1. The last CS lecture you’ll ever need! On Warner Brothers' insistence, we affirm that this 'C' does not stand for 'Chamber' and 'S' does not stand for 'Secrets.' * Caution: do not take this statement too literally or it is possible find yourself in twice as many CS lectures as you need! Aye! Aye! Aye! mateys… Our legal counsel requires us to include these footnotes… Hw #1 due next Tuesday, 9/21, at 11:59 pm CS ? This is just like magic! * Hw #0 due this Tuesday, 9/14, at 11:59 pm IS 313 Today! Choose 2 out of 3 problems Run Apache!

2. What is it? What type is it?

3. Again, this is really data. data information knowledge wisdom

4. Python Data Types bool int long float 3.14 10**100 42 True False Numeric NameExampleWhat is it? values with a fractional part integers > 2147483647 integers <= 2147483647 the results from a comparison: ==, !=,, = "Boolean value"

5. Datatypes as genes… bool Dominant int long float Recessive 41 + True 10**100 - 10**100 1.0 / 5 1 / 5 What will these results be?

6. Python Operators I’d go with parentheses over precedence Precedence * % ** / > < == + - Caution Level = Highest Lowest ** *%/><==+- = - ( ) It's not worth remembering all these %+/* things! remainder power is equal to set equal to divide as usual

7. 7 % 3 % the "mod" operator 8 % 3 9 % 3 16 % 7 x%4 == 0 x%2 == 0 For what values of x are these True ? What happens on these years? x%y returns the remainder when x is divided by y x%2 == 1

8. the "equals" operators = != == What about === ?

9. = Names Data Aiden, Braden, Kaden…? Ava, Abigail, Caylin…? Choosing the right name is more important than I thought. >> x = 41 >> y = x + 1

10. Inside the machine… x = 41 y = x + 1 name: x type: int LOC: 300 41 What is happening behind the scenes: What's happening in python: "variables as containers" memory location 300 id, del ComputationData Storage name: y type: int LOC: 312 42 memory location 312

11. Computer Memory Random Access Memory (RAM) byte = 8 bits word = 4 bytes = 32 bits is a long list of memory locations bit = 1 "bucket" of charge name: y type: int LOC: 312 4 bytes for an int on or off is it really a coincidence that this looks like the string theory picture?? 42 plus overhead…

12. Re-naming…! Aiden, Aiden, Aiden, … It's possible to lose your name in Python! >> x = 41 >> y = x + 1 >> x 41 >> y 42 >> x = x + y >> x ?? >> y ??

13. Are numbers enough? No! You need lists of numbers, as well! and strings are helpful, too. list str These are Python sequences…

14. str ing functions str len + * converts input to a string returns the string’s length str(42) returns '42' len('42') returns 2 'XL' + 'II' returns 'XLII' 'VI'*7 returns 'VIVIVIVIVIVIVI' concatenates strings repeats strings s1 = "ha" s2 = "t" Given these strings What did you say!?! s1 + s2 2*s1 + s2 + 2*(s1+s2) What are

15. String surgery s[ ] indexes into the string, returning a one-character string s = 'harvey mudd college' s[0] returns 'h' s[6] returns 0123456789 101112131415161718 s[ ] returns 'e' Which index returns 'e'? python != English s[len(s)] returns Read "s-of-zero" or "s-zero" index

16. Negative indices… s = 'harvey mudd college' 0123456789 101112131415161718 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 Negative indices count backwards from the end! s[-1] returns 'e' s[-11] returns s[-0] returns Python can suit any mood…

17. s[ : ] slices the string, returning a substring s[12:18] returns 'colleg' s[0:6] returns 'harvey' s = 'harvey mudd college' 0123456789 101112131415161718 Slicing what to do if you want a bigger piece of the pie! What's going on here? s[17:] returns 'ge' s[:] returns 'harvey mudd college'

18. s[ : ] slices the string, returning a substring s[12:18] returns 'colleg' s[0:6] returns 'harvey' s = 'harvey mudd college' 0123456789 101112131415161718 Slicing what to do if you want a bigger piece of the pie! the first index is the first character of the slice s[17:] returns 'ge' the second index is ONE AFTER the last character a missing index means the end of the string s[:] returns 'harvey mudd college'

19. s[ : ] slices the string, returning a substring s[15:-1] s[1:3] s = 'harvey mudd college' 0123456789 101112131415161718 Slicing what to do if you want a bigger piece of the pie! What are these slices? How would you get 'mud' 'e' Don't 'wor' 'e'- Be 'hap' 'e' !

