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Document that explains the chosen concept to the animator

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1 Document that explains the chosen concept to the animator
1 1

2 Course Name: Design and Analysis of Algorithm
Quick Sort Course Name: Design and Analysis of Algorithm Level: UG. Authors :-Praveen Pal Mentor :- Aruna Adil 2 2

3 Learning Objectives After interacting with this Learning Object, the learner will be able to: Sort an array using Quick sort. How Quick sort works. Advantages of quick sort over other sorting algorithm 3 3

4 1 2 3 4 5 Definitions of the components/Keywords:
Quick sort is a randomized sorting algorithm based on the divide & conquer paradigm. Divide:- If the given sequence of values (array)has two or more element then pick an element x (Called pivot) randomly from sequence and partition the array into sub-array. L(low): sub-array contains elements less than x. E(Equal): sub-array contains element equal to x. G(Greater): sub-array contains elements greater than x. Recursively sort L and G (ie. apply the same process written above for L & G) Conquer: Finally join L, E & G. This algorithm is capable to sort large number of input very quickly that’s why this algorithm is called quick sort . This sorting technique is also called the “in-place sorting” because it does not require extra space for sorting . 2 3 4 5 4 4 4

5 Master layout or diagram
INSTRUCTIONS SLIDE 1 Master layout or diagram Make a schematic diagram of the concept Explain to the animator about the beginning and ending of the process. Draw image big enough for explaining. In above image, identify and label different components of the process/phenomenon. (These are like characters in a fi lm)‏ Illustrate the basic flow of action by using arrows. Use BOLD lines in the diagram, (minimum 2pts.)‏ In the slide after that, provide the definitions of ALL the labels used in the diagram 2 3 4 5 5 5

6 IMPORTANT NOTE TO THE ANIMATOR:
All the instructions/labels or anything WRITTEN in blue are CONTENT NOT TO BE DISPLAYED! All the instructions WRITTEN in black are CONTENT TO BE DISPLAYED! This is not applicable for images as there can be overlapping of these colours there. This should be followed for all the instructions, labels,etc… Kindly keep a note of this while displaying text in the animation. 6

7 INSTRUCTIONS SLIDE Components 1 Index 2 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 3 Array or list 4 Note: 1:blue color represent the array All digit written in white letter in the array are “element” or “value at index n “(n refers to index number ex. value at index 4 = 5). . 5 7 7

8 Project OSCAR IDD Template 4.7
Master Layout Quick Sort Status:- All steps will display here Put the Start, Pause, Stop, Step, reset ,Think button to control animation. Put a slidebar to control the speed of animation. Put a “let me try” button. 1 2 3 4 5 6 7 8 9 16 28 9 2 5 7 6 4 1 3 When “Think” is pressed, the applet will run with a time delay so that user can think about the next step. When “Step” button is pressed, the applet will start, but will stop after every step until the step button is pressed. When “let me try ” button is pressed then array will display(slide 34,35) and user will select pivot by click and to swap value user click on both value which he/she want to swap. The status bar will be removed in “let me try” mode. 8 Note : Animators are free to change the color and graphics to make animation more effective. Project OSCAR IDD Template 4.7 8

9 3 Step 2: 1 2 4 5 Selecting and placing pivot 1 2 3 4 5 6 7 8 9 16 28
1 2 3 4 5 6 7 8 9 2 16 28 9 2 5 7 6 4 1 3 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) When user click on start display this array. Represent first index by i. as shown in slide. Represent last index by j. as shown in slide. Select value 6 as a pivot represent pivot by red color. Array to be sorted in ascending order. Select a pivot randomly. Select the First index (0) and Last index (9) of the array. 5

10 3 Step 2: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 16
1 2 3 4 5 6 7 8 9 2 16 28 9 2 5 7 6 4 1 3 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent first index by i. as shown in slide. Represent last index by j. as shown in slide. Select value 6 as a pivot represent pivot by red color. Rearrange elements of array so that pivot reaches to it’s final place values left of pivot must be less then or equal to pivot and values right of pivot must be greater than pivot. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 5

11 3 Step 3: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 16
1 2 3 4 5 6 7 8 9 2 16 28 9 2 5 7 6 4 1 3 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent selected index by green color. increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. Show the movement of element from one index to other during swap don’t place it directly. Compare selected index ‘s values 16 and 3 with pivot . 16 > pivot 6 and 3 < pivot 6 swap : 16,3 Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 5

