Strings - ETH Z · 2020-03-05 · 10 % 3 = 1, because 9 = 3·3 10 % 4 = 2, because 8 = 4·2 11 // 5 = 2, because 10 = 5·2 23 // 4 = 5, because 20 = 4·5 12 % 3 = 0, because 12 =

Dennis Komm

Programming and Problem-SolvingLogical Values and Control Structures

Spring 2020 – March 5, 2020

StringsRepetition

Strings

Strings are “lists of characters” (there are differences)

Characters correspond (mostly) to keys on keyboard

Strings are written in quotation marks

Access to single characters using brackets

String word = "HELLO WORLD"

word[0] is first character

word[1] is second character

. . .

word[len(word)-1] is last character

Programming and Problem-Solving – Control Structures Spring 2020 Dennis Komm 1 / 45

Characters – The Unicode Table

0–18 19–37 38–56 57–75 76–94 95–113 114–127

Dec. Char. Dec. Char. Dec. Char. Dec. Char. Dec. Char. Dec. Char. Dec. Char.

0 NUL 19 DC3 38 & 57 9 76 L 95 _ 114 r1 SOH 20 DC4 39 ’ 58 : 77 M 96 ‘ 115 s2 STX 21 NAK 40 ( 59 ; 78 N 97 a 116 t3 ETX 22 SYN 41 ) 60 < 79 O 98 b 117 u4 EOT 23 ETB 42 * 61 = 80 P 99 c 118 v5 ENQ 24 CAN 43 + 62 > 81 Q 100 d 119 w6 ACK 25 EM 44 , 63 ? 82 R 101 e 120 x7 BEL 26 SUB 45 - 64 @ 83 S 102 f 121 y8 BS 27 ESC 46 . 65 A 84 T 103 g 122 z9 HT 28 FS 47 / 66 B 85 U 104 h 123 {10 LF 29 GS 48 0 67 C 86 V 105 i 124 |11 VT 30 RS 49 1 68 D 87 W 106 j 125 }12 FF 31 US 50 2 69 E 88 X 107 k 126 ~13 CR 32 SP 51 3 70 F 89 Y 108 l 127 DEL14 SO 33 ! 52 4 71 G 90 Z 109 m . . .15 SI 34 "’ 53 5 72 H 91 [ 110 n16 DLE 35 # 54 6 73 I 92 \ 111 o17 DC1 36 $ 55 7 74 J 93 ] 112 p18 DC2 37 % 56 8 75 K 94 ˆ 113 q


Characters – The Unicode Table

Use functions ord() and chr()

ord(x) returns position of character x in Unicode table

chr(y) returns character at position y in Unicode table

x = input("Enter a character: ")print("The character", x, "is at position", ord(x))


Operators

AdditionZahlen: Arithmetische OperationListen und Strings: Zusammenfügen (bei Strings existiert kein append)

daten = [1, 4, 6]daten2 = daten + [5]satz = "Guten Tag"satz2 = satz + ", Urs"satz3 = satz2 + "."

MultiplikationZahlen: Arithmetische OperationListen und Strings: Zusammenfügen

daten = [2, 3] * 5satz = "HA" * 3


Caesar Encryption

Symmetric Encryption

Sender Recipient

plaintext

Encryption

ciphertextCommunication

medium(messenger, internet, . . . )

ciphertext

Decryption

plaintext


Caesar Encryption

Situation

Parties A and B want to communicate over an insecure channel, this timeusing Caesar encryption

Shared key k as number between 1 and 25

A encrypts message by adding k to each character

A sends encrypted message to B

B decrypts message by subtracting k from each character


Caesar Encryption

Shift characters by fixed value k by adding k

Example

A B C D E F G H I J K L MW X Y Z A B C D E F G H IN O P Q R S T U V W X Y ZJ K L M N O P Q R S T U V

Plaintext: HELLO WORLD

Ciphertext: DAHHK SKNHZ


Caesar Encryption

1. Entered letter is Unicode character between A and ZA B . . . W X Y Z65 66 . . . 87 88 89 90

2. Subtract 65 so that the result is between 0 and 25A B . . . W X Y Z0 1 . . . 22 23 24 25

3. Now add key (for instance, 3) and compute modulo 26A B . . . W X Y Z3 4 . . . 25 0 1 2

4. Finally add 65 to the resultA B . . . W X Y Z68 69 . . . 90 65 66 67


Euclidean Division (Modulo Operation)

