QUIZ. 0] Define arrays 1] Define records 2] How are arrays and records: (a) similar? (b) different?

Transcription

1 QUIZ 0] Define arrays 1] Define records 2] How are arrays and records: (a) similar? (b) different? 1

2 QUIZ 3] What are the 4 fundamental types of algorithms used to manipulate arrays? 4] What control structure is normally used to access all the elements of an array? 2

3 QUIZ 5] Explain the following search algorithms in your own words: (a) Sequential search (b) Sequential search with early termination (c) Binary/logarithmic search 3

4 Trick QUIZ Search for the key 42 in this array, using binary search: 4

5 8.5 Sorting algorithms 5

6 Sorting Sorting Arranging items in a collection so that there is an ordering on one (or more) of the fields in the items Sort Key The field (or fields) on which the ordering is based Sorting algorithms Algorithms that order the items in the collection based on the sort key 6

7 Selection Sort Figure 7.11 Example of a selection sort (sorted elements are shaded) 7

8 Handout at the end QUIZ Selection Sort Show the swapped elements with arrows. Show the sorted elements with shading

9 solution 9

10 Handout at the end Individual work for next time Show the swapped elements with arrows. Show the sorted elements with shading

11 solution 11

12 Selection Sort Pseudocode Selection Sort Set firstunsorted to 0 WHILE (not sorted yet) Find smallest unsorted item Swap firstunsorted item with the smallest Set firstunsorted to firstunsorted + 1 Red steps are abstract (not concrete) Not sorted yet current < length 1 12

13 Find smallest unsorted item Set indexofsmallest to firstunsorted Set index to firstunsorted + 1 WHILE (index <= length 1) IF (data[index] < data[indexofsmallest]) Set indexofsmallest to index Set index to index + 1 Set index to indexofsmallest Swap firstunsorted with smallest Set tempitem to data[firstunsorted] Set data[firstunsorted] to data[indexofsmallest] Set data[indexofsmallest] to tempitem 13

14 14

15 SKIP Bubble Sort and Insertion Sort, just remember that they are as fast (efficient) as Selection Sort Is it possible to devise a more efficient sorting algorithm? 15

16 Is it possible to devise a more efficient sorting algorithm? Yes, but, in order to do this, we have to understand subprograms and recursion. 16

17 7.6 Recursive Algorithms To understand Quick Sort, we need: a new control structure: subprogram a new concept: recursion 17

18 Subprogram Statements We can give a section of code a name and use that name as a statement in another part of the program When the name is encountered, the processing in the other part of the program halts while the named code is executed When execution is finished, the first part of the program resumes execution That section of code is called a subprogram 18

19 Subprogram Statements Figure 7.14 Subprogram flow of control 19

20 We already used subprograms in we called them Functions Python! int() float() ord() chr() str() etc. Do you remember what each of them does? Methods list.append() string.upper() string.find() etc. 20

21 Subprogram Statements What if the subprogram needs data from the calling unit? This data is called input. Parameters Identifiers listed in parentheses beside the subprogram declaration; sometimes called formal parameters Arguments Identifiers listed in parentheses on the subprogram call; sometimes called actual parameters 21

22 Parameters and arguments in Python def disp(a, b): print a, 'and', b x, y = 1, 2 disp(x, y) 22

23 What if the subprogram needs to give data back to the calling unit? This data is called output. Void subprograms They do not return a value, just perform certain actions >>> print( Enter a positive integer ) >>> printer(3, 4) Value-returning subprograms >>> a = input( Enter a positive integer ) The keyword RETURN is used in many programming languages 23

24 What if the subprogram needs to give data back to the calling unit? This data is called output. Void subprograms They do not return a value, just perform certain actions >>> print( Enter a positive integer ) >>> printer(3, 4) Value-returning subprograms >>> a = input( Enter a positive integer ) The keyword RETURN is used in many programming languages Do not confuse returning values with printing or displaying values. Returning means that a value is given back to the main program! 24

25 Value-returning function in Python def sum(a, b): return a + b x, y = 1, 2 print sum(x, y) Compare to the previous function, which returns void (does not return anything) 25

