IS313 Today: two I's

AI UI

hw9pr1.py

an arbitrarily-good Connect 4 player!

Player class

Hw 10 (project)

I wish there were three i's!

Hw 9 is due Wed., 12/23

Projects' final due dates are

Th. 12/17

IS313 Schedule

Wednesday, Nov. 18 - Classes + Objects, the AI !

Thursday, Nov. 19 - Board class due & proposal

Wednesday, Dec. 2 - Networks and their analysis

Thursday, Dec. 3 - progress report due – with code

Wednesday, Dec. 9 - In-class project presentations

Thursday, Dec. 10 - progress report due – with code

Wednesday, Dec. 16 - no class meeting

Thursday, Dec. 17 - Final project due!

Wednesday, Dec. 23 - Player class due (Hw #9)

Epic winsFor?

Python had no Connect-four datatype…

| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|X| |O|--------------- 0 1 2 3 4 5 6

Looking further ahead?

… but you're about to correct that!

Two-player games have been a key focus of AI as long as computers have been around…

Strategic thinking == intelligence?

In 1945, Alan Turing predicted that computers

would be better chess players than people in

~ 50 years…

and thus would have achieved intelligence.

Alan Turing memorial Manchester, England

500

1200

2000

2800

Computer Chess

early programs ~ 1960’s

Computers cut their teeth playing chess…

Ranking

beginner

amateur

world ranked

world champion

MacHack (1100) ~ 1967 MIT

Deep Thought ~ 1989 Carnegie Mellon

Slate (2070) ~ 1970’s Northwestern

Deep Blue ~ 1996 IBM

Deep Blue rematch ~ 1997 IBM

100’s of moves/sec

10,000’s of moves/sec

1,000,000’s moves/sec

3,500,000 moves/secDeep Fritz: 2002X3D Fritz: 2003 Hydra: 2006

200,000,000 moves/sec

first paper: 1950

What is Hydra's chess rating?

How humans play games…

- experts could reconstruct these perfectly - novice players did far worse…

An experiment (by A. deGroot) was performed in which chess positions were shown to novice and expert players…

How humans play games…

- experts could reconstruct these perfectly - novice players did far worse…

Random chess positions (not legal ones) were then shown to the two groups

- experts and novices did equally well (badly) at reconstructing them!

An experiment (by A. deGroot) was performed in which chess positions were shown to novice and expert players…

Two-player games have been a key focus of AI as long as computers have been around…

Strategic thinking == intelligence?

humanscomputers

good at evaluating the strength of a board for a player

good at looking ahead in the game to

find winning combinations of

moves

… humans and computers have different relative strengths in these games.

hw9 pr1

building an AI chess playeremulating a human by

evaluating a board position

ex. credit

Computer Chess…

Player data

PlayerpForX

What data does a computer AI player need?

Let's see a demo!

stringox

stringtbt

'X' 'LEFT'intply

0

DATA MEMBERS

tiebreakTypechecker, O or X moves to look ahead

surprisingly little!

How about knowledge about its opponent?

Player

Player methods

__init__(self, ox, tbt, ply)

__repr__(self)

scoreBoard(self, b)

scoresFor(self, b)

tiebreakMove(self, scores)

nextMove(self, b)

oppCh(self)

Board

__init__( self, width, height )

allowsMove( self, col )

__repr__( self )

addMove( self, col, ox )

isFull( self )

winsFor( self, ox )

hostGame( self )

delMove( self, col )

scoreBoard(self,b) ‘X’‘O’

Assigns a score to any board, b

100.0 50.0 0.0A simple system:for a win for a lossfor anything else

Score for Score for

Score for Score for

scoreBoard

Assigns a score to any board, b

100.0 50.0 0.0A simple system:for a win for a lossfor anything else

scoreBoard(self, b)

Implementation ideas…

What methods that already exist will come in handy?

This doesn't seem to be looking very

far ahead !

How can there be no 'X' or 'O' input?

What class is this method in?

