CS 5

• HW 12 (2 problems)

M/T sections

W/Th sections

due Sunday, 11/21 at midnight

due Monday, 11/22 at midnight

Recitation for HW12 -- Friday 8:00am

• Looking back / Looking ahead

Reading: weeks 12/13: Recursion

Week 12 (this week):

Week 14:

Week 15:

Recursion

Software engineering + algorithms

Is there science in CS ?

NO CS 5 next week…

Final 2 Labs: up to you

ACM results…

C SKILLS 5?C SCIENCE 5!

public static double factorial(int N){ if (N < 2) { return 1.0; } else { return N * factorial(N-1); }}

Recursion: factorial example

Base Case

Recursive Step

Natural scenes

seascapes

mountain terrain

the 2d algorithm...

N Plydouble[] s = new double[7];

for (int c=0 ; c<7 ; ++c){ if (b.allowsMove(c)) { b.addMove(c,me()); if (b.isOver()) s[c] = evaluate(b); else { Player foe = new Player(you(),N-1,2); double[] s2 = foe.findScores(b); s[c] = 100 - getMax(s2); } b.removeMove(c); } else s[c] = -1.0;}

return s;

public double[] plyN(Board b, int N){

}self-reference?

Problem 2 / Final Project

A “film database” application: 5 classesclass name

data member

data member type

??

Hw 12 Problem 2 -- Two tasks

• Implement the main menu (in the CS5App class)

Please choose an action from the following list:

0 Display All Directors 1 Display All Films 2 Display Films by Title 3 Display Films by Director 4 Display Films by Year 5 Display Films by Rating (G, PG, …) 6 Display Films by Review (0 to 10) 7 Add a New Film

8 Save film database to file 9 Load film database from file

42 Quit

• Create skeleton versions of the necessary classes...

Problem 2 - skeleton code + comments

MethodsClasses Data Members

public static void main(String[] args) public static void printMenu() public static void saveDB(String file)public static void readDB(String file)public static void readFilm()

CS5App

public Film(String title, int year, String rating, double review, Director dir)

public String getTitle() public int getYear() public String getRating() public double getReview() public void display()public void save()

Film String titleint yearString ratingdouble reviewDirector dir

all private !

static FilmDB Fstatic DirectorDB D

// comment herepublic String getRating(){ return }

MethodsClasses Data Members

Director

public FilmDB(int capacity) public boolean isFull() public int getCount() public void addFilm(Film f) public boolean checkForFilm(String fulltitle)public void saveAllFilms()public void displayAllFilms() public void displayFilmsByTitle(String titlepiece) public void displayFilmsByYear(int year) public void displayFilmsByRating(String rating) public void displayFilmsByReview(double minreview)

FilmDB int countFilm[] Films

DirectorDB

String fnameString lnameFilmDB filmDB

similar to FilmDB below – see the assignment description…

public Director(String fn, String ln, int capacity) public String getFullName() public String getFirstName()public String getLastName()public FilmDB getFilmDB()

all private !

// comment here!public FilmDB getFilmDB(){ return }

static static stuff belongs to a class, not an object

H.pl(“I’m a static method”);

getMax(double[] s);

printMenu();

Math.sqrt(Math.PI + Math.E);If static stuff is in another class, use that class’s name!

in the CS5App class

in the Player class

in the CS5App class

static double PI, E;

static FilmDB F;

in the Player class

in the Math class

in the Film class

char checker;

String title;

USING STATIC METHODS

STATIC DATA

NONSTATIC DATA

seen globally in all of the class’s methods…

data that is different for every object of the class

type

Self-referential data ?

A film database application:

class Director

class FilmString titleint year

String ratingdouble review

Director dirDirector

dir

String fname

String lname

FilmDB filmDB FilmDBfilmDB

class FilmDBint count

Film[] filmsFilm[]films

films[0] films[1]

class Director{ private String fname; private String lname; private FilmDB filmDB;

// method skeletons…

class Film{ private String title; private int year; … private Director dir;

// method skeletons

class FilmDB{ private int count; private Film[] films;

// method skeletons

Recursion

is defining something in terms of itself

5! = 5 * 4 * 3 * 2 * 1

N! = N * (N-1) * (N-2) * … * 3 * 2 * 1

factorial

Recursion -- warning !

public static double factorial(int N){ return N * factorial(N-1);}

No base case -- the calls to factorial will never stop!

