CS10 Final Review by Glenn Sugden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.Glenn Sugdenmons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 1 CS10 Final Review Programming

2 Concept Review Loops & Variables Conditionals Lists Algorithms & Complexity Concurrency Recursion Data Structures Hash Tables Lamdas & HOFs

3 Loops & Variables Correct? Multiplying operand1 by operand2

4 Loops & Variables No! Why? Multiplying operand1 by operand2

5 Loops & Variables Uninitialized Variable Multiplying operand1 by operand2

6 Loops & Variables Initialized Variable! Multiplying operand1 by operand2

7 Loops & Variables Be sure that your variables are initialized to a correct / known / sane value!

8 Loops & Variables Correct now? Multiplying operand1 by operand2

9 Loops & Variables What if operand1 is negative? Or a “real” number like 2.3? Multiplying operand1 by operand2

10 Loops & Variables Be sure that your looping conditions are valid!

11 Reports “+” for positive numbers, “-” for negative numbers. Correct? Conditionals

12 Reports “+” for positive numbers, “-” for negative numbers. No! Why? Conditionals

13 Conditionals Reports “+” for positive numbers, “-” for negative numbers. What about number = 0?

14 Conditionals Loops & Variables Be sure that your conditionals handle all possible cases! Double-check edge cases, or inputs that fall on either side of your predicate.

15 Lists Duplicate words beginning with ‘c’ Does this correctly loop over list?

16 Lists No! Why? Duplicate words beginning with ‘c’

17 Lists Index within conditional! Duplicate words beginning with ‘c’

18 Duplicate words beginning with ‘c’ Lists Correct now?

19 Lists No! Why? Duplicate words beginning with ‘c’

20 Lists Off by 1 ! Duplicate words beginning with ‘c’

21 Lists Correct now? Duplicate words beginning with ‘c’

22 Lists No! Why? Duplicate words beginning with ‘c’

23 Duplicate words beginning with ‘c’ Lists The list keeps changing size!

24 Lists The list keeps changing size! Duplicate words beginning with ‘c’

25 Lists How do you correct it? Here is one solution...

26 Duplicate words beginning with ‘c’ Lists Push the index past the inserted item...

27 Lists Seems pretty “kludgy” though... Here is a much, much better solution...

28 Duplicate words beginning with ‘c’ Lists Make a new, resulting list!

29 Lists Much better! And our original list is still intact! Duplicate words beginning with ‘c’

30 Be sure indexes are correct during the entire loop. BYOB starts list indexing at 1 If the input list changes size during the loop, your index will be off! Check-Lists

31 Algorithms & Complexity Order of growth?

32 Constant: O(c) Reason: No matter what “n” is, the loop always repeats 1000 times. Algorithms & Complexity

33 Algorithms & Complexity Order of growth?

34 Still Constant: O(c) Reason: No matter what the list is, the loop always repeats 1000 times. Algorithms & Complexity

35 Algorithms & Complexity Order of growth?

36 Linear: O(n) Reason: Number of operations proportional to the input size (n) Algorithms & Complexity

37 Algorithms & Complexity Order of growth?

38 Still Linear: O(n) Reason: Number of operations proportional to the input size (length) Algorithms & Complexity

39 Algorithms & Complexity Order of growth?

40 Reason: Number of operations proportional to the square of the size of the input data (n) Algorithms & Complexity Quadratic: O(n 2 )

41 Algorithms & Complexity Quadratic: O(n 2 ) Input size # of operations

42 Algorithms & Complexity Order of growth?

43 Algorithms & Complexity Still Quadratic: O(n 2 ) Reason: Number of operations proportional to the square of the size of the input data (length)

44 Algorithms & Complexity Order of growth?

45 Algorithms & Complexity Reason: the recursive call is run twice for each value of n. Exponential: O(c n )

46 Algorithms & Complexity Exponential: O(2 n ) Input size # of operations

47 Algorithms & Complexity Order of growth?

48 Algorithms & Complexity Reason: the number of times the loop runs grows far more slowly (square root) than “n” Logarithmic: O(Log c n)

49 # of operations Algorithms & Complexity 2 Input size Note that these have traded places! Logarithmic: O(Log n)

50 Algorithms & Complexity 2 2 Compare! Note that linear growth doesn’t even register on this graph!

51 Consider the number of times the calculation repeats, rather than specific inputs. Algorithms & Complexity

52 Algorithms & Complexity Examples Constant Linear Quadratic Exponential Logarithmic Hash Table Lookup Text or List Length Square Matrix Calcs. (Naïve) Sorting Recursive Fractals Binary Searches

53 Concurrency List adds up to 200? 53

54 Concurrency List adds up to 200? No! Why? 54

55 Concurrency List adds up to 200? No! Why? These might choose the same number at the same time! 55

56 Concurrency List adds up to 200? Anything else? 56

57 No “wait” here means these might access the same indexes (or not access them at all), by interrupting a broadcast script that is already running! Concurrency List adds up to 200? No! Why? 57

58 Recursion n=0 n=1

59 n=4 n=∞ n=2 n=3 Recursion

60 n=4 n=∞ n=2 n=3 Recursion

61 Recursion An algorithmic technique where a function, in order to accomplish a task, calls itself with some part of the task. Recursive solutions involve two major parts: 1.Base case(s), in which the problem is simple enough to be solved directly, 2.Recursive case(s). A recursive case has three components: 1.Divide the problem into one or more simpler or smaller parts of the problems, 2.Invoke the function (recursively) on each part, and 3.Combine the solutions of the parts into a solution for the problem. Depending on the problem, any of these may be trivial or complex.

62 Data Structure : Hash Tables Can we use “MapReduce” to build a hash table? (we’ll come back to that...)

63 Lambdas & HOFs What is a Lambda? What is a Higher- Order Function (HOF)?

64 Lambdas & HOFs A “First Class” Procedure “Function as Data”

65 Lambdas & HOFs What is a Higher-Order Function (HOF)? In mathematics and computer science, higher-order functions, functional forms, or functionals are functions which do at least one of the following:mathematicscomputer sciencefunctionalsfunctions ■ take one or more functions as an input ■ output a function

66 Lambdas & HOFs  Useful HOFs (you can build your own!)  map Reporter over List  Report a new list, every element E of List becoming Reporter(E)  keep items such that Predicate from List  Report a new list, keeping only elements E of List if Predicate(E)  combine with Reporter over List  Combine all the elements of List with Reporter(E)  This is also known as “reduce”  Acronym example  keep  map  combine HOF-I.pptx

67 Data Structure : Hash Tables

68 Data Structure : Hash Tables Determine size of hash table. Hashing function (algorithm) to generate keys (index) from values (items). Modulo key (index) by hash table size. Store key and value in hash table at the resulting index. Find key in table using above algorithms (reading value instead of storing it).

69 Data Structure : HOF/Hash Tables Can we use “MapReduce” to build a hash table?

70 Try to program one on your own... it’s great practice with HOFs, Lists, etc.! I will post the solution to Piazzza... Yes! Data Structure : HOF/Hash Tables