Looking further ahead…

scoreBoard looks ahead 0 movesThe "Zen" approach --

we are excellent at this!

If you look one move ahead, how many possibilities are there to consider?

0-ply

1-ply

A 1-ply lookahead player will "see" an impending victory.

turn

A score for each

column…?

scores

p42.scoresFor( b42 )

special case

Two moves ahead… ?

A 2-ply lookahead player will also "see" an opponent's

impending victory.

's

What about 3-ply?

2-ply

1-ply score

score

turn

scoresFor

scoreBoard looks ahead 0 movesThe "Zen" approach --

we are excellent at this!

If you look one move ahead, how many possibilities are there to consider?

0-ply

1-ply

scoresFor( self, b ) returns a LIST of scores, one for each column you might choose to move next…

2-ply

b

0-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

1-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

2-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

3-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

"Quiz" 'X'

'O'you - or self - is

playing 'O'

Name(s):

Fill in the N-ply score for a move to each column. The same move is evaluated at each ply! It's just evaluated farther into the future.

Looks 0 moves into the future

Looks 1 move into the future

Looks 2 moves into the future

Looks 3 moves into the future

|O| | | | | | ||X| | | |O| |X||O| | | |X|O|X||X| | | |O|O|X||X| |X| |X|O|O||X| |O|O|O|X|X|--------------- 0 1 2 3 4 5 6

| | | | | | |O|| | | | | | |O|| | | | | | |X||X| |X|O| | |O||X|O|O|X| |X|X||X|O|O|O| |O|X|--------------- 0 1 2 3 4 5 6

It is O’s move. What scores does a 1-ply lookahead for O assign to each

move? col 0 col 1 col 2 col 3 col 4 col 5 col 6

It is X’s move. What scores does a 2-ply lookahead for X assign to each

move?col 0 col 1 col 2 col 3 col 4 col 5 col 6

Which change at 3-ply?

Which change at 2-ply?

Example 1-ply and 2-ply lookahead scores

|O| | | | | | ||X| | | |O| |X||O| | | |X|O|X||X| | | |O|O|X||X| |X| |X|O|O||X| |O|O|O|X|X|--------------- 0 1 2 3 4 5 6

| | | | | | |O|| | | | | | |O|| | | | | | |X||X| |X|O| | |O||X|O|O|X| |X|X||X|O|O|O| |O|X|--------------- 0 1 2 3 4 5 6

It is O’s move. What scores does a 1-ply lookahead for O assign to each

move? col 0 col 1 col 2 col 3 col 4 col 5 col 6

It is X’s move. What scores does a 2-ply lookahead for X assign to each

move?

col 0 col 1 col 2 col 3 col 4 col 5 col 6

be careful!

-1 100 50 100 50 100 50

100 0 0 0 50 0 -1

Which change at 2-ply? 0 0

Which change at 3-ply?100

Answers to example lookahead scores

‘X’‘O’new‘X’

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b

scoresFor each column

(1) For each possible move

(2) Add it to the board

(self) 'X'

'O'

new 'X'

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT its scoresFor each board!

At what ply?

[50,50,50,50,50,100,50]

[ 0, 0, 0, 0, 0, 0, 0 ]

scoresForneeds to return a list of 7 numbers for self

these are all of the opponent's evaluations of its next move…

[ 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0 ]

[50,50,50,50,50,50,50]

[50,50,50,50,50,100,50]

(self) 'X'

'O'

new 'X'

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT its scoresFor each board!

At what ply?

[50,50,50,50,50,100,50]

[ 0, 0, 0, 0, 0, 0, 0 ]

scoresForneeds to return a list of 7 numbers for self

these are all of the opponent's evaluations of its next move…

[ 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0 ]

[50,50,50,50,50,50,50]

[50,50,50,50,50,100,50]

What score does the opponent give

each?

(self) 'X'

'O'

new 'X'

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT its scoresFor each board!

At what ply?

