Lecture 8: Control Structures I

Transcription

1 Chair of Software Engineering Einführung in die Programmierung Introduction to Programming Prof. Dr. Bertrand Meyer Lecture 8: Control Structures I

2 Intro. to Programming, lecture 8: Control structures I 2

3 The notion of algorithm General definition: An algorithm is the specification of a process to be carried out by a computer Intro. to Programming, lecture 8: Control structures I 3

4 Not quite an algorithm Intro. to Programming, lecture 8: Control structures I 4

5 5 properties of an algorithm Defines data to which process will be applied Every elementary step taken from a set of well-specified actions Describes ordering(s) of execution of these steps 2 and 3 based on precisely defined conventions, suitable for execution by an automatic computer For any data, guaranteed to terminate after finite number of steps Intro. to Programming, lecture 8: Control structures I 5

6 Algorithm vs program Algorithm usually considered a more abstract notion, indepent d of platform, programming language etc. In practice, the distinction ts to fade: Algorithms need a precise notation Programming languages becoming more abstract However: In programs, data (objects) are just as important as algorithms A program typically contains many algorithms and object structures Intro. to Programming, lecture 8: Control structures I 6

7 What makes up an algorithm Basic steps: Feature call x.f (a ) Assignment... Sequencing of these basic steps: CONTROL STRUCTURES Intro. to Programming, lecture 8: Control structures I 7

8 Control structures Definition: program construct that describes the scheduling of basic actions Three fundamental control structures: Sequence Loop Conditional They are the Control structures of Structured Programming Intro. to Programming, lecture 8: Control structures I 8

9 Control structures as problem-solving techniques Sequence: To achieve C from A, first achieve an intermediate goal B from A, then achieve C from B Loop: solve the problem on successive approximations of its input set Conditional: solve the problem separately on two or more subsets of its input set Intro. to Programming, lecture 8: Control structures I 9

10 The sequence (or Compound) instruction 1 instruction 2... instruction n Intro. to Programming, lecture 8: Control structures I 10

11 Semicolon as optional separator instruction 1 ; instruction 2 ;... ; instruction n Intro. to Programming, lecture 8: Control structures I 11

12 Not quite an algorithm Intro. to Programming, lecture 8: Control structures I 12

13 Correctness of a Compound Precondition of instruction 1 must hold initially Postcondition of each instruction i must imply precondition of each instruction i+1 Final effect is postcondition of instruction n Intro. to Programming, lecture 8: Control structures I 13

14 Conditional instruction if Condition then Instructions else Other_instructions -- Boolean_expression -- Compound -- Compound Intro. to Programming, lecture 8: Control structures I 14

15 Computing the greater of two numbers if a > b then max else max := a := b Intro. to Programming, lecture 8: Control structures I 15

16 As a function maximum (a, b : INTEGER): INTEGER do -- The higher of a and b if a > b then Result else := a Result := b Intro. to Programming, lecture 8: Control structures I 16

17 The conditional as problem-solving technique PROBLEM SPACE Region 2 Region 1 Use technique 1 Use technique 2 Intro. to Programming, lecture 8: Control structures I 17

18 Basic form if Condition then Instructions else Other_instructions Intro. to Programming, lecture 8: Control structures I 18

19 A variant of the conditional if Condition then Instructions Intro. to Programming, lecture 8: Control structures I 19

20 A variant of the conditional if Condition then Instructions (Means the same as if Condition then Instructions else with an empty else clause) Intro. to Programming, lecture 8: Control structures I 20

21 Nesting if Condition 1 then Instructions ti 1 else if Condition 2 then Instructions 2 else if Condition 3 then else... Instructions ti 3 Intro. to Programming, lecture 8: Control structures I 21

22 Nested structure Intro. to Programming, lecture 8: Control structures I 22

23 Comb-like structure Intro. to Programming, lecture 8: Control structures I 23

24 Comb-like conditional if Condition 1 then Instructions 1 elseif Condition 2 then Instructions 2 elseif Condition 3 then Instructions 3 elseif... else Instructions 0 Intro. to Programming, lecture 8: Control structures I 24