20. s[0:8:2] returns 'hre ' s[ : : ] skip-slices, returning a subsequence s = 'harvey mudd college' 0123456789 101112131415161718 Skip-Slicing if you don't want your neighbor to get any… the third index is the "stride" length it defaults to 1 'doe' I love this one. What skip-slice returns What does this return? s[1::6]

21. Lists ~ Strings of anything L = [ 3.14, [2,40], 'third', 42 ] Square brackets tell python you want a list. len(L) L[0] L[0:1] 'hi' How could you extract from L Slicing: always returns the same type Indexing: could return a different type Commas separate elements.

22. What is len(pi) pi = [3,1,4,1,5,9] What slice of pi is [3,4,5] c = 'claremont' Add parts of c, g, and u to create 'monty' What are pi[0]*(pi[1]+pi[2]) and pi[0]*(pi[1:2]+pi[2:3]) ? What is g[0:4] What is c[-1] What slice of pi is [3,1,4] Part 2Part 1 Add two slices of pi to get [3,1,1,5] g = 'graduate' u = 'university' What slice of pi is [9,1,1] What is pi[-1] Extra!! 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 What is c[:3:-2] What is c[0] + u[7:] Try it!

23. Python slices… It dices... … but wait, there's more!

24. Computational Models Picobot!?Python?!

25. Guido van Rossum Python testimonials

26. 20 years ago…

27. 9/2010 C http://www.tiobe.com/index.php/content/paperinfo/tpci/index.html Python based on the number of skilled engineers world-wide, courses and third party vendors

28. Computation's Double Identity name: x type: int LOC: 300 41 "variables as containers" memory location 300 ComputationData name: y type: int LOC: 304 42 memory location 304

29. Computation's Double Identity name: x type: int LOC: 300 41 "variables as containers" memory location 300 ComputationData name: y type: int LOC: 304 42 memory location 304 the monomers are functions…

30. # my own function! def dbl( x ): """ returns the double of x """ return 2*x How functions look Comments Docstrings (1)describes overall what the function does, and (2)explains what the inputs mean/are They become part of python's built-in help system! With each function be sure to include one that They begin with # keywords def starts the function return stops it immediately and sends back the return value Some of Python's baggage… Look good to me!

31. return != print >>> dbl(21) 42 def dbl(x): """ doubles x """ return 2*x def dblPR(x): """ doubles x """ print 2*x >>> dbl(21) 42 return provides the function call's value … print just prints >>> 2 + dbl(21) 44 >>> 2 + dbl(21) crash!

32. How functions act >>> yours = undo('caf') >>> mine = undo(undo('caf')) def undo(s): """ undo undoes its input! input: s, any string """ return 'de' + s strings, lists, numbers … all data are fair game My brain has just hit recursophobic collapse!

33. How functions work… def f(x): return 11*g(x) + g(x/2) What is demo(-4) ? def demo(x): return x + f(x) def g(x): return -1 * x This puts the fun in function!

34. How functions work… def f(x): return 11*g(x) + g(x/2) >>> demo(-4) ? def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) def g(x): return -1 * x

35. How functions work… def f(x): return 11*g(x) + g(x/2) def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f x = -4 return 11*g(x) + g(x/2) def g(x): return -1 * x >>> demo(-4) ?

36. How functions work… def f(x): return 11*g(x) + g(x/2) def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f x = -4 return 11*g(x) + g(x/2) def g(x): return -1 * x These are different x 's ! >>> demo(-4) ?

37. How functions work… def f(x): return 11*g(x) + g(x/2) def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f g x = -4 return 11*g(-4) + g(-4/2) x = -4 return -1.0 * x def g(x): return -1 * x >>> demo(-4) ?

38. How functions work… def f(x): return 11*g(x) + g(x/2) def g(x): return -1 * x def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f g x = -4 return 11* 4 + g(-4/2) x = -4 return -1 * -4 4 >>> demo(-4) ?

