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EECS 110: Lec 8: Lists of Lists

EECS 110: Lec 8: Lists of Lists. Aleksandar Kuzmanovic Northwestern University. http://networks.cs.northwestern.edu/EECS110-s14/. EECS 110 t o d a y. Hw #3 due Sunday…. Computing with language. hw3pr1.py. Computing with images. 'Krphzrun 3, Sureohp 3: Wkh Fhdvdu Flskhu'. hw3pr2.py.

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EECS 110: Lec 8: Lists of Lists

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  1. EECS 110: Lec 8: Lists of Lists Aleksandar Kuzmanovic Northwestern University http://networks.cs.northwestern.edu/EECS110-s14/

  2. EECS 110 today Hw #3 due Sunday… Computing with language hw3pr1.py Computing with images 'Krphzrun 3, Sureohp 3: Wkh Fhdvdu Flskhu' hw3pr2.py hw3pr3.py

  3. Sorting a List Sorting a List What is the input/output of the function? What data do we need to keep track of?

  4. Sorting a List Sorting a List If we had an easy way to find the maximum of the list, how could we use this to sort the list?

  5. Taking only one… def removeOne( e, L ): """ this function removes one element e from the top level of the list L """ if len(L) == 0: return L # L is empty elif e == L[0]: return L[1:] # remove this one else: return L[0:1] + removeOne(e,L[1:]) # keep the non-e element and then keep going removeOne(42, [5,7,42,8,42]) removeOne('p', 'computer programming') 'comuter programming' [5,7,8,42]

  6. sort(L) def sort( L ): """ a list of elements in L, sorted from hi to low """ if len(L) < 1: return L else:

  7. sort(L) def sort( L ): """ a list of elements in L, sorted from hi to low """ if len(L) < 1: return L else: return [max(L)] + sort(removeOne( max(L), L ))

  8. sort(L, maxFun) def sort( L, maxFun ): """ a list of elements in L, sorted using maxFun """ if len(L) < 1: return L else: return

  9. sort(L, maxFun) def sort( L, maxFun ): """ a list of elements in L, sorted using maxFun """ if len(L) < 1: return L else: return [maxFun(L)] + sort(removeOne( maxFun(L), L )) Will this work?

  10. sort(L, maxFun) def sort( L, maxFun ): """ a list of elements in L, sorted using maxFun """ if len(L) < 1: return L else: return [maxFun(L)] + sort(removeOne( maxFun(L), L ), maxFun)

  11. sort(L, maxFun) def sort( L, maxFun ): """ a list of elements in L, sorted using maxFun """ if len(L) < 1: return L else: return [maxFun(L)] + sort(removeOne( maxFun(L), L ), maxFun) What happens if you call >>>sort( L, min )

  12. Lights On! http://www.whitman.edu/mathematics/lights_out/

  13. Comprehending List Comprehensions defrunGenerations( L ): """ runGenerations keeps running evolve... """ print( L ) # display the list, L time.sleep(0.5) # pause a bit newL = evolve( L ) # evolve L into newL runGenerations( newL ) # recurse defevolve( L ): """ evolve takes in a list of integers, L, and returns a new list of integers considered to be the "next generation" """ N = len(L) # N now holds the size of the list L return [ setNewElement( L, i ) for i inrange(N) ] defsetNewElement( L, i, x=0 ): """ setNewElement returns the NEW list's ith element input L: any list of integers input i: the index of the new element to return input x: an extra, optional input for future use """ return L[i] + 1

  14. Comprehending List Comprehensions defevolve( L ): """ evolve takes in a list of integers, L, and returns a new list of integers considered to be the "next generation" """ N = len(L) # N now holds the size of the list L return [ setNewElement( L, i ) for i inrange(N) ] defsetNewElement( L, i, x=0 ): """ setNewElement returns the NEW list's ith element input L: any list of integers input i: the index of the new element to return input x: an extra, optional input for future use """ return L[i] + 1 >>> L = [42, 43, 44, 45, 46] >>> evolve(L) L 42 43 44 45 46 47 0 1 2 3 4 5 N 5 (i.e., len(L))