25 Comb-like structure Intro. to Programming, lecture 8: Control structures I 25

26 On the menu for today Loops and their invariants See what it takes to ensure that a loop terminates Look at the general problem of loop termination Examine lower-level control structures: Goto and flowcharts; see rationale for the control structures of Structured Programming Prove the undecidability of the Halting Problem Intro. to Programming, lecture 8: Control structures I26

27 Loop from Initialization variant Variant_expression invariant Invariant_expression until Exit_condition loop Body -- Compound -- Integer expression -- Condition -- Boolean_expression -- Compound Intro. to Programming, lecture 8: Control structures I 27

28 Loop, full form from Initialization invariant Invariant_expression variant Variant_expression until Exit_condition loop Body -- Compound -- Boolean_expression -- Integer_expression -- Boolean_expression -- Compound Intro. to Programming, lecture 8: Control structures I 28

29 Another loop syntax Intro. to Programming, lecture 8: Control structures I 29

30 Loop, full form from Initialization invariant Invariant_expression variant Variant_expression until Exit_condition loop Body -- Compound -- Boolean_expression -- Integer_expression -- Boolean_expression -- Compound Intro. to Programming, lecture 8: Control structures I 30

31 Looping over stations of a line from fancy.start until fancy.after loop -- Do something with fancy.item fancy.forth Previously and in the textbook: fancy_line Intro. to Programming, lecture 8: Control structures I 31

32 Operations on a list before after item 1 index count startt back forth Commands (The cursor) Queries (boolean) Intro. to Programming, lecture 8: Control structures I 32

33 Operations on a list before after item 1 index count startt forth (The cursor) Intro. to Programming, lecture 8: Control structures I 33

34 Looping over stations of a line from fancy.start until fancy.after loop -- Do something with fancy.item fancy.forth Intro. to Programming, lecture 8: Control structures I 34

35 Displaying station names from until loop fancy.start fancy.after -- Display name of next station: Console.show (fancy.item)( ) fancy.forth Intro. to Programming, lecture 8: Control structures I 35

36 Computing the maximum of station names from fancy.start ; Result := "" until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 36

37 Assignment Result := "XYZ " -- Change the value of Result to "XYZ" Intro. to Programming, lecture 8: Control structures I 37

38 Computing the maximum of station names from fancy.start ; Result := " " until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth The greater of two strings, alphabetically, e.g. greater ("ABC ", "AD ") ="AD" Intro. to Programming, lecture 8: Control structures I 38

39 In a function highest_name: STRING is do from -- Alphabetically greatest station name of line until loop fancy.start ; Result := "" fancy.after Result := greater (Result, fancy.item.name) fancy.forthforth Intro. to Programming, lecture 8: Control structures I 39

40 Postcondition? highest_name: STRING is -- Alphabetically greatest station name of line do from fancy.start ; Result := "" until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth ensure Result /= Void and then not Result.empty Intro. to Programming, lecture 8: Control structures I 40

41 Loop as approximation strategy name 1 name 2 name i name n Result = name 1 Result = Max (name 1, name 2 ) Result =Max(name 1, name 2,..., name i ) Result = Max (name 1, name 2,..., name i,..., name n ) Intro. to Programming, lecture 8: Control structures I 41

42 Computing the maximum of station names from fancy.start ; Result := " until loop fancy.afterafter Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 42

43 The loop invariant from fancy.start t ; Result := "" invariant fancy.index >= 1 fancy.index <= fancy.count Result is the alphabetically highest of the -- names of previous stations until fancy.afterafter loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 43

44 Loop invariant (Do not confuse with class invariant) Property that is: Satisfied after initialization (from clause) Preserved by every loop iteration (loop p clause) when executed with the exit condition (until clause) not satisfied Intro. to Programming, lecture 8: Control structures I 44

45 The loop invariant from fancy.start ; Result := "" invariant fancy.index >= 1 fancy.index <= fancy.count Result is the alphabetically highest of the -- names of previous stations until fancy.afterf loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 45