[50,50,50,50,50,100,50]

[ 0, 0, 0, 0, 0, 0, 0 ]

scoresForneeds to return a list of 7 numbers for self

these are all of the opponent's evaluations of its next move…

[ 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0 ]

[50,50,50,50,50,50,50]

[50,50,50,50,50,100,50]

What score does the opponent give

each?

max(S) = 0

max(S) = 100

max(S) = 0max(S) = 0

max(S) = 0max(S) = 50

max(S) = 100

What score does self give each?

100

0100

100 10050

0

def scoresFor(self, b):(1) For each possible move

(2) Add it to the board b

(3) Ask OPPONENT its scoresFor each b at ply-1

(4) self's score is 100-max!

""" MUST return a list of 7 scores!! """

Difficulty == Branching Factor

Branching Factor Estimatesfor different two-player games

Tic-tac-toe 4

Connect Four 7

Checkers 10

Othello 30

Chess 40

Go 300

• On average, there are fewer than 40 possible moves that a chess player can make from any board configuration…

0 Ply

1 Ply

2 Ply

Hydra at home in the United Arab Emirates…

Hydra looks ahead 18 ply !

Games’ Branching Factors

Branching Factor Estimatesfor different two-player games

Tic-tac-toe 4

Connect Four 7

Checkers 10

Othello 30

Chess 40

Go 300

1 Ply

2 Ply

Boundaries for qualitatively different games…

0 Ply

Games’ Branching Factors

Branching Factor Estimatesfor different two-player games

Tic-tac-toe 4

Connect Four 7

Checkers 10

Othello 30

Chess 40

Go 300

“solved” games

computer-dominated

human-dominated

1 Ply

2 Ply

0 Ply

Progress

Write tiebreakMove to return the leftmost best score

inside the list scores

def tiebreakMove(self, scores):

if self.tbt == 'LEFT':

How would 'RANDOM' and 'RIGHT' work differently?

hw11 this week

• Extra: scoreBoard4Tourney and a CS 5 C4 round-robin

http://www.stanford.edu/~ccecka/research/C4.html

Using more scores than 0, 50, and 100 !

• Problem 2: A Connect Four Player…

don't give this board a 50.0 !

• Problem 1: (Lab) Trying out a command-line user interface

User Inferfaces

No undo!

% ls

file1.txt file2.txt

file3.txt !

% rm *!

(long pause…)

Design for software and beyond

0. Conceptual

models

1. Mapping

2. Visibility

3. Feedback

4. Affordances

Don Norman's key principles:

Conceptual Models

Users always bring something "to the table"

these don't work!

Images from The Design of Everyday Things

Mapping

is matching expected (spatial) relationships

Where to plug in the keyboard and mouse?

?

Visibility

is making functionality apparent

Shower?Slide projector…

From: www.baddesigns.com

"I used to have that awful shower controller where you pull down on the nozzle to turn it on. I had to tell every guest how to do it, and when we sold our house, we got a call from the new owners about 5 days later asking how to turn on the shower. They had been taking baths for 5 days! Unbelievable." - BL

Feedback

providing information back to the user

from the UI Hall of Shame

Microsoft Access

Microsoft Outlook

http://homepage.mac.com/bradster/iarchitect/shame.htmBut some of us graphics aren't so lazy!

Affordances

are the functions that form suggests…

Opening the XO? Door handles

built-in user's manual

Where do these go wrong?Mapping

How to open this gas cap?

Visibility Feedback Affordances

This handle unfastens the seat from the

floor.

How to turn on this stove?

Set to 5 minutes?

Win NT Dialog

The designers aren't the users…

Lab time…

Remember: Board and project theme are due tomorrow evening…

Thinking about User Interfaces

Command Line Tablet / Touch

Ambient Information

Display Walls

Thinking about User Interfaces

What other types of human/computer interfaces can you think of?

#1 WI

MP

indowsconsenusointer

GUI

Affordances~ physical and cultural expectations

0. Conceptual models 1. Mapping

Matching user expectations e.g., Directory structures

Visibility and Feedback

Banks of glass doorsSlide projector

Affordances The functions that form suggests! Phone settings

Why is this a better design?