  15. Comprehending List Comprehensions defevolve( L ): """ evolve takes in a list of integers, L, and returns a new list of integers considered to be the "next generation" """ N = len(L) # N now holds the size of the list L return [ setNewElement( L, i ) for i inrange(N) ] defsetNewElement( L, i, x=0 ): """ setNewElement returns the NEW list's ith element input L: any list of integers input i: the index of the new element to return input x: an extra, optional input for future use """ return L[i] + 1 [42, 43, 44, 45, 46] L 0 1 2 3 4 >>> L = [42, 43, 44, 45, 46] >>> evolve(L) N 5 (i.e., len(L)) [ setNewElement( L, i ) for i inrange(5) ] [0, 1, 2, 3, 4] [ , , , , ] i 0 1 2 3 4

  16. Comprehending List Comprehensions defevolve( L ): """ evolve takes in a list of integers, L, and returns a new list of integers considered to be the "next generation" """ N = len(L) # N now holds the size of the list L return [ setNewElement( L, i ) for i inrange(N) ] defsetNewElement( L, i, x=0 ): """ setNewElement returns the NEW list's ith element input L: any list of integers input i: the index of the new element to return input x: an extra, optional input for future use """ return L[i] + 1 [[42, 43], [44, 45]] L 0 1 >>> L = [[42, 43], [44, 45]] >>> evolve(L) [[43, 44], [45, 46]] N 2 (i.e., len(L)) [ setNewElement( L, i ) for i inrange(2) ] What is i? What is L[i]?

  17. Comprehending List Comprehensions defevolve( L ): """ evolve takes in a list of integers, L, and returns a new list of integers considered to be the "next generation" """ N = len(L) # N now holds the size of the list L return [ setNewElement( L, i ) for i inrange(N) ] defsetNewElement( L, i, x=0 ): """ setNewElement returns the NEW list's ith element input L: any list of integers input i: the index of the new element to return input x: an extra, optional input for future use """ return L[i] + 1 Going deeper [[42, 43], [44, 45]] L 0 1 >>> L = [[42, 43], [44, 45]] >>> evolve(L) [[43, 44], [45, 46]] N 2 (i.e., len(L)) [ setNewElement( L, i ) for i inrange(2) ] What is i? What is L[i]?

  18. Comprehending List Comprehensions [ L[j][0] for j inrange(2) ] [[42, 43], [44, 45]] L [ [L[0][i]] for i inrange(2) ] [ [ L[j][i]+1 for i inrange(2) ] for j inrange(2) ]

  19. Comprehending List Comprehensions [[42, 43], [44, 45]] L [ setNewElement2d( L, i, j ) for i inrange(2) ] for j inrange(2) ] defsetNewElement2d( L, i, j, x=0, y=0 ): """ setNewElement returns the NEW list's ith element input L: any list of integers input i: the index of the new element to return input x: an extra, optional input for future use """ return L[j][i] + 1

  20. Representing Pictures

  21. Digital representations of pictures Grid of Pixels—each Pixel has a color But how is color represented?

  22. RGB Model for Representing Color • Most popular, but not only one • Each pixel represented in three parts (100, 0, 0) R G B So every Pixel has some amount of Red some amount of Green and some amount of Blue HOW MUCH?

  23. Color “levels” • Each color component or “channel” is represented with a single byte • 1 byte = 8 bits; which can represent numbers from 0 to 255 (2^8 – 1) • Each RGB value is between 0 and 255 • Examples… http://www.colorschemer.com/online.html http://www.drpeterjones.com/colorcalc/ (255, 255, 255): white (150, 150, 150): gray

  24. Brightening a Picture defmodify(pic): """ modify modifies an image to make it brighter """ pixels = getPixels(pic) if len(pixels) == 0: return newPixels = [ [setNewPixel( pixels, row, col ) for col in range(len(pixels[0]))] for row in range(len(pixels))] setPixels(pic, newPixels) defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW imanges (row, col) (r,g,b) value input pixels: a 2D list containing RGB information in the pixels in a picture input row: the row of the pixel in question input col: the column of the pixel in question """ rval= min(pixels[row][col][0]+30, 255) gval = min(pixels[row][col][1]+30, 255) bval = min(pixels[row][col][2]+30, 255) return (rval, gval, bval)

