Boolean algebra, conditional statements, loops.

Transcription

1 Boolean algebra, conditional statements, loops. Eugeniy E. Mikhailov The College of William & Mary Lecture 04 Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 1 / 19

2 Boolean algebra Variable of valuable type can have only two values true false Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

3 Boolean algebra Variable of valuable type can have only two values true (Matlab use 1 to indicate it, actually everything but zero) false Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

4 Boolean algebra Variable of valuable type can have only two values true (Matlab use 1 to indicate it, actually everything but zero) false (Matlab uses 0 ) Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

5 Boolean algebra Variable of valuable type can have only two values true (Matlab use 1 to indicate it, actually everything but zero) false (Matlab uses 0 ) There are three logical operators which are used in boolean algebra Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

6 Boolean algebra Variable of valuable type can have only two values true (Matlab use 1 to indicate it, actually everything but zero) false (Matlab uses 0 ) There are three logical operators which are used in boolean algebra - logic not, Matlab true = false false = true Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

7 Boolean algebra Variable of valuable type can have only two values true (Matlab use 1 to indicate it, actually everything but zero) false (Matlab uses 0 ) There are three logical operators which are used in boolean algebra - logic not, Matlab true = false false = true - logic and, Matlab & { true, if A=true and B=true, A B = false, otherwise Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

8 Boolean algebra Variable of valuable type can have only two values true (Matlab use 1 to indicate it, actually everything but zero) false (Matlab uses 0 ) There are three logical operators which are used in boolean algebra - logic not, Matlab true = false false = true - logic and, Matlab & { true, if A=true and B=true, A B = false, otherwise - logic or, Matlab { false, if A=false and B=false, A B = true, otherwise Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 2 / 19

9 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

10 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

11 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then A (( B)&C) Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

12 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then A (( B)&C) Thus A B&C = false Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

13 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then A (( B)&C) Thus A B&C = false Cat is an animal and cat is not an animal Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

14 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then Thus A (( B)&C) A B&C = false Cat is an animal and cat is not an animal is false statement Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

15 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then Thus A (( B)&C) A B&C = false Cat is an animal and cat is not an animal is false statement Z &Z = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

16 Boolean operators precedence in Matlab If A = false, B = true, C = true A B&C has highest precedence, then &, and then Thus A (( B)&C) A B&C = false Cat is an animal and cat is not an animal is false statement Z &Z = false Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 3 / 19

17 Boolean logic examples There is an island, which is populated by two kind of people: liars and truthlovers. Liars always lie and never speak a word of truth. Truthlovers always speak only truth. Suppose, you are landed on this island and met a person. What will be the answer to your question Who are you? Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 4 / 19

18 Boolean logic examples There is an island, which is populated by two kind of people: liars and truthlovers. Liars always lie and never speak a word of truth. Truthlovers always speak only truth. Suppose, you are landed on this island and met a person. What will be the answer to your question Who are you? The answer always will be Truthlover. Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 4 / 19

19 Boolean logic examples There is an island, which is populated by two kind of people: liars and truthlovers. Liars always lie and never speak a word of truth. Truthlovers always speak only truth. Suppose, you are landed on this island and met a person. What will be the answer to your question Who are you? The answer always will be Truthlover. Now you see a person who answers to your question. I am a liar. Is it possible? Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 4 / 19

20 Boolean logic examples There is an island, which is populated by two kind of people: liars and truthlovers. Liars always lie and never speak a word of truth. Truthlovers always speak only truth. Suppose, you are landed on this island and met a person. What will be the answer to your question Who are you? The answer always will be Truthlover. Now you see a person who answers to your question. I am a liar. Is it possible? This makes a paradox and should not ever happen on this island. Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 4 / 19

21 Matlab boolean logic examples & 12= Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

22 Matlab boolean logic examples & 12= e-6 = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

23 Matlab boolean logic examples & 12= e-6 = 0 Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

24 Matlab boolean logic examples & 12= e-6 = 0 >> B=[ , 0; , 12] B = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

25 Matlab boolean logic examples & 12= e-6 = 0 >> B=[ , 0; , 12] B = ~B Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

26 Matlab boolean logic examples & 12= e-6 = 0 >> B=[ , 0; , 12] B = ~B ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

27 Matlab boolean logic examples & 12= e-6 = 0 >> B=[ , 0; , 12] B = ~B ans = B ~B Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