Keypad numbers layout

• A case of external inconsistency

1 2 34 5 6

7 8 9

7 8 9

1 2 3

4 5 6

0 0

(a) phones, remote controls(b) calculators, computer keypads

Affordances: to give a clue• Affordances: The perceived and actual properties of an object that signal of the object can be used (from The Design of Everyday Things)

Physical Affordances

Physical Affordances

What do the Zune wheel and the door handle have in common?

Virtual AffordancesClick Me Click Me

"Quiz"

Name(s):

Note the perceivedaffordances inthis interface.Are there anythat are missing?Misleading?

0-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

1-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

2-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

3-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

Solutions

-1

-1

-1

-1

50 50 50 50 50 50

50 50 100 50 50 50

0

0

100

100

0

0

0 0 50

100

00

b ‘X’‘O’

|O| | | | | | ||X| | | |O| |X||O| | | |X|O|X||X| | | |O|O|X||X| |X| |X|O|O||X| |O|O|O|X|X|--------------- 0 1 2 3 4 5 6

It is O’s move. What scores does a 1-ply lookahead for O assign to each

move? col 0 col 1 col 2 col 3 col 4 col 5 col 6

Which change at 2-ply?

Looking further ahead …

0 ply:

2 ply: 3 ply:

Zen choice of move: here and now

| | | | | | | || | | | | | | ||O| | | | | | ||X| | | | | | ||X|O|O| | |X| ||O|X|X|O|X|O| |--------------- 0 1 2 3 4 5 6

| | | | | | | || | | | | | | || | | | |X| | || | | | |O|O| || |X|X| |X|O| ||O|X|O| |O|X| |--------------- 0 1 2 3 4 5 6

(1) Player will win

(2) Player will avoid losing

(3) Player will set up a win by forcing the opponent to avoid losing

X’s move

X‘s move

1 ply:

| | | | | | | || | | | | | | || | | | | | | || | | | | | | || |O|X| | | | ||O|X|X|X| |O|O|--------------- 0 1 2 3 4 5 6

X’s move

‘X’‘O’new‘X’

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT to score each board

(4) Which score will the opponent choose?

0.0

50.0

0.00.0

50.0

0.0

What, then, should assign for your score? (self's score)

scoresFor each column

50.0

‘X’‘O’new‘X’

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b

Choosing the best move

(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT to score each board - ply?

(4) Reverse the scores

100.0

50.0

50.0

100.0100.0

50.0

100.0

‘X’‘O’new‘X’

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b

Choosing the best move

100.0

50.0

50.0

100.0100.0

50.0

100.0

(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT to score each board - ply?

(4) Reverse the scores

(5) Find one max - that's it!

Connect Four

| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|X| |O|--------------- 0 1 2 3 4 5 6

Suppose our Board class's 2d list of lists is named self.data. What is the

name of this single spot?

For your convenience, the creators of Python’s library have included a Board class that can represent any size of Connect Four board... !

Connect Four: the object b

This is true for sufficiently broad definitions of “the creators of Python’s library” ...

Boardb

def addMove(self, col, player)

intNROWS

intNCOLS

def allowsMove(self, col)

char char char

char char char

char char char

datalist char

char

char

def winsFor(self, player)

data members

methods

What is player ?

Connect Four: the object b

This is true for sufficiently broad definitions of “the creators of Python’s library” ...

Boardb

def addMove(self, col, player)

intNROWS

intNCOLS

def allowsMove(self, col)

char char char

char char char

char char char

datalist char

char

char

def winsFor(self, player)

data members

methods

Which methods will alter b? Which leave it alone?

Connect Four: Board

Starting code for the Board class

class Board: def __init__( self, numRows, numCols ): """ our Board's constructor """ self.NROWS = numRows self.NCOLS = numCols self.data = [] for r in range(self.NROWS): onerow = [' ']*self.NCOLS self.data += [onerow]

def __repr__(self): """ thoughts? """

look familiar?