Using “%,” we obtain the residue of the integer division

Analogously, “//” the part before the decimal point

10 % 3 = 1, because 9 = 3 · 310 % 4 = 2, because 8 = 4 · 211 // 5 = 2, because 10 = 5 · 223 // 4 = 5, because 20 = 4 · 512 % 3 = 0, because 12 = 4 · 3

If x % y == 0, x is divided by y


Exercise – Caesar Encryption

Write a program that

runs through a given string

decrypts each letter with a key k

tries out each key k

uses the following formula

e = (v− 65− k) % 26 + 65

Decrypt the ciphertext DLUUQLTHUKSHBAOLBYLRHYBMANPIALZZJOVNNP


Exercise – Caesar Encryption

for k in range(0, 26):for item in ciphertext:

print(chr((ord(item) - 65 - k) % 26 + 65), end="")print()

for k in range(0, 26):for i in range(0, len(ciphertext)):

print(chr((ord(ciphertext[i]) - 65 - k) % 26 + 65), end="")print()


Changing the Step Size

Loops over Lists – Larger Steps

Traverse a list with steps of length 2

data = [5, 1, 4, 3]for i in range(0, len(data), 2):

print(data[i])

Output

All elements at even positions from 0 up to at most len(data) are outputï 5,4


The Syntax of range

for i in range(start, end, step)

Iteration over all positions from start up to end-1 with step length of step

Shorthand notation

for i in range(start,end) ⇐⇒ for i in range(start,end,1)

Another shorthand notation

for i in range(end) ⇐⇒ for i in range(0, end)


Improvement of Caesar Encryption

Use two keys alternatingly for even and odd positions

k = int(input("First key: "))l = int(input("Second key: "))x = input("Text (only uppercase, even length): ")for i in range(0, len(x), 2):

print(chr((ord(text[i])-65 + k) % 26 + 65), end="")print(chr((ord(text[i+1])-65 + l) % 26 + 65), end="")

print()

Still Caesar encryption remains insecure ï Project 1


Logical ValuesBoolean Values and Relational Operators

Boolean Values and Variables

Boolean expressions can take on one of two values F or T

F corresponds to “false”

T corresponds to “true”

George Boole [Wikimedia]

Boolean variables in Python

represent “logical values”

Domain {False, True}

Example

b = True # Variable with value TrueProgramming and Problem-Solving – Control Structures Spring 2020 Dennis Komm 15 / 45

Relational Operators

a < b (smaller than)a >= b (greater than)

a == b (equals)a != b (unequal to)

number type × number type→ {False, True}


Logical ValuesBoolean Functions and Logical Operators

Boolean Functions in Mathematics

Boolean function

f : {F, T}2 → {F, T}




x ∧ y

“logical and”

f : {F, T}2 → {F, T}



x y x ∧ y

F F F

F T F

T F F

T T T


Logical Operator and

a and b (logical and)

{False, True} × {False, True}→ {False, True}

n = -1p = 3b = (n < 0) and (0 < p) # b = True


x ∨ y

“logical or”f : {F, T}2 → {F, T}



x y x ∨ y

F F F

F T T

T F T

T T T

The logical or is always inclusive: x or y or both


Logical Operator or

a or b (logical or)

{False, True} × {False, True}→ {False, True}

n = 1p = 0b = (n < 0) or (0 < p) # b = False


¬x

“logical not”f : {F, T} → {F, T}



x ¬x

F T

T F


Logical Operator not

not b (logical not)

{False, True}→ {False, True}

n = 1b = not (n < 0) # b = True


Logical ValuesPrecedences

Precedences

not b and am

(not b) and a

a and b or c and dm

(a and b) or (c and d)

a or b and c or dm

a or (b and c) or d


Precedences

7 + x < y and y != 3 * z or not b7 + x < y and y != 3 * z or (not b)

The unary logical operator not

ï provides a stronger binding than binary arithmetic operators

ï These bind stronger than relational operators

ï and these bind stronger than binary logical operators

Some parentheses on the previous slides were actually redundant, butshould still be used


DeMorgan Rules

not (a and b) == (not a or not b)

not (a or b) == (not a and not b)

Examples

(not black and not white) == not (black or white)

not (rich and beautiful) == (poor or ugly)


Application – either . . . or (XOR)

(x or y) and not (x and y) x or y, and not both

(x or y) and (not x or not y) x or y, and one of them not

not (not x and not y) and not (x and y) not none and not both

not ((not x and not y) or (x and y)) not: both or none


Control Structures

Control Flow

So far. . .