39. How functions work… def f(x): return 11*g(x) + g(x/2) def g(x): return -1.0 * x def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f x = -4 return 11* 4 + g(-4/2) >>> demo(-4) ?

40. How functions work… def f(x): return 11*g(x) + g(x/2) def g(x): return -1 * x def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f g x = -4 return 11* 4 + g(-4/2) x = -2 return -1 * -2 2 >>> demo(-4) ?

41. How functions work… def f(x): return 11*g(x) + g(x/2) def g(x): return -1.0 * x def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f x = -4 return 11* 4 + 2 >>> demo(-4) ?

42. How functions work… def f(x): return 11*g(x) + g(x/2) def g(x): return -1.0 * x def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f x = -4 return 11* 4 + 2 46 >>> demo(-4) ?

43. How functions work… def f(x): return 11*g(x) + g(x/2) def g(x): return -1.0 * x def demo(x): return x + f(x) demo x = -4 return -4 + 46 42 >>> demo(-4) 42

44. Douglas Adams's 42 puzzle answer: 42 question: unknown

45. Function stacking def f(x): return 11*g(x) + g(x/2) def g(x): return -1 * x def demo(x): return x + f(x) demo x = -4 return -4 + f(-4) f g x = -4 return 11* 4 + g(-4/2) x = -2 return -1 * -2 2 "The stack" (1) remembers separate functions' values for variables… (2) remembers where to send results back to… >>> demo(-4) 42

46. Function design

47. Thinking sequentially 5! = 5 * 4 * 3 * 2 * 1 N! = N * (N-1) * (N-2) * … * 3 * 2 * 1 factorial 5! = 120

48. Thinking sequentially 5! = 5 * 4 * 3 * 2 * 1 N! = N * (N-1) * (N-2) * … * 3 * 2 * 1 factorial 5! = 120 Next time & beyond…

49. Recursion == self-reference! Thinking recursively 5! = 5 * 4 * 3 * 2 * 1 N! = N * (N-1) * (N-2) * … * 3 * 2 * 1 factorial 5! = 120 5! = N! =

50. Warning def fac(N): return N * fac(N-1) This is legal code! I wonder how this code will STACK up!?

51. def fac(N): return N * fac(N-1) No base case -- the calls to fac will never stop! Make sure you have a base case, then worry about the recursive step... Warning

52. def fac(N): return fac(N) Roadsigns and recursion examples of self-fulfilling danger

54. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) Base Case Recursive Step Thinking recursively ! Human: Base case and 1 stepComputer: Everything else

55. Behind the curtain… def fac(N): if N <= 1: return 1 else: return N * fac(N-1) >>> fac(1) Result: 1 The base case is No Problem!

56. Behind the curtain… def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5)

57. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) Behind the curtain…

58. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * fac(3) Behind the curtain…

59. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * fac(3) 3 * fac(2) Behind the curtain…

60. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * fac(3) 3 * fac(2) 2 * fac(1) Behind the curtain…

61. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * fac(3) 3 * fac(2) 2 * fac(1) 1 "The Stack" Remembers all of the individual calls to fac Behind the curtain…

62. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * fac(3) 3 * fac(2) 2 * 1 Behind the curtain…

63. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * fac(3) 3 * 2 Behind the curtain…

64. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * fac(4) 4 * 6 Behind the curtain…

65. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) 5 * 24 Behind the curtain…

66. def fac(N): if N <= 1: return 1 else: return N * fac(N-1) fac(5) Result: 120 0 N*** -> X 1 0 x*** -> N 0 Look familiar? Base Case Recursive Step Behind the curtain…

67. 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 ! Let recursion do the work for you.

68. But you do need to do one step yourself… def fac(N): if N <= 1: return 1 else: return fac(N) You handle the base case – the easiest possible case to think of! This will not work

69. Recursion's Big Picture? Need to see BOTH the self-similar piece AND the whole simultaneously!

71. Breaking Up… …is easy to do with Python s = "This has 2 T's" How do we get at the initial character of s? L = [ 42, 21, 7 ] How do we get at the initial element of L? How do we get at ALL THE REST of s? How do we get at ALL the REST of L?

72. Recursion Examples def mylen(s): """ input: any string, s output: the number of characters in s """ if : else: base case test!

