EECS 110: Lec 17: Review for the Final Exam Aleksandar Kuzmanovic Northwestern University akuzma/classes/EECS110-s09

EECS 110: Lec 17: Review for the Final Exam

Aleksandar Kuzmanovic

Northwestern University

http://cs.northwestern.edu/~akuzma/classes/EECS110-s09/

General Info

Wednesday, June 3, 10-11:30am, Annenberg Hall G15

To be done individually

Closed book

One 8.5” by 11” sheet of paper permitted

Please do not discuss the exam with others until everyone has taken it.

There are six questions. Each question is worth 20 points.

Hence, you can acquire 120 points in total.

Those who get > 90 points will get an A.

Those who get >80 points and <90 points will get a B, etc.

2

Final Exam

6 questions:1. Misc

2. Loops and recursion

3. Mutation

4. 2D in Python

5. Dictionaries

6. Classes and Objects3

What does this code do?

print 'It keeps on'

while True: print 'going and'

print 'Phew! I\'m done!'

Q2 (and Q1): Loops (while and for) and Recursion

Extreme Looping

Anatomy of a while loop:

print 'It keeps on'

while True: print 'going and'

print 'Phew! I\'m done!'

“while” loop

the loop keeps on running as long as this test is True

This won't print until the while loop finishes - in this case, never!

What do these two loops print?

n = 0

for c in 'forty-two':

if c not in 'aeiou':

n += 1

print n

??

n = 3while n > 1: print n if n%2 == 0: n = n/2 else: n = 3*n + 1


n = 0



n += 1

print n

7


??


n = 0



n += 1

print n

7


3


n = 0



n += 1

print n

7


310


n = 0



n += 1

print n

7


3105


n = 0



n += 1

print n

7


310516


n = 0



n += 1

print n

7


3105168


n = 0



n += 1

print n

7


31051684


n = 0



n += 1

print n

7


310516842

fore!

for x in range(8):

print 'x is', x

print 'Phew!'

x is assigned each value from this

sequence

the BODY or BLOCK of the for loop runs with that x

Code AFTER the loop will not run until the loop is finished.

1

2

3

4

LOOP back to step 1 for EACH value in the list

Two kinds of for loops

Element-based Loops

L = [ 42, -10, 4 ]

x

L = [ 42, -10, 4 ]

i0 1 2

Index-based Loops

sum = 0

for x in L: sum += x

sum = 0

for i in range(len(L)): sum += L[i]

L[i]

Q2: Recursion vs. Loops

Solve a problem using:

(a) recursion

(b) loops

Example 1a: fac(N) with recursion

Let recursion do the work for you.

def fac(N):

if N <= 1: return 1 else: return N * fac(N-1)

You handle the base case – the easiest possible case to

think of!

Recursion does almost all of the rest of the problem!

Exploit self-similarity

Produce short, elegant code

Less work !

Example 1b: fac with for (v1)

def fact( n ):

answer = 1

for x in range(n):

answer = answer * x

return answer

def fact( n ):

answer = 1

for x in range(1,n+1):

answer = answer * x

return answer

Example 1b: fac with for (v2)

def sum(L):

""" input: a list of numbers, L

output: L's sum

"""

if len(L) == 0:

return 0.0

else:

return L[0] + sum(L[1:])

Base Caseif the input

has no elements, its sum is zero

Recursive Case

if L does have an element, add

that element's value to the sum of the REST of the

list…

This input to the recursive call must be "smaller"

somehow…

Example 2a: sum(L) with recursion

Example 2b: sum(L) with for

def sum( L ):

""" returns the sum of L's elements """

sum = 0

for x in L:

sum = sum + x

return sum

Finding the sum of a list:

Accumulator!

Example 3: isPrime(n) and addPrimes(L)

Problem:

(a)Use a loop to write a Python function isPrime(n), which takes in an integer n and returns True if n is prime and False if n is composite. You may assume that n will be strictly greater than 1.

(b)Use recursion (no loops!) to write a Python function addPrimes(L), which takes in a list L of integers (all integers will be at least 2) and it returns the sum of only the prime numbers in the list L. The function should use the above isPrime(n) function.

Example 3a: isPrime(n)

def isPrime(n): if n < 2: return False for i in range(2, n/2+1): if n % i == 0: return False return True

Example 3b: addPrimes(L)

def addPrimes(L): if len(L) == 0: return 0 else: if isPrime(L[0]): return L[0] + addPrimes(L[1:]) else: return addPrimes(L[1:])

Changeable types:

dictionary

Unchangeable types:

list

tuple

string

int

float

bool

Mutable vs. Immutable data

Question 3: Mutation

Functions and (immutable) Variables

def fact(a): result = 1 while a > 0: result *= a a -= 1 return result

>>> x = 5>>> y = fact(x)>>> x??


def fact(a): result = 1 while a > 0: result *= a a -= 1 return result

>>> x = 5>>> y = fact(x)>>> x5


def swap(a, b): temp = a a = b b = temp

>>> x = 5>>> y = 10>>> swap(x, y)>>> print x, y??

x

y

a

b

temp


def swap(a, b): temp = a a = b b = temp

>>> x = 5>>> y = 10>>> swap(x, y)>>> print x, y5, 10

x

y

a

b

temp

Functions and Mutable Types

def swap(L, i1, i2): temp = L[i1] L[i1] = L[i2] L[i2] = temp

>>> MyL = [2, 3, 4, 1]>>> swap(myL, 0, 3) >>> print myL??