26 Value-returning and void Subprograms 26

27 COSC 1100 Freshman Seminar Fall Source: AP CS Principles Course and Exam Descriptions 2016

28 Subprogram Statements Subprograms are very important tools for abstraction. Other popular names for subprograms: sub subroutine function procedure module method EOL 1 28

29 Recursion Recursion The ability of a subprogram to call itself Base case The case to which we have an answer General case The case that expresses the solution in terms of a call to itself with a smaller version of the problem 29

30 Recursion The factorial of a positive integer is defined as the integer times the product of all the integers between itself and 0: N! = N But an alternate recursive definition is possible: N! = N (N 1)! Base case Fact(0) = 1 (0! is 1) General Case Fact(N) = N Fact(N-1) (for N 1) 30

31 QUIZ Binary Search How many comparisons are needed to find the key 9 (or decide that it is not in the array)? Show the left, right and middle at each step.

32 QUIZ Binary Search How many comparisons are needed to find the key 9 (or decide that it is not in the array)? Show the left, right and middle at each step. Exactly! The array must be sorted first!

33 QUIZ Binary Search How many comparisons are needed to find the key 60 in this array? Show first, last, and middle for each iteration

34 QUIZ Binary Search Array must be sorted first for Binary Search! How many comparisons are needed to find the key 60 in this array? Show first, last, and middle for each iteration

35 Two definitions for the factorial Iterative: N! = N Recursive: N! = N (N 1)! Base case Fact(0) = 1 (0! is 1) General Case Fact(N) = N Fact(N-1) (for N 1) 35

36 Is this a valid recursion? Source: 36

37 Base case Fact(1) = 1 General Case Fact(N) = N Fact(N-1) How does the genie calculate Fact(3)? 37

38 Your turn! N! = N * (N 1)! Base case Facto(0) = 1 (0! is 1) General Case Fact(N) = N * Fact(N-1) (for N 1) Calculate: 0! = 1! = 2! = 5! = 38

39 Recursive Factorial algorithm Write Enter n Read n Set result to Factorial(n) Write result + is the factorial of + n Factorial(n) IF (n equals 0) RETURN 1 ELSE RETURN n * Factorial(n-1) 39

40 QUIZ: Write this recursive function in Python Write Enter n Read n Set result to Factorial(n) Write result + is the factorial of + n Factorial(n) IF (n equals 0) RETURN 1 ELSE RETURN n * Factorial(n-1) 40

41 solution 41

42 42 Recursive Binary Search BinarySearch (first, last) IF (first > last) RETURN FALSE ELSE Set middle to (first + last)/ 2 IF (item equals data[middle]) RETURN TRUE ELSE IF (item < data[middle]) BinarySearch (first, middle 1) ELSE BinarySearch (middle + 1, last)

43 SKIP QUICKSORT Just remember that it is faster (more efficient) than Selection Sort 43

44 SKIP 7.7 Important Threads 44

45 Read and take notes: Ethical Issues Open-Source Software Development What are the advantages and disadvantages of open-source software? What does the success of Linux suggest about the future of open-source software? Should open-source software be licensed and subject to standard copyright laws? 45

46 Chapter review questions Describe the computer problem-solving process and relate it to Polya s How to Solve It list Distinguish between a simple type and a composite type Distinguish between a void subprogram and a value-returning subprogram Recognize a recursive problem and write a recursive algorithm to solve it Distinguish between an unsorted array and a sorted array Describe the Quicksort algorithm Apply the linear search, binary search, selection sort and Quicksort to an array of items by hand What are the advantages and disadvantages of open-source software? 46

47 Who am I? I am a mathematician. Why is my picture in a book about computer science? 47

48 Homework: End-of-chapter questions 30, 31, 34, 35, 36, 66 b, c Not from text: Calculate 7! by hand, showing all the recursive steps, as done in the lecture examples. 48

49 QUIZ Selection Sort Show the swapped elements with arrows. Show the sorted elements with shading

50 Individual work for next time Show the swapped elements with arrows. Show the sorted elements with shading