  25. Representing the Pixels in a Picture pixels: [ [(3, 10, 100), (3, 11, 110)], [(3, 10, 200), (10, 110, 290)] ] • Width: len(pixels[0]) • Height: len(pixels) 2x2 pixel image

  26. Tuples vs. Lists [ [(3, 10, 100), (3, 11, 110)], [(3, 10, 200), (10, 110, 290)] ] Tuples use ( ); lists use [ ] But otherwise, they are the same… (for now, almost) >>> t = (1, 2, 3) >>> t[1] 2 >>> t[1:] (2, 3) >>> (x, y, z) = t >>> x 1 >>> y 2

  27. Brightening a Picture defmodify(pic): """ modify modifies an image to make it brighter """ pixels = getPixels(pic) if len(pixels) == 0: return newPixels = [ [setNewPixel( pixels, row, col ) for col in range(len(pixels[0]))] for row in range(len(pixels))] setPixels(pic, newPixels) defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW imanges (row, col) (r,g,b) value input pixels: a 2D list containing RGB information in the pixels in a picture input row: the row of the pixel in question input col: the column of the pixel in question """ rval= min(pixels[row][col][0]+30, 255) gval = min(pixels[row][col][1]+30, 255) bval = min(pixels[row][col][2]+30, 255) return (rval, gval, bval)

  28. "Quiz“ Name(s): It's all clear to me now! Write a function that tints the top half of the picture red (how red is up to you): defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW image's (row, col) (r,g,b) value """ Write a function that copies the top half of an image to the bottom half. defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW image's (row, col) (r,g,b) value """ Want more? How would you turn only the sky red?

  29. "Quiz“ Name(s): It's all clear to me now! Write a function that tints the top half of the picture red (how red is up to you): defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW image's (row, col) (r,g,b) value """ if row <= len(pixels)//2: rval = min(pixels[row][col][0]+75,255) else: rval = pixels[row][col][0] return (rval, pixels[row][col][1], pixels[row][col][2]) Write a function that copies the top half of an image to the bottom half. defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW image's (row, col) (r,g,b) value """ Want more? How would you turn only the sky red?

  30. "Quiz“ Name(s): It's all clear to me now! Write a function that tints the top half of the picture red (how red is up to you): defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW image's (row, col) (r,g,b) value """ if row <= len(pixels)//2: rval = min(pixels[row][col][0]+75,255) else: rval = pixels[row][col][0] return (rval, pixels[row][col][1], pixels[row][col][2]) Write a function that copies the top half of an image to the bottom half. defsetNewPixel( pixels, row, col ): """ setNewPixel returns the NEW image's (row, col) (r,g,b) value """ if row > len(pixels)//2: return pixels[row-len(pixels)//2][col] else: return pixels[row][col] Want more? How would you turn only the sky red?

  31. returns returns returns returns returns returns returns Caesar Cipher: encipher 'gv vw dtwvg' 'hw wx euxwh' 'ix xy fvyxi' 'jy yz gwzyj' 'kz za hxazk' 'la ab iybal' encipher( 'gv vw dtwvg' , 0 ) encipher( 'gv vw dtwvg' , 1 ) encipher( 'gv vw dtwvg' , 2 ) encipher( 'gv vw dtwvg' , 3 ) encipher( 'gv vw dtwvg' , 4 ) … encipher( 'gv vw dtwvg' , 5 ) 'fu uv csvuf' encipher( 'gv vw dtwvg' , 25 ) should return the string s with each alphabetic character shifted/wrapped by n places in the alphabet encipher( S , n )

  32. How Strings are Represented and Stored? American Standard Code for Information Interchange ASCII is a table that tells the computer how to represent characters as bits! value: '*' 00101010 bits type:str name: Identical bits are stored in each variable! 8 bits = 1 byte The types determine how to interpret the bits; the names don't matter at all… value: 42 00101010 The SAME bits represent integers, if the variable has type int instead of str bits type:int name:

