Berkeley CS 61A Spring 2013 Midterm 1 TA Review Session

7/29/2019 Berkeley CS 61A Spring 2013 Midterm 1 TA Review Session

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TA ReviewSessionStephen Martinis, Keegan Mann, Albert Wu,Julia Oh


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Overview

Evaluation Higher Order Functions Newton's Method

Environment Diagrams Questions


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Evaluation

Process of taking an expression and executingthe commands it details according to howPython is defined as a language.

How you do anything in a program.

Here is a review of how to evaluate things.

Not exhaustive

Doesn't deal with environment diagrams


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Evaluation Rules: Names

To find a name (variable)

1. Look in localframe first

2. Look up the name in the parent frame

recursively.

3. If there is no parent frame, raise an Error


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Evaluation Rules: Assignment

To assign a value to a variable

x = add(2, 3)

1. Evaluate the right side of = sign.

2. Bind name on left side of = sign to value from

step 1


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Evaluation Rules: Functions

1. Evaluate the operator

2. Evaluate the operands

3. Apply the operator to the operands

foo(7 * 2, lambda y: x(y), add(3, mul(8,4)))


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Evaluation Rules: Definitions

To define function:def foo():

return 3

1. Create a new function

2. Label its parent as the current frame

3. Bind the function to its name in the current

frame


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Evaluation (questions)

>>> def foo(x):

def bar(x):

return x + y

y = 6

return bar

>>> y = 5

>>> foo(3)(5)

______


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Evaluation (questions) SOLN

>>> def foo(x):

def bar(x):

return x + y

y = 6

return bar

>>> y = 5

>>> foo(3)(5)

11


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>>> def doctor(who):

if knocks == 4:

return 11return 10

>>> def ood(angry):

if angry > 0:return red

return blue

>>> knocks = 4

>>> red = 2

>>> blue = 5>>> who = 0


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Eval to Outputs

doctor(15)

doctor(36) == 10

print(print(red + blue))

ood(doctor(42))

knocks -= ood(who)

print(doctor(who))

ood(knocks)


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Evaluation (questions) SOLN

Eval to Outputs

doctor(15) 11 11

doctor(36) == 10 False False

print(print(red + blue)) None 7

None

ood(doctor(42)) 2 2

knocks -= ood(who) N/A Nothing

print(doctor(who)) None 10

ood(knocks) 5 5


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Functions

Syntax

def (, , ...):

Ex:

def foo(bar, baz): return 3


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Functions (questions)

Q1

Define a function called denerowhich takes

two numbers and finds their difference.

Q2

Define a function harveywhich takes noarguments and returns the number 61.


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Functions (questions) SOLN

Q1

def denero(a, b):

return a - b

Q2

def harvey():return 61


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Higher-Order Functions

What are the inputs

and outputs?

numbers

booleans

strings

functions

def double(f):

def h(x):

return f(f(x))

return h


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Higher-Order Functions (questions)

def test(x):

def review(f):

return f(x)

return review

def half(x):print(x // 2)

Eval to Outputs

half(3) None 1

test(5)

test(5)(half)

test(5)(test)


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Higher-Order Functions (questions)SOLN

def test(x):

def review(f):

return f(x)

return review

def half(x):print(x // 2)

Eval to Outputs

half(3) None 1

test(5) FUNC FUNC

test(5)(half) None 2

test(5)(test) FUNC FUNC


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def silly(name):

def fun():

print('first')

return name(y)

print('second')

return fun

def bop(y):

return y // 10 + 1

y = 34

reserve = silly(bop)

Eval to Outputs

reserve()

silly(bop(y))

silly(print)()

bop(reserve())silly(reserve)()


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def silly(name):

def fun():

print('first')

return name(y)

print('second')

return fun

def bop(y):

return y // 10 + 1

y = 34

reserve = silly(bop)

Eval to Outputs

reserve() 4 first

4

silly(bop(y)) func secondfunc

silly(print)() None second

first

34

bop(reserve()) 1 first1

silly(reserve)() ERROR second

firstERROR


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def one(x):

def two():

def two(y):

def three(z):

return x + y + z

return x(y) + z

return three(y)

return three(z)

return threey = 4

return two(x)

return two

>>> one(lambda x: x*x)

>>> one(lambda x: x*x)()

20>>> one(lambda x: x*x)()(4)

TypeError ...

Cross out lines on the right sothat the doctests below pass.


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def one(x):

def two():

def two(y):

def three(z):

return x + y + z

return x(y) + z

return three(y)

return three(z)

return threey = 4

return two(x)

return two

>>> one(lambda x: x*x)

>>> one(lambda x: x*x)()

20>>> one(lambda x: x*x)()(4)

TypeError ...

Cross out lines on the right sothat the doctests below pass.


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Lambda Expressions

To evaluate a lambda

lambda x: 2 * x

Create a new function

Label its parent as the current frame

Do NOT evaluate the expression in the colon

yet


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Lambda Expressions

def (, ...):

return

def hi():

return 1

def square(x):

return x * x

def mul(a, b):

return a * b

= lambda :

hi = lambda : 1

square = lambda x: x * x

mul = lambda a, b: a * b

What are the intrinsic names of lambdas?


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Lambda Expressions (questions)

Q1

def one(x):def two(y):

return x + y

return two

Q2

def branch(cond):if cond:

return one(1)

return one(0)

Convert into lambda expressions.


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Lambda Expressions (questions)SOLN

Q1

def one(x):def two(y):

return x + y

return two

Q2

def branch(cond):if cond:

return one(1)

return one(0)

Convert into lambda expressions.

