Recitation Homework 5
Ionut Trestian
Northwestern University
The Game of Life: History
•Created by John Horton Conway,a British Mathematician
•Inspired by a problem presentedby John Von Neumann:
–Build a hypothetical machine that
can build copies of itself
•First presented in 1970, Scientific American
Problem 1 -- “Life”
Evolutionary rules
Grid World
• Everything depends on a cell’seight neighbors
red cells are alive
white cells are empty
• Exactly 3 neighbors give birthto a new, live cell!
• Exactly 2 or 3 neighbors keep anexisting cell alive
• Any other number of neighbors kill thecentral cell (or keep it dead)
Problem 1 -- Life
Evolutionary rules
Grid World
• Everything depends on a cell’seight neighbors
red cells are alive
white cells are empty
• Exactly 3 neighbors give birthto a new, live cell!
• Exactly 2 or 3 neighbors keep anexisting cell alive
• Any other number of neighbors kill thecentral cell (or keep it dead)
Problem 1 -- Life
Evolutionary rules
Grid World
• Everything depends on a cell’seight neighbors
red cells are alive
white cells are empty
• Exactly 3 neighbors give birthto a new, live cell!
• Exactly 2 or 3 neighbors keep anexisting cell alive
• Any other number of neighbors kill thecentral cell (or keep it dead)
Problem 1 -- Life
Evolutionary rules
Grid World
• Everything depends on a cell’seight neighbors
red cells are alive
white cells are empty
• Exactly 3 neighbors give birthto a new, live cell!
• Exactly 2 or 3 neighbors keep anexisting cell alive
• Any other number of neighbors kill thecentral cell (or keep it dead)
life out there...
Keep going!
Problem 1 -- Creating Life
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
updateNextLife(oldB, newB)
old generation or "board"
new generation or "board"
Problem 1 -- Creating Life
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
old generation or "board"
new generation or "board"
updateNextLife(oldB, newB)
Problem 1 -- Details
For each generation…
• 0 represents an empty cell
• 1 represents a living cell
• outermost edge should alwaysbe left empty (even if there are 3neighbors)
• compute all cells based on theirprevious neighbors
http://www.math.com/students/wonders/life/life.html
old generation or "board"
new generation or "board"
life out there...
updateNextLife(oldB, newB)
Problem 1 – Main Loop
def life( width, height ):
""" will become John Conway's Game of Life... """
B = createBoard(width, height)
csplot.showAndClickInIdle(B)
while True: # run forever
csplot.show(B) # show current B
time.sleep(0.25) # pause a bit
oldB = B
B = createBoard( width, height )
updateNextLife( oldB, B ) # gets a new board
Problem 1 – Main Loop
def life( width, height ):
""" will become John Conway's Game of Life... """
B = createBoard(width, height)
csplot.showAndClickInIdle(B)
while True: # run forever
csplot.show(B) # show current B
time.sleep(0.25) # pause a bit
oldB = B
B = createBoard( width, height )
updateNextLife( oldB, B ) # gets a new board
Why not just have update RETURN a new list?(i.e., why bother with mutation at all?)
Update MUTATES the list B
Problem 2 - Markov Text Generation
The text file:
I like spam. I like toast and spam.
I eat ben and jerry's ice cream too.
Technique for modeling any sequence of natural data
Each item depends on only the item immediately before it .
The Model:
1st-orderMarkovModel
For each word, keep track of the words that can follow it (and how often)
I: like, like, eat
like: spam, toast
spam.: $
$: I, I, I
toast: and
eat: ben
and: spam, jerry's
ben: and
jerry's: ice
ice: cream
cream: too.
too.: $
• We can repeat wordsto indicate frequency
• $ indicates beginningof a sentence
Generative Markov Model
Technique for modeling any sequence of natural data
Each item depends on only the item immediately before it .
A key benefit is that the model can generate feasible data!
I like spam. I like spam. I like toast and jerry's ice cream too.
Generating text:
1) start with the '$' string
2) choose a word following '$', at random. Call it w
3) choose a word following w, at random. And so on…
4) If w ends a sentence, '$' becomes the next word.
HW5 Pr 2: Need to be able to…
Read text from a file
Compute and store the model
Generate the new text
Reading Files
>>> f = file( 'a.txt' )
>>> text = f.read()
>>> text
'This is a file.\nLine 2\nLast line!\n'
>>> f.close()
In Python reading files is no problem…
Files
>>> f = file( 'a.txt' )
>>> text = f.read()
>>> text
'This is a file.\nLine 2\nLast line!\n'
>>> f.close()
In Python reading files is no problem…
opens the file and calls it f
reads the whole file and calls it text
text is a single string containing all the text in the file
closes the file (closingPython does the same)
But how to process the text from here…?
String Manupulation
>>> text
'This is a file.\nLine 2\nLast line!\n'
>>> print text
This is a file.
Line 2
Last line!
>>> text.split()
['This', 'is', 'a', 'file.', 'Line', '2', 'Last', 'line!']
>>> text
'This is a file.\nLine 2\nLast line!\n'
>>> lines = text.split('\n')
>>> lines
['This is a file.', 'Line 2', 'Last line!', '']
Returns a list of the words in the string(splitting at spaces, tabs and newlines)
Returns a list of the lines in the string(splitting at newlines)
HW5 Pr 2: Need to be able to…
Read text from a file
Compute and store the model
Generate the new text
Lists vs. Dictionaries
Lists are not perfect…
L
L[0]
L[1]
reference
5
42
Lists vs. Dictionaries
Lists are not perfect…
You can't choose what to name data.