Make sure you have a base case, then worry about the recursive step...

public static double factorial(int N){ if (N < 2) { return 1.0; } else { return N * factorial(N-1); }}

Recursion: factorial example

Base Case

Recursive Step

shorter?

public static double factorial(int N){ if (N < 2) return 1.0; else return N * factorial(N-1);}

Recursion: factorial example

Slightly shorter version without curly braces...

Even shorter versions soon!

Base Case

Recursive Step

Recursion -- how it works

factorial(5)

5 * factorial(4)

4 * factorial(3)

3 * factorial(2)

2 * factorial(1)

1.0

5 * 4 * 3 * 2 * 1.0 is 120.0

Recursion -- why ?

Exploits self-similarity

Produces short, elegant codeLess work !

Skeptical ? use the ? : operator :

double factorial(int N){

}thought

codethe ratio:

Recursion Mantra

Let recursion do the work for you.

I nodded off at the keyboard and when I woke up, my program was done!

I could do that in my sleep!Says stunned CS 5

student:

Delighted CodeWarrior user plans on more Sunday night naps!

Recursion for concise coding

public static double exp(double x, int n){ if (n < 0) return 0.0; return power(x,n)/fac(n) + exp(x,n-1);}

public static void main(String[] args){ double d = exp(2.0,10);}

Recursion with arrays

double[] A = { 4, 7, -10, 4, 1 };

sum(A, 0, 4) returns 6.0sum(A, 3, 4) returns 5.0

Base Case:

Recursive Step:

4 7 -10 4 10 1 2 3 4

array initialization

Recursion with arrays

Recursively summing an array:

double sum(double[] A, int L, int U)

Recursion -- not just numbers

Relationships

Self-similarity elsewhere... Natural phenomena

Names -- acronyms

What is an “ancestor” ?

how much stem?

GNU

A String of recursive methods

RJACKSON

GATTACA

How many A’s are in a particular string?

Base Case:

Recursive Step:

substring

String s = “RECURSION”;

s.substring(3, 5) is the string “UR”

s.substring(0, 3) is the string

is the string “ECURSION”

is the string “CURSE”

0 1 2 3 4 5 6 7 8

Hint Use +

A String of recursive methods

int countAs(String s) returns the number of A’s in the String s

“Quiz”String removeAs(String s){

}

returns a string that is the same as s, except without any A’s

boolean isAlph(String s){

}

returns true if s is in alphabetical order, false otherwise (ties OK)

Names:

Extra: what’s a six-letter English word for which

isAlph returns true?

“Quiz”

double min(double[] A, int L, int U){

write recursive code to return the minimum value in the array A between indices L and U (inclusive).

page 2 AA[0] A[4]A[1] A[2] A[3]

5.1 4.2 7.7 42 1.7

min(A,0,3) should return 4.2

Recursion can do anything!

String removeAs(String s)

boolean isAlph(String s)returns true if s is in alphabetical order, false otherwise (ties OK)

returns a string that is the same as s, except without any A’s

removeAs(“GATTACA”) returns “GTTC”

isAlph(“BART”) returns false

isAlph(“LOOPY”) returns false

isAlph(“BERT”) returns true

Problem 1

Write recursive methods for

double factorial(int N)

double power(double b, int N) raises b to the N power

double harmonic(int N) adds 1/1 + 1/2 + … + 1/N

boolean isPalindrome(String s) true if s is a palindrome; false otherwise

String reverse(String s) returns the reversal of s

void sort(double[] A, int L, int U)sorts A between index L and U (inclusive)

void moveMinToLeft(double[] A, int L, int U)swaps elements so that the smallest element between index L and U is at location L

Problem 1

Create a menu that allows a user to call each method: Welcome to the recursive roster!