12 3 Step 4: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 28 9 2 5 7 6 4 1 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent swapped element by grey color. Represent selected index by green color Show the movement of element from one index to other during swap don’t place it directly. First display text then animation. Compare selected index ‘s values 28 and 1 with pivot . 28 > pivot 6 and 1 < pivot 6 swap : 28,1 Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 5

13 3 Step 5: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 9 2 5 7 6 4 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent swapped element by grey color. Show the movement of element from one index to other during swap don’t place it directly. Represent selected index by green color First display text then animation. Compare selected index ‘s values 9 and 4 with pivot . 9 > pivot 6 and 4 < pivot 6 swap : 9,4. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 2 < pivot 6 , increment i by 1; 5<pivot 6. increment i by 1. 5

14 Note:- this and Next slide shows the comparison and swap.
j 1 2 3 4 5 6 7 8 9 3 1 4 2 5 7 6 9 28 16 i j 2< 6 increment i by 1 1 2 3 4 5 6 7 8 9 3 1 4 2 5 7 6 9 28 16 j 5< 6 increment i by 1 i 1 2 3 4 5 6 7 8 9 3 1 4 2 5 7 6 9 28 16 14

15 7 > 6 stop and move to right pointer . i
j 7 > 6 stop and move to right pointer . i 1 2 3 4 5 6 7 8 9 3 1 4 2 5 7 6 9 28 16 i j 6 = 6 (j = pivot) swap I & j; 1 2 3 4 5 6 7 8 9 3 1 4 2 5 7 6 9 28 16 6 reaches to it’s final position 1 2 3 4 5 6 7 8 9 3 1 4 2 5 6 7 9 28 16 15

16 3 Step 6: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 4 2 5 7 6 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent swapped element by grey color. Show the movement of element from one index to other during swap don’t place it directly. Represent selected index by green color First display text then animation. Compare selected index ‘s values 7 and 6 with pivot . 7 > pivot 6 and pivot 6 = pivot 6 swap : 7,6 Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 5

17 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 4 2 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent swapped element by grey color. Show the movement of element from one index to other during swap don’t place it directly. Represent selected index by green color Now 6 reaches to it’s correct position. Now array is partitioned into two sub array. Left Sub Array index ( 0 - 4): Values left of pivot have smaller or equal value than pivot . Right Sub Array index ( 6 - 9): Values right of pivot have greater values than pivot. Now sort left and right sub array recursively. 5 17

18 3 Step 7: 1 2 4 5 Selecting and placing pivot 1 2 3 4 5 6 7 8 9 3 1 4
1 2 3 4 5 6 7 8 9 2 3 1 4 2 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Now array is divided in two sub-arrays. Change the color of sub array in blue apply the same process as described in slide to each sub- array . Now array is partitioned into two sub array. Values left of pivot have smaller or equal value than pivot. Values right of pivot have greater values than pivot. Now sort left and right sub array recursively. 5 18

19 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 4 2 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Firstly sort left sub array ie. Index0 to index 4. Same process will be applied as we applied from slide Represent index 0 by i. Represent index 4 by j. Select pivot 4 .represent pivot by red color. First recursively sort left sub array. Select a pivot randomly from left sub array . Select the First index (0) and Last index (4) of the array. Rearrange elements of array so that pivot x reaches to it’s final place and values left of pivot must be less then or equal to pivot and values right of pivot must be greater than pivot. 5 19

20 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 4 2 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent selected index by green color. Same process will be applied as we applied from slide NOTE:- Please read instructions written in right hand side in all slide. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 3 < pivot 4 increment i. 1< pivot 4 increment i. j > pivot 4 decrement j. 2< pivot 4 decrement j. 5 20

21 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 4 2 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Show the movement of items from one position to another rather than swap them directly. 2< pivot 4 Swap 4,2. 5 21

22 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 2 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Now array is divided in two sub-arrays. Change the color of sub array in blue apply the same process as described in slide to each sub- array . Now 4 reaches to it’s correct position. Now array is partitioned into two sub array. Left Sub Array index (0 – 2): Values left of pivot have smaller or equal value than pivot . Right Sub Array index (4): Values right of pivot have greater values than pivot. Right sub array contain single value so no need to sort it. Now sort left and right sub array recursively. 5 22

23 3 Step 7: 1 2 4 5 Selecting and placing pivot 1 2 3 4 5 6 7 8 9 3 1 2
1 2 3 4 5 6 7 8 9 2 3 1 2 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Firstly sort left sub array ie. Index0 to index 2. Same process will be applied as we applied from slide Represent index 0 by i. Represent index 2 by j. Again sub array is partitioned in two sub array Left sub array index(0 -2) & right sub array index(4). 5 23

