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Arrays (Continue) Sorting and searching. outlines Sorting – Bubble sort Linear search – min and max Binary search.

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Presentation on theme: "Arrays (Continue) Sorting and searching. outlines Sorting – Bubble sort Linear search – min and max Binary search."— Presentation transcript:

1 Arrays (Continue) Sorting and searching

2 outlines Sorting – Bubble sort Linear search – min and max Binary search

3 Sort Bubble Sort

4 Sorting Sorting takes an unordered collection and makes it an ordered one. 5 12 3542 77 101 1 2 3 4 5 6 5 12 35 42 77101 1 2 3 4 5 6

5 "Bubbling Up" the Largest Element Traverse a collection of elements – Move from the front to the end – Bubble the largest value to the end using pair- wise comparisons and swapping 5 12 3542 77 101 1 2 3 4 5 6 Swap 4277

6 "Bubbling Up" the Largest Element Traverse a collection of elements – Move from the front to the end – Bubble the largest value to the end using pair- wise comparisons and swapping 5 12 3577 42 101 1 2 3 4 5 6 Swap 3577

7 "Bubbling Up" the Largest Element Traverse a collection of elements – Move from the front to the end – Bubble the largest value to the end using pair- wise comparisons and swapping 5 12 7735 42 101 1 2 3 4 5 6 Swap 1277

8 "Bubbling Up" the Largest Element Traverse a collection of elements – Move from the front to the end – Bubble the largest value to the end using pair- wise comparisons and swapping 5 77 1235 42 101 1 2 3 4 5 6 No need to swap

9 "Bubbling Up" the Largest Element Traverse a collection of elements – Move from the front to the end – Bubble the largest value to the end using pair- wise comparisons and swapping 5 77 1235 42 101 1 2 3 4 5 6 Swap 5101

10 "Bubbling Up" the Largest Element Traverse a collection of elements – Move from the front to the end – Bubble the largest value to the end using pair- wise comparisons and swapping 77 1235 42 5 1 2 3 4 5 6 101 Largest value correctly placed

11 The Bubble Up Algorithm for(int i = 0; iA[j+1]) { temp= A[j]; A[j]=A[j+1]; A[j+1]=temp; }

12 Items of Interest Notice that only the largest value is correctly placed All other values are still out of order So we need to repeat this process 77 1235 42 5 1 2 3 4 5 6 101 Largest value correctly placed

13 Repeat Bubble Up How Many Times? If we have N elements… And if each time we bubble an element, we place it in its correct location… Then we repeat the bubble up process N – 1 times. This guarantees well correctly place all N elements.

14 Bubbling All the Elements 77 1235 42 5 1 2 3 4 5 6 101 5 4212 35 77 1 2 3 4 5 6 10142 5 35 12 77 1 2 3 4 5 6 10142 35 5 12 77 1 2 3 4 5 6 10142 35 12 5 77 1 2 3 4 5 6 101 N - 1

15 Reducing the Number of Comparisons 12 35 42 77 101 1 2 3 4 5 6 577 1235 42 5 1 2 3 4 5 6 101 5 4212 35 77 1 2 3 4 5 6 10142 5 35 12 77 1 2 3 4 5 6 10142 35 5 12 77 1 2 3 4 5 6 101

16 for(int i = 0; iA[j+1]) { temp= A[j]; A[j]=A[j+1]; A[j+1]=temp; }

17 Already Sorted Collections? What if the collection was already sorted? What if only a few elements were out of place and after a couple of bubble ups, the collection was sorted? We want to be able to detect this and stop early! 42 35 12 5 77 1 2 3 4 5 6 101

18 Using a Boolean Flag We can use a boolean variable to determine if any swapping occurred during the bubble up. If no swapping occurred, then we know that the collection is already sorted! This boolean flag needs to be reset after each bubble up.

19 Add flag to reduce the number of iterations Boolean swap = false; for(int i = 0; iA[j+1]) { temp= A[j]; A[j]=A[j+1]; A[j+1]=temp; swap = true; }

