Announcements. Project 1 will be posted today on webpage and cvs. Due Tuesday

Transcription

1 Announcements Project 1 will be posted today on webpage and cvs Due Tuesday

2 More Loops

3 A H: either 0 or 1 Printing in base 2

4 Printing in base 2 A H: either 0 or 1 Mask

5 Printing in base 2 A H: either 0 or 1 Loop

6 Printing in base 2 A H: either 0 or 1 << Loop

7 Printing in base 2 A H: either 0 or 1 << Loop

8 Printing in base 2 A H: either 0 or 1 << Loop

9 Printing in base 2 A H: either 0 or 1 Another way?

10 Printing in base 2 A H: either 0 or 1 >>> 0 Loop

11 Printing in base 2 A H: either 0 or 1 >>> 1 Loop

12 Printing in base 2 A H: either 0 or 1 >>> 2 Loop

13 Printing in base 2 A H: either 0 or 1 >>> 3 Loop

14 Printing in base 2 A H: either 0 or 1 >>> 4 Loop

15 Printing in base 2 A H: either 0 or 1 >> Loop

16 Bitwise shift operators What arithmetic operation (+, -, *, /, %) do the following represent? n >> s ==?? n & 1 ==??

17 Bitwise shift operators What arithmetic operation (+, -, *, /, %) do the following represent? n >> s == n / 2 s n & 1 == n % 2

18 Printing in base B Base 2 (i th digit): Shift then mask

19 Printing in base B Base 2 (i th digit): (n >> i ) & 1

20 Printing in base B Base 2 (i th digit): (n / 2 i ) % 2

21 Printing in base B Base 2 (i th digit): (n / 2 i ) % 2 Base 10 (i th digit): (n / 10 i ) % 10 Base B (i th digit): (n / B i ) % B Signed two s complement visualization

22 Primality testing 19 is divisible by 1 19 is not divisible by 2 19 is not divisible by 3 19 is not divisible by is not divisible by is divisible by 19

23 While Loops while(condition) { } do something Init : you handle this case by case condition : if this condition is true, repeat the loop body Update : you also handle this case by case do something : execute a sequence of commands

24 While loops //A for loop for(int i = 0; i < 10; i++) { //do something } //An equivalent while loop int i = 0; while(i < 10) { //do something i++; }

25 do { something Do while Loops } while(condition); condition is checked after each repetition of the loop body, not before In a do-while loop, the body is always executed at least once.

26 break and continue break : If encountered in a loop body, the loop will terminate immediately continue : If encountered in a loop body, the current repetition will terminate immediately; the next repetition will begin

27 While example Casino game with loops User places a bet User wins or loses based on biased coin flip Repeat until user quits or has no money left

28 Nested loops Performing an iterative task with a loop

29 Nested loops Performing an iterative task with a loop Every iteration requires its own repetitive sub-task

30 Nested loops Performing an iterative task with a loop Every iteration requires its own repetitive sub-task Every sub-task iteration requires its own repetitive sub-sub-task

31 Nested loops Performing an iterative task with a loop Every iteration requires its own repetitive sub-task Every sub-task iteration requires its own repetitive sub-sub-task Every sub-sub-task iteration requires its own repetitive sub-sub-sub-task

32 Nested loops

33 Loops Dimensions row col 0 0

34 Loops Dimensions row col 0 1

35 Loops Dimensions row col 0 2

36 Loops Dimensions row col 0 3

37 Loops Dimensions row col 0 4

38 Loops Dimensions row 1

39 Loops Dimensions row col 1 0

40 Loops Dimensions row col 1 1

41 Loops Dimensions row col 1 2

42 Loops Dimensions row col 1 3

43 Loops Dimensions row col 1 4

44 Loops Dimensions row 2

45 Loops Dimensions row col 2 0

46 Loops Dimensions row col 2 1

47 Loops Dimensions row col 2 2

48 Loops Dimensions row col 2 3

49 Loops Dimensions row col 2 4

50 Nested loops Examples: printing shapes in the console # ## ### #### Using loop boundary conditions Using

51 More Loop Examples Calculate e (Brothers) e = n=0 Calculate π (Wallis) 2n + 2 2n + 1! π 2 = 2n 2n 1 n=1 2n 2n + 1 =

52 More Loop Examples Integration Parabola: f x = x 2 Bell curve: ρ x = 1 2π e x2 /2 Histogram of Math.random() Calculate φ (Ratio of successive Fibonaccis) Hailstone sequence (Collatz conjecture) N i+1 = N i 2 3N i + 1 if N i is even if N i is odd

53 More Loop Examples Print Pascal s triangle in the console Reflect the binary print-out Use an infinite loop to print a continuous wave in the console Super-impose multiple waves Zap impulse: speed up the wave over time