24 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 3
1 2 3 4 5 6 7 8 9 2 3 1 2 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Same process will be applied as we applied from slide Represent index 0 by i. Represent index 2 by j. Select pivot 2 .represent pivot by red color. NOTE:- Please read instructions written in right hand side in all slide. Select a pivot randomly . Select the First index (0) and Last index (2) of the array. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 3> pivot 2 and 2=pivot 2. Swap 3,2. 5 24

25 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 2
1 2 3 4 5 6 7 8 9 2 2 1 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Firstly sort left sub array ie. Index0 to index 2. Same process will be applied as we applied from slide Represent index 0 by i. Represent index 2 by j. Select pivot 2 .represent pivot by red color. NOTE:- Please read instructions written in right hand side in all slide. Select a pivot randomly. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 3> pivot 2 and 2=pivot 2. Swap 3,2. 5 25

26 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 2
1 2 3 4 5 6 7 8 9 2 2 1 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Firstly sort left sub array ie. Index0 to index 2. Same process will be applied as we applied from slide Represent index 0 by i. Represent index 2 by j. Select pivot 2 .represent pivot by red color. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 1< 2 swap 1,2. 5 26

27 3 Step 7: 1 2 4 5 Selecting and placing pivot i j 1 2 3 4 5 6 7 8 9 1
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Firstly sort left sub array ie. Index0 to index 2. Same process will be applied as we applied from slide Represent index 0 by i. Represent index 2 by j. Select pivot 2 .represent pivot by red color. Now left sub array is completely sorted Same process is applied for right sub array. Index 6-9. 5 27

28 3 Step 7: 1 2 4 5 Selecting and placing pivot 1 2 3 4 5 6 7 8 9 1 2 3
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Now left sub array is completely sorted Same process is applied for right sub array. Index 6-9. 5 28

29 3 Step 7: 1 2 4 5 Selecting and placing pivot (right sub array) 1 2 3
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Same process will be applied as we applied from slide Represent index 6 by i. Represent index 9 by j. Select pivot 9 .represent pivot by red color. Select a pivot randomly . Select the First index (6) and Last index (9) of the array. Rearrange elements of array so that pivot x reaches to it’s final place and values left of pivot must be less then or equal to pivot and values right of pivot must be greater than pivot. 5 29

30 3 Step 7: 1 2 4 5 Selecting and placing pivot (right sub array) i j 1
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Represent selected index by green color. Represent index 6 by i. Represent index 9 by j. Select pivot 9 .represent pivot by red color. NOTE:- Please read instructions written in right hand side in all slide. Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. All values are on correct place so no need to swap. Now sort the right sub array index (8-9). 5 30

31 3 Step 7: 1 2 4 5 Selecting and placing pivot (right sub array) i j 1
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) NOTE:- Please read instructions written in right hand side in all slide. All values are on correct place so no need to swap. Now sort the right sub array index (8-9). 5 31

32 3 Step 7: 1 2 4 5 Selecting and placing pivot (right sub array) 1 2 3
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Same process will be applied as we applied from slide Represent index 8 by i. Represent index 9 by j. Select pivot 28 .represent pivot by red color. Select a pivot randomly 5 32

33 3 Step 7: 1 2 4 5 Selecting and placing pivot (right sub array) i j 1
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 28 16 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Same process will be applied as we applied from slide Increment i by 1 until it reach to a value greater than pivot & decrement j by one until it reach to a value smaller than pivot. 28> 16 swap 16,28 5 33

34 3 Step 7: 1 2 4 5 Selecting and placing pivot (right sub array) 1 2 3
1 2 3 4 5 6 7 8 9 2 1 2 3 4 5 6 7 9 16 28 3 Array elements to be sorted. Pivot element. Selected Index value Swapped Index value 4 Instruction for the animator Text to be displayed in the working area (DT) Same process will be applied as we applied from slide Represent index 8 by i. Represent index 9 by j. Select pivot 28 .represent pivot by red color. Quick sort complete. 5 34

35 Interactivity and Boundary limits
1 Interactivity and Boundary limits In this section, you will add the ‘Interactivity’ options to the animation. Use the template in the next slide to give the details. Insert the image of the step/s (explained earlier in the Section 3) in the box, and provide the details in the table below. The details of Interactivity could be: Types: Drop down, Slider bar, Data inputs etc. Options: Select one, Multiple selections etc Boundary Limits: Values of the parameters, which won’t show results after a particular point Results: Explain the effect of the interaction in this column Add more slides if necessary 2 3 4 5 35 35