46 The loop invariant (better) from fancy.start t ; Result := "" invariant index >= 1 index <= count If there are any previous stations, -- Result is the alphabetically highest of their names until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 46

47 Loop as approximation strategy name 1 name 2 name i name n Result = name 1 Result = Max (name 1, name 2 ) Result =Max(name 1, name 2,..., name i ) Result = Max (name 1, name 2,..., name i,..., name n ) Intro. to Programming, lecture 8: Control structures I 47

48 In a function highest_name: STRING is do from until loop -- Alphabetically ll greatest t station ti name of line fancy.start ; Result := "" fancy.after Result := greater (Result, fancy.item.name) ) fancy.forthforth Intro. to Programming, lecture 8: Control structures I 48

49 Postcondition? highest_name: STRING is -- Alphabetically greatest station name of line do from fancy.start ; Result := "" until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth ensure Result /= Void and then not Result.empty Intro. to Programming, lecture 8: Control structures I 49

50 Loop as approximation strategy name 1 name 2 name i name n Result = name 1 Result = Max (name 1, name 2 ) Result =Max(name 1, name 2,..., name i ) Result = Max (name 1, name 2,..., name i,..., name n ) Intro. to Programming, lecture 8: Control structures I 50

51 The loop invariant from fancy.start ; Result := " invariant fancy.index >= 1 fancy.index <= fancy.count Result is the alphabetically highest of the -- names of previous stations until fancy.afterafter loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 51

52 Loop invariant (Do not confuse with class invariant) Property that is: Satisfied after initialization (from clause) Preserved by every loop iteration (loop p clause) when executed with the exit condition (until clause) not satisfied Intro. to Programming, lecture 8: Control structures I 52

53 The loop invariant from fancy.start ; Result := "" invariant fancy.index >= 1 fancy.index <= fancy.count Result is highest of previous station names until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 53

54 The loop invariant (better) from fancy.start ; Result := "" invariant index >= 1 index <= count If there are any previous stations, -- Result is the alphabetically ll highest h of their names until fancy.after loop Result := greater (Result, fancy.item.name) fancy.forth Intro. to Programming, lecture 8: Control structures I 54

55 The effect of the loop from fancy.start ; Result := "" invariant index >= 1 index <= count Result is highest of previous station names until fancy.after Exit condition loop satisfied at Result := greater (Result, fancy.item.name) Invariant satisfied after initialization Invariant satisfied after each iteration fancy.forth At : invariant and exit condition All stations visited (fancy.after ) Result is highest of their names Intro. to Programming, lecture 8: Control structures I 55

56 Quiz: what s the invariant? xxx (a, b: INTEGER): INTEGER is --????????????????????????????????? require a > 0;b b > 0 local m, n : INTEGER do from m := a ; n := b invariant --???????? variant???????? until m = n loop if m > n then m := m n else n := n m Result := m Intro. to Programming, lecture 8: Control structures I 56

57 Quiz: what s the invariant? xxx (a, b: INTEGER): INTEGER is --????????????????????????????????? require a > 0;b b > 0 local m, n : INTEGER do from m := a ; n := b invariant --???????? variant???????? until m = n loop if m > n then m := m n else n := n m Result := m Intro. to Programming, lecture 8: Control structures I 57

58 Quiz: what s the invariant? euclid (a, b: INTEGER): INTEGER is -- Greatest common divisor of a and b require a > 0;b b > 0 local m, n : INTEGER do from m := a ; n := b invariant --???????? variant???????? until m = n loop if m > n then m := m n else n := n m Result := m Intro. to Programming, lecture 8: Control structures I 58

59 What we have seen Intro. to Programming, lecture 8: Control structures I 59

60 What we have seen The notion of algorithm Basic properties Difference with program The notion of control structure Correctness of an instruction Control structure: sequence Control structure: conditional Nesting, and how to avoid it Intro. to Programming, lecture 8: Control structures I 60

61 End of lecture 8 Intro. to Programming, lecture 8: Control structures I 61