L[0], L[1], …
L
L[0]
L[1]
reference
5
42
Lists vs. Dictionaries
Lists are not perfect…
L[1988] = 'dragon'
You can't choose what to name data.
You have to start at 0.
L[0], L[1], …
L
L[0]
L[1]
reference
5
42
L[1989] = 'snake'
Lists vs. Dictionaries
Lists are not perfect…
L[1988] = 'dragon'
You can't choose what to name data.
You have to start at 0.
Some operations can be slow for big lists …
L[0], L[1], …
L
L[0]
L[1]
reference
5
42
L[1989] = 'snake'
if 'dragon' in L:
Lists vs. Dictionaries
In Python a dictionary is a set of key - value pairs.
It's a list where the index can be anyimmutable-type key.
>>> d = {}
>>> d[1988] = 'dragon'
>>> d[1989] = 'snake'
>>> d
{1988: 'dragon', 1989: 'snake'}
>>> d[1988]
'dragon'
>>> d[1987]
key error
Lists vs. Dictionaries
In Python a dictionary is a set of key - value pairs.
It's a list where the index can be anyimmutable-type key.
>>> d = {}
>>> d[1988] = 'dragon'
>>> d[1989] = 'snake'
>>> d
{1988: 'dragon', 1989: 'snake'}
>>> d[1988]
'dragon'
>>> d[1987]
key error
creates an empty dictionary, d
1988 is the key
'dragon' is the value
1989 is the key
'snake' is the value
Anyone seenthis before?
Retrieve data as with lists…
or almost !
More on dictionaries
Dictionaries have lots of built-in methods:
>>> d = {1988: 'dragon', 1989: 'snake'}
>>> d.keys()
[ 1989, 1988 ]
>>> d.has_key( 1988 )
True
>>> d.has_key( 1969 )
False
>>> d.pop( 1988 )
'dragon'
delete a key(and its value)
check if a key is present
get all keys
Markov Model
{ 'toast': ['and'],
'and' : ['spam.', "jerry's"],
'like' : ['spam.', 'toast'],
'ben' : ['and'],
'I' : ['like', 'like', 'eat'],
'$' : ['I', 'I', 'I'],
The text file:
I like spam. I like toast and spam.
I eat ben and jerry's ice cream too.
Technique for modeling any sequence of natural data
Each item depends on only the item immediately before it .
The Model:
Extra credit Problem 3
printSquare( 3, '$' )
$ $ $
$ $ $
$ $ $
printRect( 4, 6, '%' )
% % % %
% % % %
% % % %
% % % %
% % % %
% % % %
printTriangle( 3, '@', True )
@
@ @
@ @ @
printTriangle( 3, '@', False )
@ @ @
@ @
@
printBumps( 4, '%', '#' )
%
#
%
% %
# #
#
%
% %
% % %
# # #
# #
#
%
% %
% % %
% % % %
# # # #
# # #
# #
#
printDiamond( 3, '&' )
&
& &
& & &
& &
&
printStripedDiamond( 7, '.', '%' )
.
. %
. % .
. % . %
. % . % .
. % . % . %
. % . % . % .
% . % . % .
. % . % .
% . % .
. % .
% .
.
printCrazyStripedDiamond( 7, '.','%', 2, 1 )
.
. .
. . %
. . % .
. . % . .
. . % . . %
. . % . . % .
. % . . % .
% . . % .
. . % .
. % .
% .
.
Extra credit Problem 3
EC Problem 4 A program that reads
Flesch Index (FI)
FI = 206.835 - 84.6 * numSyls/numWords - 1.015 * numWords/numSents
numSyls is the total number of syllables in the text
numWords is the total number of words in the text
numSents is the total number of sentences in the text
flesch() function
Extra Credit Problem 4
flesch() function
Welcome to the text readability calculator!
Your options include:
(1) Count sentences
(2) Count words
(3) Count syllables in one word
(4) Calculate readability
(9) Quit
What option would you like?
sentences(text)
words(text)
syllables(oneword)
Extra Credit Problem 4
Split
Remove punctuation
We will say that a sentence has occurred any time that one of its raw words ends in aperiod . question mark ? or exclamation point ! Note that this means that a plainperiod, question mark, or exclamation point counts as a sentence.
A vowel is a capital or lowercase a, e, i, o, u, or y.
A syllable occurs in a punctuation-stripped word whenever:
Rule 1: a vowel is at the start of a word
Rule 2: a vowel follows a consonant in a word
Rule 3: there is one exception: if a lone vowel e or E is at the end of a (punctuation-stripped) word, then that vowel does not count as a syllable.
Rule 4: finally, everything that is a word must always count as having at least onesyllable.
Extra Credit Problem 5 Matrix Multiplication
- Gaussian elimination - another name for the process of using row operations in orderto bring a matrix to reduced-row-echelon form.
(1) Enter the size and values of an array
(2) Print the array
(3) Multiply an array row by a constant
(4) Add one row into another
(5) Add a multiple of one row to another
(6) Solve!
(7) Invert! [This is extra...]
(9) Quit
Which choice would you like?
Extra Credit Problem 5 Matrix Multiplication
for col in range(len(A)):
# do the appropriate thing here
for row in range(len(A)):
# do the appropriate thing here when row != col