Programmeren IK 2019 Jelle van Assema Vorige week Jupyter - - PowerPoint PPT Presentation

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programmeren ik 2019

Programmeren IK 2019 Jelle van Assema Vorige week Jupyter - - PowerPoint PPT Presentation

Feb 28, 2024 674 likes •1.66k views

Programmeren IK 2019 Jelle van Assema Vorige week Jupyter Notebook Comprehensions File IO Deze week Oefenen met alles Python Constructieve zoekalgoritmes Recursie Wachtwoord kraken 10 x 10 x 26 x 26 x 26 x 10

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SLIDE 1

Programmeren IK 2019

Jelle van Assema

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SLIDE 2

Vorige week

Jupyter Notebook
Comprehensions
File IO

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SLIDE 3

Deze week

Oefenen met alles Python
Constructieve zoekalgoritmes
Recursie

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SLIDE 4

Wachtwoord kraken

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SLIDE 5

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SLIDE 6

10 x 10 x 26 x 26 x 26 x 10 17,576,000

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SLIDE 7

Een wachtwoord van 10 tekens, bestaande uit:

Letters (groot en klein)
Cijfers
De tekens: ! , .

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SLIDE 8

Een wachtwoord van 10 tekens, bestaande uit:

Letters (groot en klein)
Cijfers
De tekens: ! , .

(26 + 26 + 10 + 3)10 1.3462743 * 1018

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SLIDE 9

Een wachtwoord van 10 tekens kraken?

Bij 1 miljard wachtwoorden per seconde: (1.3462743 * 1018) / 109 = 1.3462743 * 109 seconden 373965 uur 42.69 jaar

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SLIDE 10

Een wachtwoord van 10 tekens kraken?

Wachtwoorden zijn vaak niet willekeurig. In praktijk:

Patronen
Dictionary attacks
0000

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SLIDE 11

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SLIDE 12

Sudoku’s

Een bord van 9 x 9, met elk op vakje 9 mogelijkheden

981 1.9662705 * 1077

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SLIDE 13

1.9662705 * 1077 It is estimated that there are between 1078 to 1082 atoms in the known,

bservable universe.

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SLIDE 14

1.9662705 * 1077 6,670,903,752,021,072,936,9 60 / (2.9475324 * 1055)

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SLIDE 15

Sudoku’s oplossen

Probleemgrootte is maar een fractie van:

6,670,903,752,021,072,936,960

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SLIDE 16

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SLIDE 17

Sudoku’s oplossen

51 lege vakjes
951 mogelijkheden toch?
Dat zijn 6.9531773 * 1026 keer zoveel mogelijkheden

dan er sudoku’s bestaan

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SLIDE 18

Sudoku’s oplossen

51 lege vakjes
Naïeve manier van oplossen
Manier voor doorzoeken met enkel geldige sudoku’s.

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SLIDE 19

Constructief oplossen

Een opbouwende manier van

gestructureerd zoeken

Naïeve manier van oplossen
Manier voor doorzoeken met enkel geldige sudoku’s.

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SLIDE 20

Constructief oplossen

Een opbouwende manier van

gestructureerd zoeken

Naïeve manier van oplossen
Manier voor doorzoeken met enkel geldige sudoku’s.

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SLIDE 21

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SLIDE 22

1

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SLIDE 23

Breadth-First Search (BFS)

1 2 4

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SLIDE 24

Breadth-First Search (BFS)

1 2 4 1 2 4 1 2 4

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SLIDE 25

Breadth-First Search (BFS)

1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4

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SLIDE 26

Depth-First Search (DFS)

1 2 4

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SLIDE 27

Depth-First Search (DFS)

1 2 4 1 2 4 1 2 4

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SLIDE 28

DFS BFS

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SLIDE 29

Wachtwoord kraken

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SLIDE 30

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

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SLIDE 31

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

V

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SLIDE 32

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V

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SLIDE 33

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V

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SLIDE 34

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V

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SLIDE 35

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V

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SLIDE 36

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 1

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SLIDE 37

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 1 W

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SLIDE 38

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 1 W

1

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SLIDE 39

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 1 W

1

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SLIDE 40

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 1 W

1 1

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SLIDE 41

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 2 W

1 1

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SLIDE 42

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 2 W

1

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SLIDE 43

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 2 W

1 2

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SLIDE 44

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 2 W

1 2

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SLIDE 45

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 2 W

1 2 2

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SLIDE 46

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2 2

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SLIDE 47

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2

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SLIDE 48

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2 4

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SLIDE 49

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2 4

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SLIDE 50

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2 4 4

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SLIDE 51

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2 4 4

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SLIDE 52

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 4 W

1 2 4 4

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SLIDE 53

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 7 W

1 2 47 4 43 7 4

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DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 7 W

1 2 47 47 43

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SLIDE 55

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 7 W

1 2 47 47 43

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SLIDE 56

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 7 W

1 2 47 43

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SLIDE 57

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 7 W

1 2 47 43

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SLIDE 58

DFS algoritme

1 function DFS(V) 2 let S be a stack 3 S.push(V) 4 while S is not empty 5 V = S.pop() 6 for all candidates C from V do 7 let W be a copy of V 8 apply C to W 9 if W is a solution do 10 return W 11 S.push(W)

S V C 7 W

1 47 2

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SLIDE 59

DFS algoritme

Eerst de diepte in
Kom je niet verder, backtracken!

