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### Programming for Engineers in Python

Recitation 4

Agenda

- Sample problems
- Hash functions & dictionaries (or next week)
- Car simulation

A function can be an argument

defdo_twice(f):

f()

f()

defprint_spam():

print\'spam\'

>>> do_twice(print_spam)

spam

spam

Fermat’s last theorem

- Fermat’s famous theorem claims that for any n>2, there are no three positive integers a, b, and c such that:
- Let’s check it!

defcheck_fermat(a,b,c,n):

if n>2 and a**n + b**n == c**n:

print"Fermat was wrong!"

else:

print"No, that doesn\'t work"

Pierre de Fermat

1601-1665

Fermat’s last theorem

>>> check_fermat(3,4,5,2)

No, that doesn\'t work

>>> check_fermat(3,4,5,3)

No, that doesn\'t work

- Dirty shortcut since 1995:

defcheck_fermat(a,b,c,n):

print"Wiles proved it doesn’t work"

Sir Andrew John Wiles

1953-

Cumulative sum

- For a given list A we will return a list B such that

B[n] = A[0]+A[1]+…A[n]

- Take 1:

defcumulative_sum(lst):

summ = [ lst[0] ] * len(lst)

for i inrange(1, len(lst)):

summ[i] = summ[i-1] + lst[i]

returnsumm

- Take 2:

defcumulative_sum(lst):

return [sum(lst[0:n]) for n inrange(1, len(lst)+1)]

Estimating e by it’s Taylor expansion

frommath import factorial, e

term = 1

summ= 0

k = 0

whileterm > 1e-15:

term = 1.0/factorial(k)

summ+= term

k += 1

print"Python e:", e

print“Taylor’s e:", summ

print “Iterations:”, k

Brook Taylor, 1685-1731

Estimating π by the Basel problem

frommath import factorial, pi, sqrt

term = 1

summ= 0

k = 1

whileterm > 1e-15:

term = 1.0/k**2

summ+= term

k += 1

summ = sqrt(summ*6.0)

print"Python pi:", pi

print“Euler’s pi:", summ

print “Iterations:”, k

Leonard Euler,

1707-1783

Ramanujan’sπ estimation (optional)

frommath import factorial, pi

term = 1

summ= 0

k = 0

whileterm > 1e-15:

term = factorial(4.0*k) / factorial(k)**4.0

term *= (1103.0+26390.0*k) / 396.0**(4.0*k)

summ += term

k += 1

summ =1.0/(summ * 2.0*2.0**0.5 / 9801.0)

print"Python Pi:", pi

print"Ramanujan Pi:", summ

print “Iterations:”, k

SrinivasaRamanujan,

1887-1920

Triple Double Word

- We want to find a word that has three double letters in it, like aabbcc (which is not a word!)
- Almost qualifiers:
- Committee
- Mississippi
- Write a function to check if a word qualifies
- Write a function that reads a text file and checks all the words
- Code: http://www.greenteapress.com/thinkpython/code/cartalk.py
- Corpus: http://www.csie.ntu.edu.tw/~pangfeng/Fortran%20examples/words.txt

PyGame

- A set of Python modules designed for writing computer games
- Download & install:

http://pygame.org/ftp/pygame-1.9.2a0.win32-py2.7.msi

Car game

- Control a car moving on the screen
- YouTube demo: http://www.youtube.com/watch?v=DMOj3HpjemE
- Code: https://gist.github.com/1372753 or in car.py
- Car controlled by

arrows

- Honk with Enter
- Exit with ESC

ToDo List:

- Fix stirring problem
- Honk by pressing space
- Car will go from the bottom to top and from one side to the other (instead of getting stuck)
- Switch to turtle!

2 players car game

- Collision avoidance simulator:
- When the cars are too close one of them honks
- Players need to maneuver the cars to avoid honks
- Code: https://gist.github.com/1380291 or cars.py
- Red car controlled by arrows
- Blue car controlled by z, x, c, s

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