Connect Four: Boardclass Board: def __init__( self, numRows, numCols ): """ our Board's constructor """ self.NROWS = numRows self.NCOLS = numCols self.data = [] for r in range(self.NR): onerow = [' ']*self.NC self.data += [onerow]

def __repr__(self): """ thoughts? """ s = '\n' for r in range(self.NROWS): s += '|' for c in range(self.NCOLS): s += self.data[r][c] + '|'

return s

look familiar?

a bit more to go !

Problem 2

class Board

__init__

allowsMove

__repr__

addMove

isFull

winsFor

the “constructor”

checks if allowed

places a checker

outputs to screen

checks if space left

checks if a player has won

Hw11 Pr2: Connect Four Board

hostGame play!

What's trickiest here?

Problem 2

class Board

__init__

allowsMove

__repr__

addMove

isFull

winsFor

the “constructor”

checks if allowed

places a checker

outputs to screen

checks if space left

checks if a player has won

Hw11 Pr2: Connect Four Board

hostGame play!

What's trickiest here?

What's wrong here?

| | | | | | | || | | | | | | || | | | | | | || | | |O|O| | ||X|X| |O|X|X|X||X|O|O|O|O|X|X|--------------- 0 1 2 3 4 5 6

def winsForHoriz(self, player): inarow = 0

for r in range(self.NROWS): for c in range(self.NCOLS):

if self.data[r][c] == player: inarow += 1 else: inarow = 0

if inarow == 4: return True

return False

Strategies?

horizontals

verticals

diagonals ??| | | | | | | || | | | | | | || | | | | | | || | | |O|O| | ||X|X| |O|X|X|X||X|O|O|O|O|X|X|--------------- 0 1 2 3 4 5 6

“Quiz”

class Board{ # __init__ and __repr__ methods here… # 3 data members: # self.NR == number of rows # self.NC == number of cols # self.data == the 2d list of lists of chars

def mysteryMethod(self, col, ox): r = 0 while r < self.NR and self.data[r][col] == ' ': r += 1 self.data[r-1][col] = ox

def allowsMove(self, col):

}

Briefly, what is each line of the

mysteryMethod doing? Which method is it?

Write allowsMove to return whether the input col is a valid column to move.

(True or False)

1

2

3

Could it go wrong?

Problem 2

class Board

__init__

allowsMove

__repr__

addMove

isFull

winsFor

the “constructor”

checks if allowed

places a checker

outputs to screen

checks if space left

checks if a player has won

Hw11 Pr2: Connect Four Board

hostGame play!

What's trickiest here?

def scoresFor(self, b):(1) For each possible move

(2) Add it to the board

(3) Ask OPPONENT to score each board at ply-1

(4) self's score is 100-max

Problem 2

class Board

__init__

allowsMove

__repr__

addMove

isFull

winsFor

the “constructor”

checks if allowed

places a checker

outputs to screen

checks if space left

checks if a player has won

Hw11 Pr2: Connect Four Board

hostGame play!

What's trickiest here?

Strategies?

horizontals

verticals

diagonals ??| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|O| |O|--------------- 0 1 2 3 4 5 6

|O| | | | | | ||X| | | |O| |X||O| | | |X|O|X||X| | | |O|O|X||X| |X| |X|O|O||X| |O|O|O|X|X|--------------- 0 1 2 3 4 5 6

It is O’s move. What scores does a 1-ply lookahead for O assign to each

move? col 0 col 1 col 2 col 3 col 4 col 5 col 6

Which change at 2-ply?

Example 1-ply and 2-ply lookahead scores

0-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

1-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

2-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

3-ply scores for O:

col 0 col 1 col 2 col 3 col 4 col 5 col 6

Solutions

-1

-1

-1

-1

50 50 50 50 50 50

50 50 100 50 50 50

0

0

100

100

0

0

0 0 50

100

00

b ‘X’‘O’

Connect Four: the object b

Boardb

intwidthstr str str

str str str

str str str

datalist str

str

str

data

intheight

What is the name of the method that will construct this data?