Up to now linear (from top to bottom)

for loop to repeat blocks

x = int(input("Input: "))

for i in range(1, x+1):print(i*i)


Control StructuresSelection Statements

Selection Statements

Implement branches

if statement

if-else statement

if-elif-else statement (later)


if Statement

if condition:statement

a = int(input("Input: "))if a % 2 == 0:

print("even")

If condition is true,then statement is executed

statement:arbitrary statementbody of the if-Statement

condition: Boolean expression


if-else Statement

if condition:statement1

else:statement2

a = int(input("Input: "))if a % 2 == 0:

print("even")else:

print("odd")

If condition is true,then statement1 is executed,otherwise statement2 is executed


statement1:body of the if-branch

statement2:body of the else-branch


Layout

a = int(input("Input: "))

if a % 2 == 0:print("even")

else:print("odd")

Indentation

Indentation


Control Structureswhile Loops

while Loops

while condition:statement Indentation

statement:arbitrary statementbody of the while loop



while Loops

while condition:statement

condition is evaluatedTrue: iteration starts

statement is executedFalse: while loop ends


while Loops

s = 0i = 1while i <= 2:

s = s + ii = i + 1

i condition s

i = 1 true s = 1i = 2 true s = 3i = 3 false s = 3


Incrementation of Variables

Use simplified syntax for changing values of variables

n = n + 1 is written as n += 1

n = n + i is written as n += i

n = n - 15 is written as n -= 15

n = n * j is written as n *= j

n = n ** 4 is written as n **= 4

. . .


The Jump Statements break

break

Immediately leave the enclosing loop

Useful in order to be able to break a loop “in the middle”

s = 0

while True:x = int(input("Enter a positive number, abort with 0: "))if x == 0:

breaks += x

print(s)


Control StructuresTermination

Termination

i = 1while i <= n:

s += ii += 1

Here and commonly

statement changes its value that appears in condition

After a finite number of iterations condition becomes false

ï Termination


Infinite Loops

Infinite loops are easy to generate

while True:print("0")

while not False:print("1")

while 2 > 1:print("2")

. . . but can in general not be automatically detected


Halting Problem

Undecidability of the Halting Problem [Alan Turing, 1936]

There is no Python program that can determine, foreach Python program P and each input I, whether P

terminates with the input I

This means that the termination of programs can ingeneral not be automatically checked

Theoretical questions of this kind were the main motivation for Turing to designhis computing machine

Alan Turing [Wikimedia]


The Collatz Sequence

Sequence of natural numbers n0, n1, n2, n3, n4, n5, . . .

n0 = n

for every i ≥ 1, ni =

ni−1/2 if ni−1 even

3 · ni−1 + 1 if ni−1 odd

Example for n = 5

5, 16, 8, 4, 2, 1, 4, 2, 1, . . . (repetition at 1)


Exercise – The Collatz Sequence

Write a program that

takes an integer n as input

outputs the Collatz sequence usingn0 = n and

ni =

ni−1/2 if ni−1 even

3 · ni−1 + 1 if ni−1 odd


Exercise – The Collatz Sequence

n = int(input("Compute the Collatz sequence for n = "))

while n > 1: # stop when 1 is reachedif n % 2 == 0: # n is even

n //= 2else: # n is odd

n = 3 * n + 1print(n, end=" ")



Example for n = 27

27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121364 182 91 274 137 412 206 103 310 155 466 233 700 350 175526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 27341367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 4331300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 16080 40 20 10 5 16 8 4 2 1



The Collatz Concecture [Lothar Collatz, 1937]

For every n ≥ 1, 1 will occur in the sequence

Nobody could prove the conjecture so far

If it is wrong, then the while loop for computing theCollatz sequence can be an endless loop for some n

as input

Lothar Collatz [Wikimedia]


Strings - ETH Z · 2020-03-05 · 10 % 3 = 1, because 9 = 3·3 10 % 4 = 2, because 8 = 4·2 11 // 5 = 2, because 10 = 5·2 23 // 4 = 5, because 20 = 4·5 12 % 3 = 0, because 12 =

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