1. Week 10 - Wednesday
CS 113

2. Last time What did we talk about last time? Traveling salesman problem
Other hard problems
NP-completeness
P vs. NP

3. Questions?

4. Project 3

5. Turing Machines

6. Turing machine A Turing machine is a model of computation
It consists of a head, an infinitely long tape, a set of possible states, and an alphabet of characters that can be written on the tape
A finite list of rules says what it should write and whether it should move left or right given the current symbol and state A 1

7. Turing machine example
3 state, 2 symbol “busy beaver” Turing machine:
Starting state A
Tape Symbol
State A
State B
State C
Write
Move
Next 1 R B C L
HALT A

8. Computational power
Computational power means the ability to solve a problem
The ability to run an algorithm
Speed is not related to computational power
Turing machines have as much computational power as any known computer
Any algorithm that can be run on any computer can be run on a Turing machine

9. Do you own a Turing machine?
A desktop or laptop computer can simulate the action of a Turing machine
Anything that can simulate a Turing machine has the same computational power as a Turing machine
Of course, the concept of a Turing machine requires infinite tape
There are some things that a "true" Turing machine could compute that would cause your computer to run out of memory

10. Are you a Turing machine?
If a Turing machine is the most powerful tool for computation there is, then you can't be more powerful than a Turing machine
Does your brain simply change from one state to another according to a series of fixed rules?
Some neurologists think that we're closer to that than we'd like to admit
Perhaps our ability to break rules makes us strong
Maybe it doesn't matter…

11. Halting Problem

12. Trouble!
There are some computational problems that you cannot design an algorithm for
No computer can ever solve the general problem (though sometimes you can solve instances of the problem)
Examples
It's impossible to write a Python program that can tell if any Python program will run to completion

13. Halting problem
Given a Turing machine and input x, does it reach the halt state?
This problem is undecidable
That means that there is no algorithm that can be to determine if any Turing machine will go into an infinite loop
Consequently, there is no algorithm that can take any program and check to see if it goes into an infinite loop

14.    Turntables Douglas Hofstadter uses the metaphor of turntables
Imagine that evil people design records that will shake turntables apart when they're played
Maybe turntable A can play record A and turntable B can play record B
However, if turntable A plays record B, it will shatter  

15. Stuff you have to buy for this proof
Turing machines can perform all possible computations
It's possible to encode the way a Turing machine works such that another Turing machine can read it
It's easy to make a slight change to a Turing machine so that it gives back the opposite answer (or goes into an infinite loop)

16. Proof by contradictionH m x
YES NO
You've got a Turing machine M with encoding m
You want to see if M will halt on input x
Assume there is a machine H that can take encoding m and input x
H(m,x) is YES if it halts
H(m,x) is NO if it loops forever
We create (evil) machine E that takes description m and runs H(m,m)
If H(m,m) is YES, E loops forever
If H(m,m) is NO, E returns YES H
YES NO E m
Loop
forever

17. A mind-bending proof Let's say that e is the description of E
What happens if you feed description e into E?
E(e) says what E will do with itself as input
If it returns YES, that means that E on input e loops forever
But it can't, because it just returned YES
If it loops forever, then E on input e would return YES
But it can't, because it's looping forever!
Our assumption that machine H exists must be wrong

18. Post correspondence problem
Given two finite lists of words A and B, can you pick k words (repetitions allowed) from A and k words (repetitions allowed) from B so that the words from A concatenated are exactly the same string as the words from B concatenated
Example:
Solution:
aa + bb + bb = aabbbb = a + a + bbbb
The Post correspondence problem (PCP) is undecidable (there is no algorithm that can solve all instances of it) A B aa
bbbb
aba a bb
abba

19. Python Review

20. Variables
In Python, the first time we assign a value to a name it creates a variable
The = sign is the assignment operator
Think of it as an arrow that points left, storing whatever is on the right into the variable
We can use whatever is stored in a variable like it's a value
person = "Walter White"
print(person)

21. Conversion to an integer
Sometimes you need to convert a string value to an integer, especially if you read it from a file
Use the int() function
In other cases, you want to convert a string to a floating point value (a decimal)
Then, use the float() function
word = "125"
number = int(word) # number is now 125
text = "6.125"
value = float(text) # value is now 6.125

22. Visual Python Be familiar with the following shapes for the exam Box:
Sphere:
The pos attribute gives the location of the center of each
All shapes also have a color attribute
box(pos=vector(x,y,z),size=vector(l,h,w))
sphere(pos=vector(x,y,z),radius=r)

23. while loops The while loop runs as long as a condition is true
In this case, when countdown becomes 0, the loop stops (since 0 is not less than 0)
Note that while loops use the same relational operators as if statements
countdown = 10
while countdown > 0:
print(countdown)
countdown = countdown – 1
print("Blast-off!")