Connect Four: constructor

class Board: """ a datatype representing a C4 board with an arbitrary number of rows and cols """ def __init__( self, width, height ): """ the constructor for objects of type Board """ self.width = width self.height = height self.data = [] # this will be the board for row in range( 6 ): boardRow = [] for col in range( 7 ): boardRow += [' '] # add a space to this row self.data += [boardRow]

Bad magic?

Connect Four: the object b

Boardb

intwidthstr str str

str str str

str str str

datalist str

str

str

intheight

| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|X| |O|--------------- 0 1 2 3 4 5 6

What is the name of the method that will print this data?

def __repr__(self): """ this method returns a string representation for an object of type Board """ s = '' for row in range( 6 ): s += '|' for col in range( 7 ): s += self.data[row][col] + '|' s += '\n'

return s

Connect Four: __repr__

To remove?

To add?

which row is row 0, row 1, and so on?

Examples

def addMove(self, col, ox):

row = self.height-1 while True: if self.data[row][col] == ' ': self.data[row][col] = ox

row -= 1

def allowsMove(self, col):

Step through this addMove method.

How does it work?

What's wrong?

a C4 board

col #'X' or 'O'

allowsMove should return True if col is a valid move;

False otherwise.

C4 Board class: methods

__init__( self, width, height )

allowsMove( self, col )

__repr__( self )

addMove( self, col, ox )

isFull( self )

winsFor( self, ox )

the “constructor”

checks if allowed

places a checker

outputs a string

checks if any space is left

checks if a player has won

hostGame( self )play!

delMove( self, col )removes a checker

Which is trickiest… ?

Checking wins… ?

Thought

s?

X O

b

corner cases?

A whole new class of programming

CS 5 today

Mon., 11/26Wed., 11/28

Mon., 12/3

Software Engineering

Final projects

TheoComp !

Exam review

Python's Date class

Wed., 12/5Mon., 12/10

Lab and HW #11

Hey! How did you get a

body?

Choose your side…

Exam 2

Exam 2

Problem 1b Problem 2

def zerospan( L, hi, low ):

for i in range(len(L)):

if low <= L[i] <= hi:

L[i] = 0.0

def zerospan( L, hi, low ):

for x in L:

if low <= x <= hi:

x = 0.0

def ROOKnotcastle( B, r, c ):

for row in range(len(B)):

for col in range(len(B[0])):

if row == r or col == c:

B[row][col] = 1

This does not change L!

def zerospan( L, hi, low ):

for x in L:

if low <= x <= hi:

x = 0.0

CAUTION: This does not change L!

Sets values between low and hi to 0.0.

Exam 2Problem 3

00 read r1 # input to r1

01 add r2 r2 r1 # add into r2

02 jnez r1 00 # if r1 != 0: goto 00

03 write r2 # else: write the sum

using the stack -- Aargh!adding in place :-)

Exam 2Problem 5

ruler( 1 )

ruler( 2 )

'1'

'212'

ruler( 3 ) '3231323'

ruler( 4 ) '434243414342434'

s si

def ruler( n ):

s = ''

for i in range(n,0,-1):

s += str(i) + s

return s

Exam 2

Exam 2

A whole new class of programming

CS 5 today

Mon., 11/26Wed., 11/28

Mon., 12/3

Software Engineering

Final projects

TheoComp !

Exam review

Python's Date class

Wed., 12/5Mon., 12/10

Lab and HW #11

Hey! How did you get a

body?

Choose your side…

Exam 2

Exam 2

Exam 2

Two-player games have been a key focus of AI as long as computers have been around…

Strategic thinking == intelligence?

… humans and computers have different relative strengths in these games.

humanscomputers

good at evaluating the strength of a board for a player

good at looking ahead in the game to

find winning combinations of

moves