![Cumulative sum
6
For a given list A we will return a list B such that
B[n] = A[0]+A[1]+…A[n]
Take 1:
def cumulative_sum(lst):
summ = [ lst[0] ] * len(lst)
for i in range(1, len(lst)):
summ[i] = summ[i-1] + lst[i]
return summ
Take 2:
def cumulative_sum(lst):
return [sum(lst[0:n]) for n in range(1, len(lst)+1)]](https://image.slidesharecdn.com/programmingforengineersinpython-160504183156/85/Programming-for-engineers-in-python-6-320.jpg)
Programming for engineers in python
- 1. Recitation 4 Programming for Engineers in Python
- 2. Agenda Sample problems Hash functions & dictionaries (or next week) Car simulation 2
- 3. A function can be an argument 3 def do_twice(f): f() f() def print_spam(): print 'spam' >>> do_twice(print_spam) spam spam
- 4. Fermat’s last theorem 4 Fermat’s famous theorem claims that for any n>2, there are no three positive integers a, b, and c such that: 𝑎 𝑛 + 𝑏 𝑛 = 𝑐 𝑛 Let’s check it! def check_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
- 5. Fermat’s last theorem 5 >>> 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: def check_fermat(a,b,c,n): print "Wiles proved it doesn’t work" Sir Andrew John Wiles 1953-
- 6. Cumulative sum 6 For a given list A we will return a list B such that B[n] = A[0]+A[1]+…A[n] Take 1: def cumulative_sum(lst): summ = [ lst[0] ] * len(lst) for i in range(1, len(lst)): summ[i] = summ[i-1] + lst[i] return summ Take 2: def cumulative_sum(lst): return [sum(lst[0:n]) for n in range(1, len(lst)+1)]
- 7. Estimating e by it’s Taylor expansion 7 from math import factorial, e term = 1 summ = 0 k = 0 while term > 1e-15: term = 1.0/factorial(k) summ += term k += 1 print "Python e:", e print “Taylor’s e:", summ print “Iterations:”, k 𝑒 = 𝑘=0 ∞ 1 𝑘! = 2 + 1 2 + 1 6 + 1 24 + ⋯ Brook Taylor, 1685-1731
- 8. Estimating π by the Basel problem 8 from math import factorial, pi, sqrt term = 1 summ = 0 k = 1 while term > 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 𝜋2 6 = 𝑘=1 ∞ 1 𝑘2 = 1 + 1 4 + 1 9 + 1 16 + ⋯ Leonard Euler, 1707-1783
- 9. Ramanujan’s π estimation (optional) 9 from math import factorial, pi term = 1 summ = 0 k = 0 while term > 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 Srinivasa Ramanujan, 1887-1920
- 10. Triple Double Word 10 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/carta lk.py Corpus: http://www.csie.ntu.edu.tw/~pangfeng/Fortran%20exa mples/words.txt
- 11. PyGame 11 A set of Python modules designed for writing computer games Download & install: http://pygame.org/ftp/pygame-1.9.2a0.win32- py2.7.msi
- 12. Car game 12 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
- 13. ToDo List: 13 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!
- 14. 2 players car game 14 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