24. for loops
If you want to do something, say, 10 times in Python, you can use a for loop
But you need to call the range() method to generate a list of numbers for you
In this case, the loop will run 10 times, and the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 will print out
for i in range(10):
print(i)

25. if statements
In Python, the primary way to make a choice is with an if statement
Whatever code is under the if and tabbed in will only be executed if the condition is true
Optionally, an else section can be added if you want to do something if the condition is false
Conditions often use the following relational operators to make a comparison: ==, !=, <, <=, >, >=
if phrase == "open sesame":
print("Welcome, Ali Baba!")
else:
print("Access denied!")

26. Else
It is often the case that we want to do one thing if a certain condition is met and something else if it is not
Example:
If it's raining:
I'll bring an umbrella
Otherwise:
I'll eat lunch in the park
Python uses the keyword else to mark code that will be executed if the condition was false

27. Things to watch out for
The condition of an if must be followed by a colon (:)
Never use = in a condition (always use ==)
It's easy to be off by one (x < 5 is not the same as x <= 5)
An else also has a colon after it
An else never has a condition
It marks what gets done when the if's condition is false
Using an else is not required
But you can't have an else without and if

28. Operations on Booleans
The condition of an if or a while is a Boolean value
Booleans are either True or False
To make complex decisions, we may need to combine multiple Boolean values together
You might be familiar with these operations if you have taken a course in logic

29. The not operator The not operator
Changes a True into a False or a False into a True x
not(x)
True
False

30. The and operator The and operator
It gives back True only if both things being combined are True
If I can swim AND the pool is not filled with acid, then I will survive x y
x and y
True
False

31. The or operator The or operator
It gives back True if either or both things being combined are True
If I get punched in the face OR kicked in the stomach, then I will be in pain x y
x or y
True
False

32. Example of and
The following code will check if a number x has a single digit
The same effect could be achieved with an if statement inside of an if statement, but this form is cleaner
if x >= 0 and x < 10:
print("Your number has a single digit!")

33. Multiple options
Sometimes you want to make a choice between more than two things
Essentially, you want a long list of mutually exclusive options
This can be done by nesting another if inside of an else
And then an if inside of its else …
But if you have a long list of options, your level of indentation gets crazy

34. elif Python has a special keyword elif that combines else and if
Start with an if for the first condition, use an elif for each condition in between, and almost always finish with a final else
if condition1:
statement1
elif condition2:
statement2
elif condition3:
statement3
elif condition4:
statement4
else:
statement5

35. Functions

36. Idea of a function
Functions allow you to package up some code to run over and over
Functions usually take some input (like numbers or text) so that they can be customized
Functions often give back an answer (like the square root of a number)
Also called methods in some other languages
The customizable purple blocks played the role of functions in Scratch

37. Advantages of functions
More modular programming
Break a program into separate tasks
Each task could be assigned to a different programmer
Code reusability
Use code over and over
Even from other programs
Less code duplication
Improved readability
Each function can do a few, clear tasks

38. Defining a function Name of 1st argument Function name
def name( arg1, … , argn ):
statement1
statement2 …
statementm
Required syntax
Name of
last argument
Code done by function

39. Simple function example
Given two numbers, find the smaller:
def smaller(a, b):
if a < b:
return a
else :
return b

40. Value returning functions
It is possible to divide functions into two types:
Functions that return values
Functions that don't return values
Functions that do return values give an answer:
It's as if the function is replaced by whatever answer is returned
x = 3
y = 4
small = smaller(x, y) #small contains 3

41. Functions that don't return values
A function doesn't have to return an answer:
This function only prints things to the screen
A function that doesn't return anything does some task but doesn't give back an answer
def callForHelp(times):
for i in range(times):
print("Help!")

42. return statements
Like most code in Python, the code inside of a function executes line by line
Of course, you are allowed to put if statements and loops inside methods
You can also put in return statements
A function will stop executing and jump back to wherever it was called from when it hits a return
The return statement is where you put the value that will be given back to the caller

43. Calling functions Defining a function is only half the game
You have to call functions to use them
Calling a function means giving it the parameters (or arguments) it needs and then waiting for its answer
By now, you have done many function calls
print()
sin()
You can call your own functions the same way

44. Calling functions callForHelp(3) #calls for help 3 times
You type the name of the function and then its arguments in parentheses
If it's a value returning function, you can store the answer it gives back
The arguments you give can be values or variables
You have to give the function the right number of arguments or the program will have an error
callForHelp(3) #calls for help 3 times
result = smaller(9, 2)

45. Key syntax Every function starts with def
Then comes the name of the function
Followed by the names of the arguments in parentheses
Followed by a colon (:)
Like loops and if statements, the code inside a function is indented one level
Call the function in other code by typing the name and the correct number of arguments in parentheses

46. Lists in Python

47. Strings Strings hold text
They are lists of characters (letters, digits, punctuation, etc.)
A string literal in Python is text with either single or double quotes around it
It doesn't matter which you use, but you can't mix them in one string
line = "Stop, collaborate, and listen!"
countdown = 'Launching in 5, 4, 3, 2, 1... Blast off!'