RAM

MyL

L

i1

i2

42

43

44

45

Functions and Mutable Types

def swap(L, i1, i2): temp = L[i1] L[i1] = L[i2] L[i2] = temp

>>> MyL = [2, 3, 4, 1]>>> swap(myL, 0, 3) >>> print myL[1,3,4,2]

RAM

MyL

L

i1

i2

42

43

44

45

The conclusion

You can change the contents of lists in functions that take those lists as input.

Those changes will be visible everywhere.

(actually, lists or any mutable objects)

(immutable objects are safe, however)

Example 1

def zeroOdd1( L ): for i in range(len(L)): if L[i] % 2 == 1: L[i] = 0

def zeroOdd2( L ): for i in L: if i % 2 == 1: i = 0

>>> L = [1, 2, 3, 4, 5]>>> zeroOdd1(L)>>> L??>>> L = [1, 2, 3, 4, 5]>>> zeroOdd2(L)>>> L

Example 1



>>> L = [1, 2, 3, 4, 5]>>> zeroOdd1(L)>>> L[0,2,0,4,0]>>> L = [1, 2, 3, 4, 5]>>> zeroOdd2(L)>>> L??

Example 1



>>> L = [1, 2, 3, 4, 5]>>> zeroOdd1(L)>>> L[0,2,0,4,0]>>> L = [1, 2, 3, 4, 5]>>> zeroOdd2(L)>>> L[1,2,3,4,5]

Example 2

What are the values of A, B, C and D at the indicated points?def mystery1(L1, N, C): for i in L1: if i == N: C += 1 return C def mystery2(C): for i in range(len(C)): C[i] *= 2

>>> A = [22, 10, 30]>>> B = 22>>> C = 0>>> D = mystery1(A, B, C) >>> mystery2(A)

12

1)

2)

Example 2


>>> A = [22, 10, 30]>>> B = 22>>> C = 0>>> D = mystery1(A, B, C) >>> mystery2(A)>>> A

1

1)

2)

A = [22, 10, 30]B = 22C = 0D = 1

2

Example 2


>>> A = [22, 10, 30]>>> B = 22>>> C = 0>>> D = mystery1(A, B, C) >>> mystery2(A)>>> A

1

2

1)

2)

A = [22, 10, 30]B = 22C = 0D = 1

A = [44, 20, 60]

Example 3: avoiding mutation

Problem:

Write function x(L), …., The list L should NOT mutate, i.e., it should stay the same.

Example 3: avoiding mutation

def x(L): # some function

…

L2=copyList(L)

… # manipulate L2, not L

def copyList(L): L2 = [] for x in L: L2 += [x] return L2

Handling rectangular arrays …

listA

list

list

list

A[0]

A[1]

A[2]

How many rows does A have, in general ?

How many columns does A have, in general ?

A[2][3]

A[0][0]

Question 4: 2D in Python

Rectangular arrays


listA

list

list

list

A[0]

A[1]

A[2]



A[2][3]

A[0][0]

len(A)

Rectangular arrays


listA

list

list

list

A[0]

A[1]

A[2]



A[2][3]

A[0][0]

len(A)

len(A[0])

Which one works?

How could we create a rectangular array (of default data, 0),given its height and width ?

or

A = [ [0]*width ]*height

A = [ [0]*height ]*width

Which one works?

How could we create a rectangular array (of default data, 0), given its height and width ?


A = [ [0]*height ]*width

What's really going on?


inner = [0]*widthA = [inner]*height

Creating a 2d array

def create2dArray( width, height ): """ does just that """

A = [] # start with nothing

for row in range( height ):

for col in range( width ):

Creating a 2d array

def create2dArray( width, height ): """ does just that """

A = [] # start with nothing

for row in range( height ): A = A + [[]] for col in range( width ): A[row] = A[row] + [0] return A

Example 1: What 2d loops would create a checkerboard image?

def checkerboard():

# loop over each pixel for col in range(width):

for row in range(height):

Example 1: What 2d loops would create a checkerboard image?

def checkerboard():

# loop over each pixel for col in range(width):

for row in range(height): if (col/20 + row/20)%2 == 0:

image.plotPoint( col, row )

Example 2: Write a function that returns the number of all-zero rows

Example 2: Write a function that returns the number of all-zero rows

def num_zero_rows(L): width = len(L[0]) height = len(L) n = 0 for row in range(height): k = 0 for col in range(width): if L[row][col] != 0: k = 1 if k == 0: n += 1 return n

In Python a dictionary is a set of key - value pairs.

