CS 10: Problem solving via Object Oriented Programming Winter 2017

Transcription

1 CS : Problem solving via Object Oriented Programming Winter 27 Tim Pierson 26 (255) Sudikoff Day 9 PaHern Matching

2 Agenda. Regular expressions 2. Finite automata 3. ValidaSng input 4. Modeling a complex system 2

3 SomeSmes it is useful to be able to detect or require paherns addresses follow a pahern: mailbox@domain.tld example: tjp@cs.dartmouth.edu We can specify a pahern or rules for addresses: <characters>.<com edu org > One or more characters Followed One or more characters Followed by. Followed by one of a set predefined of values 3

4 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a 4

5 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a ConcatenaSon: One acer the other cat matches c then a then t R R 2 5

6 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a ConcatenaSon: One acer the other cat matches c then a then t R R 2 AlternaSve: R R 2 One or the other a e i o u matches any vowel 6

7 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a ConcatenaSon: One acer the other cat matches c then a then t R R 2 AlternaSve: R R 2 One or the other a e i o u matches any vowel Grouping: (R) Establishes order; allows reference/extracson c(a o)t matches cat or cot 7

8 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a ConcatenaSon: One acer the other cat matches c then a then t R R 2 AlternaSve: R R 2 One or the other a e i o u matches any vowel Grouping: (R) Character classes [c - c 2 ] and [^c - c 2 ] Establishes order; allows reference/extracson AlternaSve characters and excluded characters c(a o)t matches cat or cot [a- c] matches a or b or c, while [^a- c] matches any but abc 8

9 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a ConcatenaSon: One acer the other cat matches c then a then t R R 2 AlternaSve: R R 2 One or the other a e i o u matches any vowel Grouping: (R) Character classes [c - c 2 ] and [^c - c 2 ] Establishes order; allows reference/extracson AlternaSve characters and excluded characters c(a o)t matches cat or cot [a- c] matches a or b or c, while [^a- c] matches any but abc RepeSSon: R* Matches or more Smes ca*t matches ct, cat, caat 9

10 Regular expressions (RegEx) are a common way of looking for paherns in Strings Regular expressions (regex) Most programming languages have support for regex Can be really complex and messy, but there are basic paherns Opera2on Meaning Example Character Match a character next a matches a ConcatenaSon: One acer the other cat matches c then a then t R R 2 AlternaSve: R R 2 One or the other a e i o u matches any vowel Grouping: (R) Character classes [c - c 2 ] and [^c - c 2 ] Establishes order; allows reference/extracson AlternaSve characters and excluded characters c(a o)t matches cat or cot [a- c] matches a or b or c, while [^a- c] matches any but abc RepeSSon: R* Matches or more Smes ca*t matches ct, cat, caat Non- zero repesson: R+ Matches or more Smes ca+t matches cat or caat or caaat, but not ct

11 We can use RegEx to see if an address is valid addresses follow a pahern: mailbox@domain.tld example: tjp@cs.dartmouth.edu We can specify a pahern or rules for addresses: <characters>.<com edu org > As a simple RegEx: [a- z]+@[a- z.]* [a- z]+. (com edu org ) Check: tjp@cs.dartmouth.edu - - valid Blob.x - - invalid

12 A Graph can implement a RegEx addresses follow a pahern: mailbox@domain.tld example: tjp@cs.dartmouth.edu com a- a- z. edu We can specify a pahern or rules for addresses: <characters>.<com edu org > A Graph can represent the pahern for addresses Sample addresses can be easily verified if in correct form 2 org...

13 Key points. We can define a set of rules that must be followed 2. We can represent those rules with a graph 3

14 Agenda. Regular expressions 2. Finite automata 3. ValidaSng input 4. Modeling a complex system 4

15 Finite Automata (FA) can be used for many problems, two uses are common Common Finite Automata use cases. ValidaSng input 2. Tracking the state of a system, changing state as a response to events 5

16 We can model States as versces and TransiSons as edges in a directed graph Finite Automata valida2ng input A States as versces TransiSon from A to B if input, else C Edges as transisons C B,, Stay in C regardless if given or Edges can loop back to same vertex Set of labels called alphabet Double circle indicates valid end states What does this do? Accepts any input starsng with 6

17 Agenda. Regular expressions 2. Finite automata 3. ValidaSng input 4. Modeling a complex system 7

18 Assume leaves represent valid end states Can loop back to root from leaf Invalid if input ends and not at end state Extension of Huffman, go back to root acer finding leaf Finite Automata can validate input Finite Automata valida2ng input Input a Result c a b

19 Assume leaves represent valid end states Can loop back to root from leaf Invalid if input ends and not at end state Extension of Huffman, go back to root acer finding leaf Finite Automata can validate input Finite Automata valida2ng input Input Result a b c a b

20 Assume leaves represent valid end states Can loop back to root from leaf Invalid if input ends and not at end state Extension of Huffman, go back to root acer finding leaf Finite Automata can validate input Finite Automata valida2ng input c Input Result a b c a b

21 Assume leaves represent valid end states Can loop back to root from leaf Invalid if input ends and not at end state Extension of Huffman, go back to root acer finding leaf Finite Automata can validate input Finite Automata valida2ng input c Input Result a b c invalid a b

22 Assume leaves represent valid end states Can loop back to root from leaf Invalid if input ends and not at end state Extension of Huffman, go back to root acer finding leaf Finite Automata can validate input Finite Automata valida2ng input c Input Result a b c Invalid acca a b

