful for defining local, reusable functionality
def plus(x,y):
return x + y
return reduce(plus,l) # reduce is a little different from Haskell folds: it does not use an initial value
def short_sum(l):
return reduce(lambda x,y:x+y,l) # observe the syntax for lambdas
==== List comprehensions ====
List comprehensions are widely used programming tools in Python. Usage examples:
# adding 1 to each element of a list
l1 = [x+1 for x in [1,2,3]]
# [2,3,4]
# packing elements into pairs
l2 = [(x,x+1) for x in [1,2,3]]
# [(1,2), (2,3), (3,4)]
# unpacking pairs in the for notation
l3 = [x+y for (x,y) in [(1,2), (2,3), (3,4)]]
# [3,5,7]
# combined list comprehensions
l4 = [(x,y) for x in [1,2,3] for y in [4,5,6]]
# [(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)]
# filters
l5 = [x for x in [1,2,3,4] if x>2]
# [3,4]
**Exercise 1.8.** Write a function which takes a list of records //first name, last name, CNP// (encoded as tuples), and returns a list of **the last names** and **ages** of all females which are younger than the average of the entire list. E.g. ''[ ("Mary", "Smith", "2030602123456"), ("Anne", "Doe", "2121092123456"), ("Matei", "Dan", "1121202123456"), ("Maggie", "Byrne", "2121078123456")]'' yields ''[("Smith",19), ("Doe",29)]''. Maggie was born in '78, whereas Mary, Anne and Matei were born in '94, '92 and 2002, respectively.
from functools import reduce
def getYouth(l):
# this function computes the age of a given CNP
def age(cnp):
# conversion to integer of the two-character year code
if int(cnp[5:8]) <= 21:
return 2021 - int("20"+cnp[5:7])
else:
return 2021 - int("19"+cnp[5:7])
# computing the average ages (a map could have also been used)
avg = reduce(lambda a,b:a+b, [age(x[-1]) for x in l]) / len(l)
# we return the last name and the age of the filtered list l
return [(ln,age(cnp)) for (fn,ln,cnp) in l if cnp[0]=='2' and age(cnp) <= avg]
/*
==== Classes and inheritance ====
We discuss a few basics on classes and inheritance starting from the following example:
class Tree:
def size(self):
pass
def contains(self, key):
pass
class Void(Tree):
def __init__(self):
pass
def __str__(self):
return "Nil"
def size(self):
return 0
def contains(self,key):
return False
In the previous example, the class ''Tree'' acts as an interface. Python does not natively support interfaces, but class inheritance is supported. The instruction ''pass'' does nothing, and it helps us defer the method implementation.
The definition:
class Void(Tree)
tells us that class ''Void'' inherits ''Tree''. Note that this //contract// is not binding in Python.
The program will be interpreted even if ''Void'' does not correctly implement the methods in ''Tree''.
The function
def __init__(self):
is the class constructor. We cannot explicitly define multiple constructors (but workarounds exist). Also note the mandatory presence of ''self'', which is the Python equivalent of ''this''. Each member class must mark as first argument ''self'', otherwise it is not a proper member of the class, and just a nested function.
The function
def __str__(self):
is the Python equivalent for ''toString()''. An object can be displayed using the function ''str''
**Exercise 9** Create the class ''Node'' which models non-empty trees. Implement methods ''size'' and ''contains''.
==== List of exercises ====
* Write a function which prints EACH repeating character from a string. (Hint: strings are lists of characters).
* Write a function returns the number of repetitions of each character from a text. (Hint: use dictionaries to store the number of repetitions).
* Write a function returns the number of unique characters from a list. Use Python sets.
* Write a function which takes a pattern and a text and prints all indexes where an occurrence of pattern in text are found. Use Python list slicing.
* Write a function which searches for a list of patterns in a text, by extending the stub below. Whenever possible, use ''map'' instead of ''for''.
def find_patterns (pattern_list, text):
# checks if pattern is found at position index in text
def inner_search (pattern,index):
* Extend the class example shown previously to include class ''Node'' which models non-empty trees. Implement methods ''size'' and ''contains''.
*/
===== Practice =====
A labelled graph is encoded as a file where:
* **the first line** consists of the number of nodes
* **each subsequent line** is an edge '' ''
Example:
5
0 r 1
0 r 2
0 g 1
1 g 2
1 b 3
1 r 4
4 g 1
3 b 2
2 r 2
2 g 3
* Suppose we encode streets as labelled graphs, where each label 'r', 'g' or 'b' denotes a street color. These colors can be any alphabetical character, not necessarily just rgb.
* Given a **start node** and a **sequence of colors**, find all the destination nodes that can be accessed by traversing streets in that particular color.
* Example: Starting from 0, on the sequence ''rrg'', the destination node are ''1'' (0 red to 1 red to 4 green to 1) and ''3'' (0 red to 2, red to 2, red to 3)
* (Hint1: google //Python read lines// to see how to read from a file; also, google ''split'' in Python)
* (Hint2: you will need a dictionary to store, for each node and label l, the list of its l-successors)
===== Python typing annotations =====
Newer versions of python support type annotations and pre-runtime type checking (supported by some code editors).
The typing module allows programmers to provide hints regarding the types of different objects, the signature (parameters and return value types) of functions and methods, and create generic classes.
To create such hints the syntax is as follows:
* for variables: '': [= expr]'':
x: int
y: int = 5
z: str = 'hello world'
t: MyCustomType
* for functions/methods: ''def ([, ...]) -> '':
def hello() -> str:
...
def get_item_at(index: int) -> Any:
...
class MyCustomType():
def method(self, param1: Any, param2: int) -> str
...
* for generic classes: extend either a generic class (such as list[_], set[_] or tuple[_]) or extend the Generic class (introduced by the typing module):
from typing import TypeVar, Generic
StateType = TypeVar("StateType") # !!! important: type variables must be declared and initialised before they are used
class DFA(Generic[StateType]):
def next_state(self, from_state: StateType, token: str) -> StateType:
...
...
dfa: DFA[int] = DFA[int](...)
A = TypeVar("A")
B = TypeVar("B")
class TupleLinkedList(Generic[A,B]):
value: tuple[A,B]
next: 'TupleLinkedList[A,B]' | None # !!! important: in most python versions, if you need to use the
# type of the class within its own definition, you
# need to quote its name (this delays the evaluation
# of the hint until after the class is fully defined)
...
class IntList(list[int]):
...
Useful type hints:
* ''int, str, bool, float etc.'' : the basic datatypes (charaters are hinted as strings, as python does not make the distinction)
* ''list[type], set[type], frozenset[type], dict[key_type, val_type]'': basic data collections (items introduced in ''set''s and ''frozenset''s and the keys of dictionaries need to be hashable: see the [[lfa:dictionaries|appendix for python hashing]])
* ''Any'': a type is compatible with any other type (if no type hint is specified, this is what type checkers usually default to)
* ''Callable[ [...], ]'': this defines a function with a given signature
* '' | '': the ''|'' operator allows us to indicate that a given object can be one of two(or more) types
* ''None'': represents the lack of a value (or an explicit None value); useful to mark functions which have no return value, or that a value may be purposefully missing (in combination with the ''|'' operator), and a None check may be necessary
full documentation of the python typing module: [[https://docs.python.org/3/library/typing.html]]
===== Solutions =====
[[https://github.com/NethDR/LFA-LAB1-solutions|click here for spoilers/solutions]]