Options:

(1) factorial

(2) power

(3) harmonic series

(4) palindrome checker

(5) string reverser

(6) min mover

(7) list sorter

(8) longest common subsequence [Extra]

(9) quit

each of these will be a recursive method in the CS5App class

Lab Today

Extra credit: a biological application

Take advantage of us!

Given two strings, what is a longest common subsequence?

public static String LCS(String s1, String s2)

s1 = “hamburger”

s2 = “cheeseburger”

s1 = “GATTTCAAGTGAC”

s2 = “CTTAGACATAGGT”

LCS(s1,s2) returns “hburger” LCS(s1,s2) returns “TTCAAGG”

Testing N Ply ‘X’‘O’

With a 4-ply lookahead, X will think everything looks equivalent in this case

With a 5-ply lookahead, X will know to move to column 3

0 1 2 3 4 5 6

Recursion Mantra

Let recursion do the work for you.

Natural scenes

seascapes

mountain terrain

the 2d algorithm...

Recursive Data

Can data contain other data of the same type?

class Wart{ int idNumber; Wart neighbor;}

Wartwally

Wart

int

neighbor

idNumber

wally wally.neighborwally.neighbor

.neighborwally.neighbor .nei

ghbor.neighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

wally wally.neighborwally.neighbor

.neighborwally.neighbor .nei

ghbor.neighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

Recursive Data

Can data contain other data of the same type?

class Wart{ int idNumber; Wart neighbor;}

Wartwally

Wart

int

neighbor

idNumber

wally wally.neighborwally.neighbor

.neighborwally.neighbor .nei

ghbor.neighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

intidNumber

Wartneighbor

Ridiculously short code!

Using the ? : operator...

double factorial(int n){ return n<2 ? 1 : n*factorial(n-1);}

double sum(double[] arr, int L, int H){ return L>H ? 0.0 : arr[L]+sum(arr,L+1,H);}

addMove

Class: Board

Object: b

b.addMove(3,‘X’)

‘X’‘O’

changes b by adding checker ‘X’ into row 3

new‘X’

b before

b after

Self-referential data ?

A film database application:

class FilmDB

class Director

class FilmString titleint year

String ratingdouble review

Director dirDirector

dir

String fname

String lname

FilmDB filmDB FilmDBfilmDB

int countFilm[] films

Film[]films

films[0] films[1]

(Non) deterministic recursion

Koch snowflake

Deterministic recursion

Recursion with randomness

Recursion can do anything!

String removeAs(String s)

boolean isAlph(String s)returns true if s is in alphabetical

order, false otherwise

returns a string that is the same as s, except without any A’s

No base case -- the calls to factorial will never stop!

As with mathematical induction, base cases are critical...

When writing recursive codeMake sure you have a base case !

Check that the base case is correct !!

double sum(double[] arr, int L, int H){ return L>H ? 0.0 : arr[L]+sum(arr,L+1,H);}

s = “GATTACA”;

Computer Science 5

• HW 12 (2 problems + E.C.)

M/T sections

W/Th sections

due Sunday, 11/24 at midnight

due Monday, 11/25 at midnight

Recitation for HW12 -- Friday 8:00am

• Looking back / Looking ahead

• Connect Four Results...

Reading: Week 12 re: recursion

Week 12 (this week):

Week 14:

Week 15:

Recursion

Software engineering + algorithms

Is there science in CS ?

• Midterm 2 Results...

Recursion -- not just numbers

Relationships

Self-similarity elsewhere... Natural phenomena

Names -- acronyms

What is an “ancestor” ?

EMACS

EINE

ZWEI

all stem!

Extra credit: N-ply search

Board Evaluation

Depth of Search1-ply search 2-ply search 3-ply search N-ply search

evaluate

(N-1) - ply...

advantage: black

advantage: red

1 - ply 2 - ply

int chooseMove(Board b, char ox, int ply)

chooseMove1Ply chooseMove2Ply chooseMove3Ply

Problem 2 / Final Project

class name

data member

data member type

CS5App (for main)