  33. ASCII American Standard Code for Information Interchange ASCII is a table that tells the computer how to represent characters as #s chr convert to char. convert to number ord

  34. chr and ord abcdefghijklmnopqrstuvwxyz ASCII VALUES 97 99 101 103 105 107 109 111 113 115 117 119 122 ABCDEFGHIJKLMNOPQRSTUVWXYZ 65 67 69 71 73 75 77 79 81 83 85 87 90 Input: a string of one character, c ord( c ) Output: an integer, the ASCII value of c CONVERTERS Input: an integer in range(255) chr( n ) Output: a one-char. string of that ASCII value [ [i,chr(i)] for i in range(128) ] try these! [ ord(i) for i in '**** CS! ****' ]

  35. chr and ord abcdefghijklmnopqrstuvwxyz ASCII VALUES 97 99 101 103 105 107 109 111 113 115 117 119 122 ABCDEFGHIJKLMNOPQRSTUVWXYZ 65 67 69 71 73 75 77 79 81 83 85 87 90 ord('a') is ? chr(66) is ? What ischr( ord('i')+13 ) ? What ischr( ord('P')+13 ) ?

  36. chr and ord abcdefghijklmnopqrstuvwxyz ASCII VALUES 97 99 101 103 105 107 109 111 113 115 117 119 122 ABCDEFGHIJKLMNOPQRSTUVWXYZ 65 67 69 71 73 75 77 79 81 83 85 87 90 ord('a') is 97 chr(66) is ? What ischr( ord('i')+13 ) ? What ischr( ord('P')+13 ) ?

  37. chr and ord abcdefghijklmnopqrstuvwxyz ASCII VALUES 97 99 101 103 105 107 109 111 113 115 117 119 122 ABCDEFGHIJKLMNOPQRSTUVWXYZ 65 67 69 71 73 75 77 79 81 83 85 87 90 ord('a') is 97 chr(66) is 'B' What ischr( ord('i')+13 ) ? What ischr( ord('P')+13 ) ?

  38. chr and ord abcdefghijklmnopqrstuvwxyz ASCII VALUES 97 99 101 103 105 107 109 111 113 115 117 119 122 ABCDEFGHIJKLMNOPQRSTUVWXYZ 65 67 69 71 73 75 77 79 81 83 85 87 90 ord('a') is 97 chr(66) is 'B' What ischr( ord('i')+13 )'v' What ischr( ord('P')+13 ) ?

  39. chr and ord abcdefghijklmnopqrstuvwxyz ASCII VALUES 97 99 101 103 105 107 109 111 113 115 117 119 122 ABCDEFGHIJKLMNOPQRSTUVWXYZ 65 67 69 71 73 75 77 79 81 83 85 87 90 ord('a') is 97 chr(66) is 'B' What ischr( ord('i')+13 )'v' What ischr( ord('P')+13 ) ']' How can we wrap this around?

  40. Rot 13 def adv13( c ): """ rotates c by 13 chars, "wrapping" as needed NON-LETTERS DO NOT CHANGE! """ if'a' <= c <= 'z': neword = ord(c) + 13 if neword <= ord('z'): return chr(neword) # no wrapping else: return elif else: How would you rotate an entire string?

  41. Rot 13 def adv13( c ): """ rotates c by 13 chars, "wrapping" as needed NON-LETTERS DO NOT CHANGE! """ if'a' <= c <= 'z': neword = ord(c) + 13 if neword <= ord('z'): return chr(neword) # no wrapping else: returnchr(ord('a')+neword-ord('z')-1) elif else: How would you rotate an entire string?

  42. Rot 13 def adv13( c ): """ rotates c by 13 chars, "wrapping" as needed NON-LETTERS DO NOT CHANGE! """ if'a' <= c <= 'z': neword = ord(c) + 13 if neword <= ord('z'): return chr(neword) # no wrapping else: returnchr(ord('a')+neword-ord('z')-1) elif 'A' <= c <= 'Z': # same as above, only use 'A' and 'Z' else: return c How would you rotate an entire string?