28 Matlab boolean logic examples & 12= e-6 = 0 >> B=[ , 0; , 12] B = ~B ans = B ~B To be or not to be ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 5 / 19

29 Matlab boolean logic examples >> B=[ , 0; , 12] B = >> A=[56, 655; 0, 24.4] A = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 6 / 19

30 Matlab boolean logic examples >> B=[ , 0; , 12] B = >> A=[56, 655; 0, 24.4] A = B&A Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 6 / 19

31 Matlab boolean logic examples >> B=[ , 0; , 12] B = >> A=[56, 655; 0, 24.4] A = B&A ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 6 / 19

32 Matlab boolean logic examples >> B=[ , 0; , 12] B = >> A=[56, 655; 0, 24.4] A = B&A A ~B ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 6 / 19

33 Matlab boolean logic examples >> B=[ , 0; , 12] B = >> A=[56, 655; 0, 24.4] A = B&A ans = A ~B ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 6 / 19

34 Comparison operators Math Matlab = == double equal sign! = < < <= > > >= Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 7 / 19

35 Comparison operators Math x=[1,2,3,4,5] x = Matlab = == double equal sign! = < < <= > > >= Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 7 / 19

36 Comparison operators Math x=[1,2,3,4,5] x = x >= 3 Matlab = == double equal sign! = < < <= > > >= Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 7 / 19

37 Comparison operators Math x=[1,2,3,4,5] x = x >= 3 ans = Matlab = == double equal sign! = < < <= > > >= Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 7 / 19

38 Comparison operators Math x=[1,2,3,4,5] x = Matlab = == double equal sign! = < < <= > > >= x >= 3 ans = % chose such x where x>=3 x(x >= 3) Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 7 / 19

39 Comparison operators Math x=[1,2,3,4,5] x = Matlab = == double equal sign! = < < <= > > >= x >= 3 ans = % chose such x where x>=3 x(x >= 3) ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 7 / 19

40 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

41 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = A>=2 Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

42 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = A>=2 ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

43 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = A>=2 A(A>=2) ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

44 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = A>=2 ans = A(A>=2) ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

45 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = A>=2 ans = A(A>=2) ans = B(A>=2) Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

46 Comparison with matrices >> A=[1,2;3,4] A = >> B=[33,11;53,42] B = A>=2 ans = A(A>=2) ans = B(A>=2) ans = Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 8 / 19

47 if-else- statement if expression this part is executed only if expression is true else this part is executed only if expression is false Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 9 / 19

48 if-else- statement if expression this part is executed only if expression is true else this part is executed only if expression is false if hungry buy some food else keep working Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 9 / 19

49 if-else- statement if expression this part is executed only if expression is true else this part is executed only if expression is false if hungry buy some food else keep working if (x>=0) y=sqrt(x); else error( cannot do ); Eugeniy Mikhailov (W&M) Practical Computing Lecture 04 9 / 19

50 Common mistake in the if statement if (x=y) D=4; Z=45; C=12; else D=2; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

51 Common mistake in the if statement if (x=y) D=4; Z=45; C=12; else D=2; the value of D is always 4, except the case when y=0 Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

52 Common mistake in the if statement if (x=y) D=4; Z=45; C=12; else D=2; the value of D is always 4, except the case when y=0 someone used assignment operator (=) instead of comparison (==) Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

53 Short form of if- statement if expression this part is executed only if expression is true Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

54 Short form of if- statement if expression this part is executed only if expression is true if won a million go party Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

55 Short form of if- statement if expression this part is executed only if expression is true if won a million go party if (deviation<=0) exit; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

56 The while statement while expression this part is executed while expression is true Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

57 The while statement while expression this part is executed while expression is true while hungry keep eating Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

58 The while statement while expression this part is executed while expression is true while hungry keep eating i=1; while (i<=10) c=a+b; z=c*4+5; i=i+2; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

59 The while statement while expression this part is executed while expression is true while hungry keep eating i=1; while (i<=10) c=a+b; z=c*4+5; i=i+2; while loop is extremely useful but they are not guaranteed to finish. For a bit more complicated conditional statement and loop it is impossible to predict if the loop will finish. Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