Q1one = lambda x: lambda y: x + y

Q2branch = lambda cond: one(1) if cond else one(0)


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Lambda Expressions (questions)


curry = lambda f: lambda x: lambda y: f(x, y)

new_mul = curry(mul)(3)

Eval to Outputs

curry(mul)

new_mul(4)

curry(curry)(5)

curry(curry)(1)(2)

(lambda x, y: mul(y, x))(3, 2)


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Lambda Expressions (questions)SOLN


curry = lambda f: lambda x: lambda y: f(x, y)

new_mul = curry(mul)(3)

Eval to Outputs

curry(mul) FUNC FUNC

new_mul(4) 12 12

curry(curry)(5) FUNC FUNC

curry(curry)(1)(2) ERROR ERROR

(lambda x, y: mul(y, x))(3, 2) 6 6


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Newton's Method (questions)

Wikipedia article

Write a function that returns the x-value at whicha local maximum or minimum occurs.

You may use approx_deriv(), andnewtons_method()

def find_max(fn, guess):

return______
http://en.wikipedia.org/wiki/Newtons_method


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Newton's Method (questions) SOLN

Wikipedia article

Write a function that returns the x-value at whicha local maximum or minimum occurs.You may use approx_deriv(), andnewtons_method()

def find_max(fn, guess):

returnnewtons_method(lambda x: approx_deriv(fn),guess)
http://en.wikipedia.org/wiki/Newtons_method


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Newton's Method (questions)

def newtons_method(fn, guess=1):

ALLOWED_ERROR_MARGIN = 0.0000001

while abs(fn(guess)) > ALLOWED_ERROR_MARGIN:

guess -= fn(guess) / deriv(fn, guess)return guess

True orFalse?

newtons_method will always terminate. fn is called 3 times in a single while loop.

removing abs could break the function


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Newton's Method (questions) SOLN

def newtons_method(fn, guess=1):

ALLOWED_ERROR_MARGIN = 0.0000001

while abs(fn(guess)) > ALLOWED_ERROR_MARGIN:

guess -= fn(guess) / deriv(fn, guess)return guess

True orFalse?

newtons_method will always terminate. F fn is called 3 times in a single while loop. F

removing abs could break the function. T


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Environment Diagrams

Show how Python executes code

Rules: http://www-inst.eecs.berkeley.

edu/~cs61a/sp13/pdfs/environment-diagrams.pdf

Online Python Tutor:http://inst.eecs.berkeley.edu/~cs61a-py/OnlinePythonTutor/v3/tutor.html
http://inst.eecs.berkeley.edu/~cs61a-py/OnlinePythonTutor/v3/tutor.htmlhttp://www-inst.eecs.berkeley.edu/~cs61a/sp13/pdfs/environment-diagrams.pdfhttp://inst.eecs.berkeley.edu/~cs61a-py/OnlinePythonTutor/v3/tutor.htmlhttp://inst.eecs.berkeley.edu/~cs61a-py/OnlinePythonTutor/v3/tutor.htmlhttp://www-inst.eecs.berkeley.edu/~cs61a/sp13/pdfs/environment-diagrams.pdfhttp://www-inst.eecs.berkeley.edu/~cs61a/sp13/pdfs/environment-diagrams.pdfhttp://www-inst.eecs.berkeley.edu/~cs61a/sp13/pdfs/environment-diagrams.pdf


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Environment Diagrams (rules)

Assignment

1. Evaluate right-hand expression2. Write name in current frame

3. Bind expression to name

Function call

1. Draw frame (label p frame, intrinsic name)2. Bind formal parameters3. Evaluate function body


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Lookup

1. Check for name in current frame2. If not found, check in parent frame

3. If no parent, error


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DO NOT:

draw a new frame when defining functions

draw frames forbuilt-in functions

point variables to other variables

forget to label the frame's parent

forget to label the frame's intrinsic name

give Global a return value


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Environment Diagrams (questions)

def mul(a, b):

if b == 1:return a

return a + mul(a, b - 1)

mul(3, 3)


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Environment Diagrams (questions)SOLN

def mul(a, b):

if b == 1:return a

return a + mul(a, b - 1)

mul(3, 3)

http://bit.ly/151Qkrb
http://bit.ly/151Qkrbhttp://bit.ly/151Qkrb


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def dream1(f):

kick = lambda x: mind()

def dream2(secret):

mind = f(secret)

kick(2)

return dream2

inception = lambda secret: lambda: secret

real = dream1(inception)(42)


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def dream1(f):

kick = lambda x: mind()

def dream2(secret):

mind = f(secret)

kick(2)

return dream2

inception = lambda secret: lambda: secret

real = dream1(inception)(42)

http://bit.ly/WKB3WY
http://bit.ly/WKB3WYhttp://bit.ly/WKB3WYhttp://bit.ly/WKB3WY


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the = 4

def boom(goes):

def dynamite():

return boom(goes-1)

if goes < the:

return 9

goes += 4

return dynamite

the = boom(5)()

boom(10)


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the = 4

def boom(goes):

def dynamite():

return boom(goes-1)

if goes < the:

return 9

goes += 4

return dynamite

the = boom(5)()

boom(10)

http://bit.ly/VMjpFM
http://bit.ly/VMjpFMhttp://bit.ly/VMjpFM


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Conclusion

Good luck! Don't panic, and you'll be fine. Questions?

Documents

Berkeley CS 61A Spring 2013 Midterm 1 TA Review Session