It's a list where the index can be any immutable-type key.

>>> d = {}

>>> d[1988] = 'dragon'

>>> d[1989] = 'snake'

>>> d

{1988: 'dragon', 1989: 'snake'}

>>> d[1988]

'dragon'

>>> d[1987]

key error

Question 5: Dictionaries

Lists vs. Dictionaries

In Python a dictionary is a set of key - value pairs.

It's a list where the index can be any immutable-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 seen this 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

A family dictionary?

A family dictionary…

T = {'abe' :['homer','herb'], 'jackie':['marge','patty','selma'], 'homer' :['hugo','bart','lisa','maggie'], 'marge' :['hugo','bart','lisa','maggie']}

keys can be any immutable type

values can be any type at all…

T['abe']

How to get 'selma' from T?





T['abe']


['homer','herb']





T['abe']


['homer','herb']

T['jackie'][2]

(T['jackie'] is a list)

Example 1: favChild

def favChild( person, Tree ): """ person is a name (a string) Tree is a dictionary of children returns person's favorite child """

if Tree.has_key( person ): Kids = Tree[person] Kids.sort() return Kids[0] else: return 'no children'

Who is favored ?

Side effects ?

Example 2: addChild

def addChild( person, Tree, jr ):""" adds person's new child to Tree ""“

For example, >>> addChild( 'lisa', T, 'abejr' )

def addChild( person, Tree, jr ):""" adds person's new child to Tree ""“if Tree.has_key(person):

kids = Tree[person]kids += [jr]

For example, >>> addChild( 'lisa', T, 'abejr' )

Example 2: addChild

EXAMPLE 3: Based on favChild, write favGChild to return the first grandchild

alphabetically - or return 'no one' if there are none.

def favChild( person, Tree ): if Tree.has_key( person ): Kids = Tree[person] Kids.sort() return Kids[0] else: return 'no children'

EXAMPLE 3: Based on favChild, write favGChild to return the first grandchild

alphabetically - or return 'no one' if there are none.

def favGChild( person, Tree ): gChildren = [] if Tree.has_key( person ): for child in Tree[person]: if Tree.has_key( child ): gChildren += Tree[child] if gChildren == []: return 'no one' else: gChildren.sort() return gChildren[0]

def favChild( person, Tree ): if Tree.has_key( person ):

Kids = Tree[person] Kids.sort()

return Kids[0] else:

return 'no children'

An object-oriented programming language allows you to build your own customized types of variables.

(1) A class is a type of variable.

(2) An object is one such variable.

There will typically be MANY objects of

a single class.

Question 6: Classes and Objects

Objects

An object is a data structure (like a list), except

(1) Its data elements have names chosen by

the programmer.

(2) Data elements are chosen & organized

by the programmer

(3) An object can have behaviors built-in

by the programmer.

Objects

An object is a data structure (like a list), except

(1) Its data elements have names chosen by

the programmer.

(2) Data elements are chosen & organized

by the programmer

(3) An object can have behaviors built-in

by the programmer.usually called "methods" instead of functions

class Date: """ a blueprint (class) for objects that represent calendar days """ def __init__( self, mo, dy, yr ): """ the Date constructor """ self.month = mo self.day = dy self.year = yr

def __repr__( self ): """ used for printing Dates """ s = "%02d/%02d/%04d" % (self.month, self.day, self.year) return s

The Date class

The Date Class

this is an object of type Date

>>> d = Date(1,1,2008)

>>> d

1/1/2008

this is a CONSTRUCTOR …

the representation of a particular object of type Date

class Date: def __init__( self, mo, dy, yr ): def __repr__(self): def isLeapYear(self):

def copy(self): """ returns a DIFFERENT object w/SAME date! """

def equals(self, d2): """ returns True if they represent the same date; False otherwise """

More Date


def copy(self): """ returns a DIFFERENT object w/SAME date! ""“

return Date(self.month, self.day, self.year)

def equals(self, d2): """ returns True if they represent the same date; False otherwise """

More Date


def copy(self): """ returns a DIFFERENT object w/SAME date! ""“

return Date(self.month, self.day, self.year)

def equals(self, d2): """ returns True if they represent the same date; False otherwise ""“

return self.month == d2.month and self.day == d2.day and self.year == d2.year

More Date

Good luck with the Exam!

EECS 110: Lec 17: Review for the Final Exam Aleksandar Kuzmanovic Northwestern University akuzma/classes/EECS110-s09

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