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SLIDE 60

Recursie

Een functie die zichzelf aanroept

def forever(): print(“hello”) forever()

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SLIDE 61

Recursie

Basecase
Reductiestap

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Is een getal even?

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SLIDE 63

Is een getal even?

0 is een even getal => true 1 is een oneven getal => false

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SLIDE 64

Is een getal even?

0 is een even getal => true 1 is een oneven getal => false is_even(n) = is_even(n - 2)

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SLIDE 65

Recursie, is een getal even?

def even(n): if n == 0: return True if n == 1: return False return even(n - 2)

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SLIDE 66

Recursie, binary search

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SLIDE 67

Recursie, binary search

naald gevonden => true niks meer te doorzoeken => false

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SLIDE 68

Recursie, binary search

naald gevonden => true niks meer te doorzoeken => false needle < midden? doorzoek linkerhelft needle > midden? Doorzoek rechterhelft

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SLIDE 69

Recursie, binary search

def binary_search(numbers, n): if len(numbers) == 0: return False mid = len(numbers) // 2 if numbers[mid] == n: return True ...

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SLIDE 70

Recursie, binary search

def binary_search(numbers, n): if len(numbers) == 0: return False mid = len(numbers) // 2 if numbers[mid] == n: return True if numbers[mid] > n: return binary_search(numbers[:n]) else: return binary_search(numbers[n + 1:])

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SLIDE 71

Recursie, wachtwoord kraken

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SLIDE 72

Recursie, wachtwoord kraken

guess is gelijk aan wachtwoord? => True lengte van gok is max_lengte? => False

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SLIDE 73

Recursie, wachtwoord kraken

guess is gelijk aan wachtwoord? => True lengte van gok is max_lengte? => False voor elke optie: crack(guess + optie)

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SLIDE 74

Recursie, sudoku

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SLIDE 75

Recursie, sudoku

Alles ingevuld => opgelost Geen optie meer te verkennen => onopgelost

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SLIDE 76

Recursie, sudoku

Alles ingevuld => opgelost Geen optie meer te verkennen => onopgelost Vul een vakje in

Ga van een sudoku met n lege vakjes, naar n - 1

lege vakjes

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SLIDE 77

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V

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SLIDE 78

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

DFSrec ( )

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SLIDE 79

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V DFSrec ( )

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SLIDE 80

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V DFSrec ( )

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SLIDE 81

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V C 1 DFSrec ( )

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SLIDE 82

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V C 1

1

DFSrec ( )

1

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SLIDE 83

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V C 1

1

DFSrec ( ) DFSrec ( )

1 1

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SLIDE 84

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

1

DFSrec ( ) DFSrec ( )

1 1

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SLIDE 85

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

1

DFSrec ( ) DFSrec ( )

1 1

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SLIDE 86

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V C 3

1

DFSrec ( ) DFSrec ( )

1 1

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SLIDE 87

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V C 3

13

DFSrec ( ) DFSrec ( )

13 13

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SLIDE 88

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V C 3

13

DFSrec ( ) DFSrec ( )

13 13

DFSrec ( )

13

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SLIDE 89

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

13

DFSrec ( ) DFSrec ( )

13 13

DFSrec ( )

13

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SLIDE 90

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

13

DFSrec ( ) DFSrec ( )

13 13

DFSrec ( )

13

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SLIDE 91

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

13

DFSrec ( ) DFSrec ( )

13 13

DFSrec ( )

13

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SLIDE 92

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

13

DFSrec ( ) DFSrec ( )

13 13

C 3

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SLIDE 93

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

1

DFSrec ( ) DFSrec ( )

1 1

C 3

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SLIDE 94

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

1

DFSrec ( ) DFSrec ( )

1 1

C 7

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SLIDE 95

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

17

DFSrec ( ) DFSrec ( )

17 17

C 7

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SLIDE 96

DFS recursief

1 function DFS-recursive(V) 2 if V is solved 3 return V 4 5 for all candidates C from V do 6 apply C to V 7 DFS-recursive(V) 8 if V is solved 9 return V 10 undo C to V Callstack

V

17

DFSrec ( ) DFSrec ( )

17 17

C 7 DFSrec ( )

17

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SLIDE 97

DFS algoritme

Verschillende implementaties mogelijk
Hacker editie: iteratief DFS met generators

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SLIDE 98

Deeltentamen 2