  43. Caesar Cipher: decipher >>> decipher('Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.') 'Caesar cipher? I prefer Caesar salad.' >>> decipher('Hu lkbjhapvu pz doha ylthpuz hmaly dl mvynla '\ 'lclyfaopun dl ohcl slhyulk.') 'An education is what remains after we forget everything we have learned.' >>> decipher('gv vw dtwvg') >>> decipher('Uifz xpsl ju pvu xjui b qfodjm!') But how ?

  44. Caesar Cipher: decipher gv vw dtwvg hw wx euxwh ix xy fvyxi jy yz gwzyj kz za hxazk la ab iybal mb bc jzcbm nc cd kadcn od de lbedo pe ef mcfep qf fg ndgfq rg gh oehgr sh hi pfihs ti ij qgjit uj jk rhkju vk kl silkv wl lm tjmlw xm mn uknmx yn no vlony zo op wmpoz ap pq xnqpa bq qr yorqb cr rs zpsrc ds st aqtsd et tu brute fu uv csvuf Caesar Brutus >>> decipher('gv vw dtwvg') Strategy using max: (1) consider all possible answers (2) give them each a score (3) use our techniques to get max Score for "Englishness"? up to you… all 26 possibilities

  45. Caesar Cipher: decipher [0, 'cr rs zpsrc'] [0, 'gv vw dtwvg'] [0, 'jy yz gwzyj'] [0, 'mb bc jzcbm'] [0, 'qf fg ndgfq'] [0, 'wl lm tjmlw'] [1, 'bq qr yorqb'] [1, 'ds st aqtsd'] [1, 'nc cd kadcn'] [1, 'vk kl silkv'] [1, 'xm mn uknmx'] [2, 'ap pq xnqpa'] [2, 'hw wx euxwh'] [2, 'ix xy fvyxi'] [2, 'kz za hxazk'] [2, 'rg gh oehgr'] [2, 'sh hi pfihs'] [2, 'uj jk rhkju'] [2, 'yn no vlony'] [3, 'fu uv csvuf'] [3, 'pe ef mcfep'] [3, 'ti ij qgjit'] [3, 'zo op wmpoz'] [4, 'et tu brute'] [4, 'la ab iybal'] [4, 'od de lbedo'] Caesar Brutus >>> decipher('gv vw dtwvg') 'od de lbedo' Strategy using max: (1) consider all possible answers (2) give them each a score (3) use our techniques with max number-of-vowels score won't always be correct! all 26 possibilities

  46. Caesar Cipher: decipher [0.4680, 'jy yz gwzyj'] [0.4960, 'mb bc jzcbm'] [0.5420, 'uj jk rhkju'] [0.5567, 'ix xy fvyxi'] [0.5597, 'qf fg ndgfq'] [0.5718, 'fu uv csvuf'] [0.5753, 'bq qr yorqb'] [0.5833, 'kz za hxazk'] [0.5859, 'xm mn uknmx'] [0.5880, 'gv vw dtwvg'] [0.5902, 'vk kl silkv'] [0.6110, 'ap pq xnqpa'] [0.6304, 'zo op wmpoz'] [0.6318, 'wl lm tjmlw'] [0.6717, 'cr rs zpsrc'] [0.6735, 'hw wx euxwh'] [0.6963, 'nc cd kadcn'] [0.7153, 'ti ij qgjit'] [0.7398, 'la ab iybal'] [0.7442, 'yn no vlony'] [0.7867, 'pe ef mcfep'] [0.7880, 'sh hi pfihs'] [0.7918, 'rg gh oehgr'] [0.8213, 'ds st aqtsd'] [0.8609, 'od de lbedo'] [0.9082, 'et tu brute'] Caesar Brutus >>> decipher('gv vw dtwvg') 'et tu brute' Strategy using max: (1) consider all possible answers (2) give them each a score (3) use our techniques with max letter- probability score not always correct, but better! all 26 possibilities

  47. 'Weet bksa ed Xecumeha 3!'

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