PFP Homework 1

Automatons

Usually, a finite automaton defined as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (Q, \Sigma, \delta, q_0, F)} where Q represents a states, next is input alphabet, then transitions (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q \times \Sigma \rightarrow Q} ), Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_0} is starting state and finaly there is a set of final states.

In our case, an finite automaton is represented by types:

type Transition = (Int, Char, Int)
type Automaton = (Int, String, [Transition], Int, [Int])

where:

• first number N defines number of states - states will be coded by integer numbers in interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <0, N)} ;
• second element is a string containing the input symbols - you can safely assume, it contains no duplicities;
• third is a list defining the trasition function - elementary transition is a triple (q1, a, q2) representing a transition: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_1 \times a \rightarrow q_2} ;
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_0} is a number from interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <0, N)} ;
• finally, there is a list of number representing posible states that are final in defined automaton.

As examples we can use following automatons:

ex1 :: Automaton 
ex1 = (3, [0], [2], "ab", [(0,'a',1), (0,'b',0), (1,'a',1), (1,'b',2), (2,'a',1), (2,'b',0)])

ex2 :: Automaton 
ex2 = (3, [0], [2], "ab", [(0,'a',1), (0,'a',0), (0,'b',0), (1,'b',2)])

• Create a function, that sorts an array using quicksort algorithm quicksort. Inside, you must use the mutable array STArray.

quickSort :: Array Int Int -> Array Int Int

ghci> elems $ quickSort $  listArray (0,5) [8,4,9,6,7,1] 
[1,4,6,7,8,9]