73. Recursion Examples def mylen(s): """ input: any string, s output: the number of characters in s """ if s == '': return 0 else: rest = s[1:] len_of_rest = mylen( rest ) total_len = 1 + len_of_rest return total_len

74. Recursion Examples def mylen(s): """ input: any string, s output: the number of characters in s """ if s == '': return 0 else: rest = s[1:] len_of_rest = mylen( rest ) return 1 + len_of_rest

75. Recursion Examples def mylen(s): """ input: any string, s output: the number of characters in s """ if s == '': return 0 else: rest = s[1:] return 1 + mylen( rest )

76. Recursion Examples def mylen(s): """ input: any string, s output: the number of characters in s """ if s == '': return 0 else: return 1 + mylen(s[1:]) There's not much len left here!

77. Recursion Examples def mymax(L): """ input: a NONEMPTY list, L output: L's maximum element """ if : elif : else: base case test! another case…

78. Recursion Examples def mymax(L): """ input: a NONEMPTY list, L output: L's maximum element """ if len(L) == 1: return L[0] elif L[0] < L[1]: return mymax( L[1:] ) else: return mymax( L[0:1] + L[2:] ) Hey - do I get a slice?!

79. Try it! def power(b,p): """ returns b to the p power using recursion, not ** inputs: int b, int p output: a float """ power(5,2) == 25.0 def sajak(s): sajak('wheel of fortune') == 6 What seven-letter English word w maximizes sajak( w ) ? What about y ? You decide… """ returns the number of vowels in the input string, s """ Want more Pat? if : Base case test elif else: Base case test else: Remember: b p == b * b p-1

80. >>> 3*'i' in 'alien' False The in thing >>> 'i' in 'team' False >>> 'cs' in 'physics' True >>> 'sleep' not in 'CS 5' True >>> 42 in [41,42,43] True >>> 42 in [ [42], '42' ] ?? python is badly confused here… but otherwise it seems pretty perceptive! a little bit different for lists… What’s out here?

81. def sajak(s): if len(s) == 0: return 0 elif s[0] in 'aeiou': return 1 + sajak(s[1:]) else: return sajak(s[1:]) if it is NOT a vowel, the answer is just the number of vowels in the rest of s if it IS a vowel, the answer is 1 + the number of vowels in the rest of s Base Case Rec. Steps

82. Good luck with Homeworks #0 and #1 ! The key to understanding recursion is to first understand recursion… - advice from one of last year's students

83. def power(b,p): """ inputs: base b and power p (an int) implements: b**p """ if p == 0: return else: return Recursion is power!

84. behind the curtain power(2,3)

85. def sajak(s): Base case? when there are no letters, there are ZERO vowels if it is NOT a vowel, the answer is Rec. step? Look at the initial character. if it IS a vowel, the answer is

86. def sajak(s): Base case? when there are no letters, there are ZERO vowels if it is NOT a vowel, the answer is just the number of vowels in the rest of s Rec. step? Look at the initial character. if it IS a vowel, the answer is 1 + the number of vowels in the rest of s

87. def sajak(s): if s == '': return 0 elif s[0]=='a' or s[0]=='e' or… Checking for a vowel: Try #1 Base Case

88. sajak('eerier') behind the curtain

89. Recursion: not just numbers Relationships Self-similarity elsewhere... Natural phenomena Names / Acronyms What is an “ancestor” ? how much here is leaf vs. stem? GNU == "GNU’s Not Unix"

90. Recursion: not just numbers Relationships Self-similarity elsewhere... Natural phenomena Names / Acronyms What is an “ancestor” ? GNU all stem! An ancestor is a parent OR an ancestor of a parent… == GNU’s Not Unix

91. Can all information be represented using lists ? Networks Images/Video Sounds/Speech { 2, 3, 5, 7, 11 } Data and lists? ‘Many years later, as he faced the firing squad, Colonel Aureliano Buendia was to remember that distant afternoon when his father took him to discover ice.’ Text Sets Ideas? "sequences"

92. crazy recursion…

93. Recursion is the root of all computation since it trades description for time. - Alan Perlis Recursion is the secret to all happiness in writing short, powerful functional programs!

