# Quick Sort. Implementation

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1 Implementation Next, recall that our goal is to partition all remaining elements based on whether they are smaller than or greater than the pivot We will find two entries: One larger than the pivot (staring from the front) One smaller than the pivot (starting from the back) which are out of order and then correct the ordering I.e., swap them 1

2 Implementation Continue doing so until the appropriate entries you find are actually in order The index to the larger entry we found would be the first large entry in the list (as seen from the left) Therefore, we could move this entry into the last entry of the list We can fill this spot with the pivot 2

3 Example First, we examine the first, middle, and last entries of the full list The span below will indicate which list we are currently sorting 3

4 Example We select 57 to be our pivot We move 24 into the first location 4

5 Example Starting at the 2 nd and 2 nd -last locations: we search forward until we find 70 > 57 we search backward until we find 49 < 57 5

6 Example We swap 70 and 49, placing them in order with respect to eachother 6

7 Example We search forward until we find 97 > 57 We search backward until we find 16 < 57 7

8 Example We swap 16 and 97 which are now in order with respect to each other 8

9 Example We search forward until we find 63 > 57 We search backward until we find 55 < 57 9

10 Example We swap 63 and 55 10

11 Example We search forward until we find 85 > 57 We search backward until we find 36 < 57 11

12 Example We swap 85 and 36, placing them in order with respect to each other 12

13 Example We search forward until we find 68 > 57 We search backward until we find 9 < 57 13

14 Example We swap 68 and 9 14

15 Example We search forward until we find 76 > 57 We search backward until we find 9 < 57 The indices are out of order, so we stop 15

16 Example We move the larger indexed item to the vacancy at the end of the array We fill the empty location with the pivot, 57 The pivot is now in the correct location 16

17 Example We will now recursively call quick sort on the first half of the list When we are finished, all entries < 57 will be sorted 17

18 Example We examine the first, middle, and last elements of this sub list 18

19 Example We choose 24 to be our pivot We move 9 into the first location in this sub-list 19

20 Example We search forward until we find 49 > 24 We search backward until we find 21 < 24 20

21 Example We swap 49 and 21, placing them in order with respect to eachother 21

22 Example We search forward until we find 38 > 24 We search backward until we find 16 < 24 The indices are reversed, so we stop 22

23 Example We move 38 to the vacant location and move the pivot 24 into the location previously occupied by is now in the correct location 23

24 Example We will now recursively call quick sort on the left and right halves of those entries which are < 57 24

25 Example The first partition has three entries, so we sort it using insertion sort 25

26 Example The second partition also has only four entries, so again, we use insertion sort 26

27 Example First we examine the first, middle, and last entries of the sub-list 27

28 Example We choose 74 to be our pivot We move 76 to the vacancy left by 74 28

29 Example We search forward until we find 81 > 74 We search backward until we find 70 < 74 29

30 Example We swap 70 and 84 placing them in order 30

31 Example We search forward until we find 85 > 74 We search backward until we find 61 < 74 31

32 Example We swap 85 and 61 placing them in order 32

33 Example We search forward until we find 79 > 74 We search backward until we find 63 < 74 The indices are reversed, so we stop 33

34 Example We move 79 to the vacant location and move the pivot 74 into the location previously occupied by is now in the correct location 34

35 Example We sort the left sub-list first It has four elements, so we simply use insertion sort 35

36 Example Having sorted the four elements, we focus on the remaining sub-list of seven entries 36

37 Example To sort the next sub-list, we examine the first, middle, and last entries 37

38 Example We select 79 as our pivot and move: 76 into the lowest position 85 into the highest position 38

39 Example We search forward until we find 85 > 79 We search backward until we find 77 < 79 39

40 Example We swap 85 and 77, placing them in order 40

41 Example We search forward until we find 97 > 79 We search backward until we find 77 < 79 The indices are reversed, so we stop 41

42 Example Finally, we move 97 to the vacant location and copy 79 into the appropriate location 79 is now in the correct location 42

43 Example This splits the sub-list into two sub-lists of size 2 and 4 We use insertion sort for the first sub-list 43

44 Example We are left with one sub-list with four entries, so again, we use insertion sort 44

45 Example Sorting the last sub-list, we arrive at an ordered list 45

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