48. String operations
You can use + to concatenate two strings together (to get a third string that is both of them stuck together)
You can use * to get repetitions of a string
place = "boon" + "docks"
print(place) #prints boondocks
comment = "yeah " * 3
print(comment) #prints yeah yeah yeah

49. String operations continued
You can use the len() function to get the length of a string
You can use square brackets to get a particular character in the string
Indexes start at 0
The first character in a string is at 0, the last is at its length - 1
author = "Thomas Pynchon"
print( len(author) ) #prints 14
movie = "Dr. Strangelove"
print(movie[4]) #prints S

50. Slices
If you want to get more than one character from a string, you can use the slice notation
Two numbers with a colon (:) in between
The first number is the starting point, the second number is the location after the ending point
If you subtract the first from the last, you'll get the length of the result
adjective = "dysfunctional"
noun = adjective[3:6] #noun contains "fun"

51. Lists You can think of a string as a list of characters
Python provides a way to make lists of other things too
To make a list, you can put a collection of objects inside square brackets
They can even be different types
days = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
stuff = ["Danger!", 3, True, 1.7]

52. Accessing an element
As with strings, use square brackets and a number to access an element in the list
Like strings, elements are numbered from 0 to the length – 1
You can use the len() function to get the length of a list
days = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
bleh = days[0] #contains "Monday"
count = len(days) #contains 7

53. Changing elements in a list
You can also change the elements in a list using the square bracket notation
This is one of the bigger differences between strings and general lists
You cannot change the characters in a string
You have to make a new string
birds = ["Duck", "Duck", "Duck"]
birds[2] = "Goose"
print(birds) #prints ['Duck', 'Duck', 'Goose']

54. Slices on lists
Just like strings, you can use the slice notation to get a copy of part of a list
There are shortcuts too
Python assumes 0 if you leave off the first number
It assumes the length if you leave off the last number
days = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
weekend = days[5:7]
print(weekend) #prints ['Saturday', 'Sunday']
weekdays = days[:5] #Monday through Friday

55. For loops and lists
A for loop can be used to iterate over all the elements in a list
Since a string is a special kind of list, you can iterate over the characters in them too
days = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
for day in days:
print( day ) #prints each day on a line
word = "HEY"
for letter in word:
print( letter ) #H E Y on separate lines

56. split() method Sometimes you get a string that contains a lot of words
You'd like to split the string up into a list of those individual words so that you can deal with each
Calling the split(" ") method returns just such a list, breaking apart the string wherever there is a space character (" ")
sentence = "I seem to be having tremendous difficulty with my lifestyle."
words = sentence.split(" ")
print(words[5]) #prints tremendous
print( len(words) ) #prints 10

57. Files

58. Files A file is simply a sequence of bytes
Or characters, if you want of think of it that way
All files are binary files, in the sense that the data is ultimately 1s and 0s
Some files are also text files
A text file can be read by a human, not just a computer
If you can open the file with Notepad and read something meaningful, it's a text file
Python (.py) files are a good example of text files
Word (.doc or .docx) files are not text files, since they are formatted in a way that only the Word program can read

59. Reading text files Python makes it easy to read text files
Unfortunately, GlowScript.org uses a more complicated command
The first step is to open the file
If you put this at the top of your program, there will be a Choose File button that will let you pick a file on your computer
Inside the variable you store into (file, in this case) is a field called text, which will contain the contents of the file you pick, as a string
file = read_local_file(scene.title_anchor, wait)

60. Printing a file to the screen
To print a file to the screen, we open it and loop through everything in it
We want to divide file (a giant string) into a list of lines, using the split() method
Between every line in the file is a special character "\n", which means end of line
file = read_local_file(scene.title_anchor, wait)
lines = file.text.split("\n")
for line in lines:
print( line )

61. Adding up the numbers in a file
What if a file contains a bunch of numbers, with each one on a separate line?
We could add them up and print out the sum
file = read_local_file(scene.title_anchor, wait)
lines = file.text.split("\n")
sum = 0
for line in lines:
sum = sum + int(line) #convert line to int
print("Sum: " + sum)

62. Quiz

63. Upcoming

64. Next time…
Finish review for Exam 2
Lab 10

65. Reminders Work on Project 4 Work on Design Document for Final Project
Due Friday!
Exam 2 is next Monday
We'll finish the review on Friday