94. Monty Hall Let’s make a deal ’63-’86 Sept. 1990 inspiring the “Monty Hall paradox”

95. Problem #2: montyhall() Write a program that plays the part of Monty…

96. while we're here… import random comp = random.choice( range(0,100) ) while True: user = input('Your choice: ') print user, '?' if user == comp: print 'Yes!' break else: print 'No...'

97. "Quiz" on recursion def power(b,p):def sajak(s): sajak('wheel of fortune') == 6 What five-letter English word w maximizes sajak( w ) ? Names: What about y ? You decide… Handle negative values of p, as well. """ returns the number of vowels in the input string, s """ """ returns b to the p power using recursion and not ** inputs: b and p are ints output: should be a float """ Want more Pat? Want more power ? power(5,2) == 25.0 For example, power(5,-1) == 0.2 (or so)

98. Any real computing with strings/lists? Some strings are more equal than others…

99. Our DNA's nucleotides: DNA http://genome.ucsc.edu/cgi-bin/hgGateway AGCT

100. Genetic disease expression CTG repeats Myotonic Dystrophy neuromuscular weakness in the face/torso in the 3' UTR (three prime untranslated region), a particular section of messenger RNA DNA "Christmas Tree cataracts" Its computational basis www.neuro.wustl.edu/neuromuscular/musdist/pe-eom.html#myd

101. One sequence-checking algorithm… def check(geneseq): """ seeks evidence of Myo. Dys. """ if 'ctg'*50 in geneseq: return True else: return False Why problems might this algorithm run into? What if we hadn't discovered the CTG-repeats yet? Can we make this algorithm more concise? What information might we prefer to know? checks if one string is contained in another

102. One sequence-checking algorithm… def check(geneseq): """ seeks evidence of Myo. Dys. """ if 'ctg'*50 in geneseq: return 'Trouble' elif 'ctg'*500 in geneseq : return 'BIG Trouble' else: return "You're OK!" Will this work as a two-diagnosis system? Or is something awry?

103. One sequence-checking algorithm… def check(geneseq): """ seeks evidence of Myo. Dys. """ if 'ctg'*500 in geneseq: return 'BIG Trouble' elif 'ctg'*50 in geneseq : return 'Trouble' else: return "You're OK!" Feeling much better! most constrained least constrained

104. Any real computing with strings/lists? Some strings are more equal than others…

105. Our DNA's nucleotides: DNA http://genome.ucsc.edu/cgi-bin/hgGateway AGCT

106. Genetic disease expression CTG repeats Myotonic Dystrophy neuromuscular weakness in the face/torso in the 3' UTR (three prime untranslated region), a particular section of messenger RNA DNA "Christmas Tree cataracts" Its computational basis www.neuro.wustl.edu/neuromuscular/musdist/pe-eom.html#myd

107. One sequence-checking algorithm… def check(geneseq): """ seeks evidence of Myo. Dys. """ if 'ctg'*50 in geneseq: return True else: return False Why problems might this algorithm run into? What if we hadn't discovered the CTG-repeats yet? Can we make this algorithm more concise? What information might we prefer to know? checks if one string is contained in another

108. Functioning in Python Some basic, built-in functions: abs max min sum range round bool float int long list str these change data from one type to another absolute value of lists creates lists only as accurately as it can! help dir These are the most important: You call that a language?!

109. Functioning in Python Far more are available in separate files, or modules: import math math.sqrt( 1764 ) dir(math) from math import * pi sin( pi/2 ) accesses math.py 's functions lists all of math.py 's functions same, but without typing math. all of the time… help() help modules

110. Functioning in Python This doesn't look quite right… # my own function! def dbl( x ): """ returns double its input, x """ return 2x

111. Functioning in Python # my own function! def dbl( x ): """ returns double its input, x """ return 2*x

112. # my own function! def dbl( x ): """ returns double its input, x """ return 2*x Functioning in Python Comments Docstrings (1)describes overall what the function does, and (2)explains what the inputs mean/are They become part of python's built-in help system! With each function be sure to include one that They begin with # keywords def starts the function return stops it immediately and sends back the return value Some of Python's baggage…

113. Functioning in Python >>> yours = undo('caf') >>> mine = undo(undo('caf')) def undo(s): """ this "undoes" its input, s """ return 'de' + s strings, lists, numbers … all data are fair game