60 The while statement while expression this part is executed while expression is true while hungry keep eating i=1; while (i<=10) c=a+b; z=c*4+5; i=i+2; while loop is extremely useful but they are not guaranteed to finish. For a bit more complicated conditional statement and loop it is impossible to predict if the loop will finish. Yet another common mistake is i=1; while (i<=10) c=a+b; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

61 The while statement while expression this part is executed while expression is true while hungry keep eating i=1; while (i<=10) c=a+b; z=c*4+5; i=i+2; while loop is extremely useful but they are not guaranteed to finish. For a bit more complicated conditional statement and loop it is impossible to predict if the loop will finish. Yet another common mistake is i=1; while (i<=10) c=a+b; not updating the term leading to fulfillment of the while condition Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

62 The for statement for variable = expression do something In this case variable is assigned concequently with columns of the expression, and then statements inside of the loop are executed Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

63 The for statement for variable = expression do something In this case variable is assigned concequently with columns of the expression, and then statements inside of the loop are executed sum=0; x=[1,3,5,6] for v=x sum=sum+v; >> sum sum = 15 Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

64 The for statement for variable = expression do something In this case variable is assigned concequently with columns of the expression, and then statements inside of the loop are executed sum=0; x=[1,3,5,6] for v=x sum=sum+v; >> sum sum = 15 for loops are guaranteed to complete after predictable number of iterations (the amount of columns in expression). Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

65 Example 100 S = i = i=1 Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

66 Example 100 S = i = i=1 S=0; i=1; while(i<=100) S=S+i; i=i+1; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

67 Example 100 S = i = i=1 S=0; i=1; while(i<=100) S=S+i; i=i+1; S=0; for i=1:100 S=S+i; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

68 Example S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

69 Example S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. S=0; k=1; while( (k<=100) & (k^-k >= 1e-5) ) S=S+k^-k; k=k+1; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

70 Example S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. S=0; k=1; while( (k<=100) & (k^-k >= 1e-5) ) S=S+k^-k; k=k+1; >> S S = Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

71 Example S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. S=0; k=1; while( (k<=100) & (k^-k >= 1e-5) ) S=S+k^-k; k=k+1; >> S S = S=0; k=1; while( k<=100 ) a_k=k^-k; if (a_k < 1e-5) break; S=S+a_k; k=k+1; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

72 Example S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. S=0; k=1; while( (k<=100) & (k^-k >= 1e-5) ) S=S+k^-k; k=k+1; >> S S = S=0; k=1; while( k<=100 ) a_k=k^-k; if (a_k < 1e-5) break; S=S+a_k; k=k+1; >> S S = Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

73 Same example with for loop S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

74 Same example with for loop S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. S=0; for k=1:100 a_k=k^-k; if (a_k < 1e-5) break; S=S+a_k; Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

75 Same example with for loop S = k=1 a k Until k<=100 and a k < 10 5, where a k = k k. S=0; for k=1:100 a_k=k^-k; if (a_k < 1e-5) break; S=S+a_k; >> S S = Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

76 Interest rate related example Suppose bank gave you 50% interest rate (let s call it x ), and you put one dollar in. How much would you get at the of the year? one payment at the of the year M 1 = 1 (1 + x) = 1 (1 +.5) = 1.5 Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

77 Interest rate related example Suppose bank gave you 50% interest rate (let s call it x ), and you put one dollar in. How much would you get at the of the year? one payment at the of the year M 1 = 1 (1 + x) = 1 (1 +.5) = 1.5 interest payment every half a year M 2 = 1 (1 + x/2) (1 + x/2) = 1 (1 +.5/2) 2 = Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

78 Interest rate related example Suppose bank gave you 50% interest rate (let s call it x ), and you put one dollar in. How much would you get at the of the year? one payment at the of the year M 1 = 1 (1 + x) = 1 (1 +.5) = 1.5 interest payment every half a year M 2 = 1 (1 + x/2) (1 + x/2) = 1 (1 +.5/2) 2 = interest payment every month M 12 = 1 (1 + x/12) 12 = Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

79 Interest rate related example Now let s find how you money growth (M N ) deps on the number of payments per year N_max=100; N=1:N_max; M=0*(N); x=.5; for i=n M(i)=(1+x/i)^i; plot(n,m, - ); xlabel( N, number of payments per year ); ylabel( Money grows ); title( Money grows vs number of payments per year ); Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19

80 Interest rate related example Eugeniy Mikhailov (W&M) Practical Computing Lecture / 19