36 Test your understanding
Electrical Engineering Slide 4 Slide 4 Slide Slide 41 Introduction Definitions Analogy Test your understanding (questionnaire)‏ Lets Sum up (summary)‏ Want to know more… (Further Reading)‏ Interactivity: Array Size : Values : : Try it yourself Place an input box to enter the size of array not more than 15. Place an another input box to enter values to be sorted of size specified in above input box. Place an enter button to enter the value. . After entering the selected values, master layout1 procedure is to be done In the input box the user will input all the numerical values that he/she wants to sort. Display array of size entered above as input , with it’s index and values . Allow values to be entered one by one. 36 Credits

37 3 1 2 4 5 Let me try (allow user to select and sort) 1 2 3 4 5 6 68 75
1 2 3 4 5 6 2 68 75 89 37 84 72 82 3 4 Instruction for the animator Text to be displayed in the working area (DT) If user click on “let me try” button then display this array and allow user to do all the tasks by own. Give four chances to user to select correct answer after that correct the answer and move the user to next step. If user click four or more time right answer then give a greeting to user “very good you are going right” 5

38 3 1 2 4 5 Let me try (allow user to select and sort) 1 2 3 4 5 6 68 75
1 2 3 4 5 6 68 75 89 37 84 72 82 3 4 Instruction for the animator Text to be displayed in the working area (DT) user select pivot randomly, color the selected pivot red. . Allow user to arrange value ,so that values left of pivot must be less or equal to pivot and values right of pivot must be greater than pivot. To swap value user click on both value which he/she want to swap. Restrict user to select only correct value on wrong value show the error. Now arrange value such that values left of pivot must be less or equal to pivot and values right of pivot must be greater than pivot. 5

39 Self- Assessment Questionnaire for Learners
INSTRUCTIONS SLIDE Self- Assessment Questionnaire for Learners Please provide a set of questions that a user can answer based on the LO. They can be of the following types: These questions should be 5 in number and can be of objective type (like MCQ, Match the columns, Yes or No, Sequencing, Odd One Out). The questions can also be open-ended. The user would be asked to think about the question. The author is requested to provide hints if possible, but a full answer is not necessary. One can include questions, for which the user will need to interact with the LO (with certain parameters) in order to answer it. 39 39

40 Questionnaire for users to test their understanding
INSTRUCTIONS SLIDE Questionnaire for users to test their understanding Please make sure that the questions can be answered by interacting with the LO. It is better to avoid questions based purely on recall. 40 40

41 Project OSCAR IDD Template 4.7
Question 1: Which one is the fastest algorithm. Answers: Selection sort Insertion sort 3. Quick sort all Correct answer: Quick sort Feedback/Justification to be displayed: If user clicks correct answer then display ____ Correct ____ If user clicks incorrect answer then display ____Incorrect 3 is correct answer, go to the animation again_______. Project OSCAR IDD Template 4.7 41 41

42 Project OSCAR IDD Template 4.7
Question 2: In selecting pivot for quick-sort which one is the best choice for optimal partition. Answers: The first element of the array. 2. The last element of the array. The middle element of array. The median of array. Correct answer: The median of array. Feedback/Justification to be displayed: If user clicks correct answer then display ____ Correct ____ If user clicks incorrect answer then display ____Incorrect. 4 is correct answer because median guarantees even partition of array_______. Project OSCAR IDD Template 4.7 42 42

43 Project OSCAR IDD Template 4.7
Question 3: What will be the impact on running time if every time largest element or smallest element is selected as a pivot. Answers: Worst case running time . 2. Best case running time. Average case running time. no effect. Correct answer: worst case running time. Feedback/Justification to be displayed: If user clicks correct answer then display ____ Correct ____ If user clicks incorrect answer then display ____Incorrect. 1 is correct answer because largest or smallest element always give the quadratic run time_______. Project OSCAR IDD Template 4.7 43 43

44 Project OSCAR IDD Template 4.7
Question 4:-quick sort is fast for? Answers: For large size list. For small size list . works for both large and small size list. none Correct answer: works for both large and small size list. Feedback/Justification to be displayed: If user clicks correct answer then display ____ Correct ____ If user clicks incorrect answer then display ____Incorrect 3 is correct answer _______. Project OSCAR IDD Template 4.7 44 44

45 Project OSCAR IDD Template 4.7
References Website links for further reading: Books: “Introduction to Algorithm” Thomas H. Coremen Project OSCAR IDD Template 4.7 45 45


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