23 Finite Automata come in two flavors, DeterminisSc and NondeterminisSc A Determinis2c Finite Automaton (DFA) B C,, Nondeterminis2c Finite Automaton (NFA) A B May have,, or more choices for transison from each state, Exactly one choice for each possible input No ambiguity These both do the same thing 23

24 With DFAs we have to specify each State transison, with NFAs we do not NFA valida2ng input c o t Valid inputs: cot or cat a t All else invalid There are,, or more choices for each leher

25 With NFAs we can have, or more choices for each input NFA valida2ng input c o a t coat or cot t c o a t coat or cot c o t

26 SomeSmes we cannot map from a State a single next State NFAs can have mul2ple next States A, B E Key Input Paths A {B,C} A {B} C D 26

27 SomeSmes we cannot map from a State a single next State NFAs can have mul2ple next States A, B E Key Input Paths A {B,C} A {B} B {A} B {E} C D 27

28 SomeSmes we cannot map from a State a single next State NFAs can have mul2ple next States A C, B D E Key Input Paths A {B,C} A {B} B {A} B {E} C {} C {D} 28

29 SomeSmes we cannot map from a State a single next State NFAs can have mul2ple next States A C,, B D E Key Input Paths A {B,C} A {B} B {A} B {E} C {} C {D} D {B,D} D {} 29

30 SomeSmes we cannot map from a State a single next State NFAs can have mul2ple next States A C,, B D E Key Input Paths A {B,C} A {B} B {A} B {E} C {} C {D} D {B,D} D {} E {} E {} 3

31 In that case, must keep track of all possible States NFAs can have mul2ple next States Input Possible States A, B E {A}, C D 3

32 In that case, must keep track of all possible States NFAs can have mul2ple next States Input Possible States A, B E {A} {B,C}, C D 32

33 In that case, must keep track of all possible States NFAs can have mul2ple next States Input Possible States A, B E {A} {B,C}, {E,D} C D 33

34 In that case, must keep track of all possible States NFAs can have mul2ple next States Input Possible States A, B E {A} {B,C}, {E,D} {B,D} C D 34

35 In that case, must keep track of all possible States NFAs can have mul2ple next States Input Possible States A, B E {A} {B,C}, {E,D} {B,D} C D 35

36 In that case, must keep track of all possible States NFAs can have mul2ple next States Input Possible States A, B E {A} {B,C}, {E,D} {B,D} C D 36

37 What does this NFA do?, A B C, E, D 37

38 Agenda. Regular expressions 2. Finite automata 3. ValidaSng input 4. Modeling a complex system 38

39 Finite Automata are also used to track the State of a system as event occur Sensors detect arrival and departure of cars in spaces Image: Fybr.com 39

40 Finite Automata are also used to track the State of a system as event occur Parking meters detect payments and payment expira2ons Image: Fybr.com 4

41 Combine data for all spaces on a block to show drivers where they can find parking Fisherman s Wharf in San Francisco, CA Green < 75% occupied, yellow = 75-9% occupied, red > 9% occupied Image: sfpark.org 4

42 CombinaSon of occupancy and payments leads to four states for each space Simplified automobile parking Payment status Vacant Not Paid Vacant Not paid Paid Vacant Paid Occupancy Occupied Occupied Not paid Occupied Paid 42

43 Occupancy and payment events can occur and change the state of the space Simplified automobile parking Payment status Vacant Not Paid Vacant Not paid Paid Vacant Paid Occupancy event raised by sensor: Vehicle arrives Vehicle departs Occupancy Occupied Occupied Not paid Occupied Paid Payment events raised by parking meter: Payment made Time expires Events cause the system to transi2on between states 43

44 The parking space could be modeled with a complicated if- then structure Simplified automobile parking Payment status Vacant Not Paid Vacant Not paid Paid Vacant Paid Occupancy Occupied Occupied Not paid Occupied Paid void handleevent(event e) { if (event== Payment ) { if (occupancy== Occupied && payment== Not Paid ) { //add Sme on meter elseif (occupancy= Occupied && payment== Paid ) { //increment Sme on meter 44

45 The parking space could be modeled more simply with a Finite Automata Simplified automobile parking Meter paid Vacant, Not Paid Payment expired Sensor detects vehicle arrival Sensor detects vehicle departure Payment expired Occupied, Not Paid Meter paid Vacant, Paid Sensor detects vehicle departure Sensor detects vehicle arrival Occupied, Paid 45

46 The parking space could be modeled more simply with a Finite Automata Simplified automobile parking Meter paid Vacant, Not Paid Payment expired Sensor detects vehicle arrival Sensor detects vehicle departure Payment expired Occupied, Not Paid Meter paid Sensor probably missed vehicle arrival, go figure out why! Vacant, Paid Sensor detects vehicle departure Sensor detects vehicle arrival Occupied, Paid 46

47 Code review DFA.java Store start as String Store ends as a Set (could be mulsple ends) Constructor Takes set of States (with and Ends labeled) and transisons (A,B, means from A go to B if given ) Track start and end versces Track transisons as Map (state- > Map(character, next state)) match with current = start For each input Ensure transison to next state is valid Move to next state Return final state 47

48 Code review NFA.java Store start as String Store ends as a Set (could be mulsple ends) TransiSons now store list of possible states Constructor Takes set of States (with and Ends labeled) and transisons (A,B, means from A go to B if given ) Track start and end versces TransacSons: Map (state- > Map(character, List(String))) match with currentstates = start (could be mulsple valid current states!) For each input Check possible next states from all valid current states 48