20 An Animated Example 674523146339842 1 2 3 4 5 6 7 8 j index 0 A.length 8 swap true

21 An Animated Example 674523146339842 1 2 3 4 5 6 7 8 to_do index 0 1 A.lenght 8 did_swap false

22 An Animated Example 674523146339842 1 2 3 4 5 6 7 8 to_do index 0 1 N 8 Swap did_swap false

23 An Animated Example 674598146332342 1 2 3 4 5 6 7 8 to_do index 0 1 N 8 Swap did_swap true

24 An Animated Example 674598146332342 1 2 3 4 5 6 7 8 j index 7 2 A.length 8 did_swap true

25 An Animated Example 674598146332342 1 2 3 4 5 6 7 8 to_do index 7 2 N 8 Swap did_swap true

26 An Animated Example 679845146332342 1 2 3 4 5 6 7 8 j index 0 2 A.length 8 Swap did_swap true

27 An Animated Example 679845146332342 1 2 3 4 5 6 7 8 j index 0 3 A.length 8 swap true

28 An Animated Example 679845146332342 1 2 3 4 5 6 7 8 j index 0 3 A.lengt 8 Swap swap true

29 An Animated Example 671445986332342 1 2 3 4 5 6 7 8 j index 0 3 A.lengt 8 Swap swap true

30 An Animated Example 671445986332342 1 2 3 4 5 6 7 8 j index 0 4 A.lengt 8 swap true

31 An Animated Example 671445986332342 1 2 3 4 5 6 7 8 j index 0 4 A.length 8 Swap did_swap true

32 An Animated Example 671445698332342 1 2 3 4 5 6 7 8 j index 0 4 A.length 8 Swap did_swap true

33 An Animated Example 671445698332342 1 2 3 4 5 6 7 8 j index 0 5 A.lengt 8 swap true

34 An Animated Example 671445698332342 1 2 3 4 5 6 7 8 j index 0 5 A.lengt 8 Swap swap true

35 An Animated Example 981445667332342 1 2 3 4 5 6 7 8 j index 0 5 A.length 8 Swap did_swap true

36 An Animated Example 981445667332342 1 2 3 4 5 6 7 8 j index 0 6 A.length 8 swap true

37 An Animated Example 981445667332342 1 2 3 4 5 6 7 8 j index 0 6 A.lengt 8 Swap swap true

38 An Animated Example 331445667982342 1 2 3 4 5 6 7 8 j index 0 6 A.lengt 8 Swap swap true

39 An Animated Example 331445667982342 1 2 3 4 5 6 7 8 j index 0 7 A.lengt 8 swap true

40 An Animated Example 331445667982342 1 2 3 4 5 6 7 8 j index 0 7 A.length 8 Swap swap true

41 An Animated Example 331445667422398 1 2 3 4 5 6 7 8 j index 0 7 A.length 8 Swap swap true

42 After First Pass of Outer Loop 331445667422398 1 2 3 4 5 6 7 8 j index 0 8 A.length 8 Finished first Bubble Up swap true

43 The Second Bubble Up 331445667422398 1 2 3 4 5 6 7 8 j index 2 1 A.length 8 swap false

44 The Second Bubble Up 331445667422398 1 2 3 4 5 6 7 8 j index 2 1 A.length 8 swap false No Swap

45 The Second Bubble Up 331445667422398 1 2 3 4 5 6 7 8 j index 1 2 A.length 8 swap false

46 The Second Bubble Up 331445667422398 1 2 3 4 5 6 7 8 j index 1 2 A.length 8 did_swap false Swap

47 The Second Bubble Up 334514667422398 1 2 3 4 5 6 7 8 j index 1 2 A.length 8 did_swap true Swap

48 The Second Bubble Up 334514667422398 1 2 3 4 5 6 7 8 j index 1 3 A.length 8 swap true

49 The Second Bubble Up 334514667422398 1 2 3 4 5 6 7 8 j index 1 3 A.length 8 did_swap true Swap

50 The Second Bubble Up 336144567422398 1 2 3 4 5 6 7 8 j index 1 3 A.length 8 swap true Swap

51 The Second Bubble Up 336144567422398 1 2 3 4 5 6 7 8 j index 1 4 A.length 8 did_swap true

52 The Second Bubble Up 336144567422398 1 2 3 4 5 6 7 8 to_do index 1 4 N 8 swap true No Swap

53 The Second Bubble Up 336144567422398 1 2 3 4 5 6 7 8 to_do index 1 5 N 8 swap true

54 The Second Bubble Up 336144567422398 1 2 3 4 5 6 7 8 to_do index 1 5 N 8 swap true Swap

55 The Second Bubble Up 676144533422398 1 2 3 4 5 6 7 8 j index 1 5 A.length 8 swap true Swap

56 The Second Bubble Up 676144533422398 1 2 3 4 5 6 7 8 j index 1 6 A.length 8 swap true

57 The Second Bubble Up 676144533422398 1 2 3 4 5 6 7 8 to_do index 1 6 N 8 swap true Swap

58 The Second Bubble Up 426144533672398 1 2 3 4 5 6 7 8 to_do index 1 6 N 8 swap true Swap

59 After Second Pass of Outer Loop 426144533672398 1 2 3 4 5 6 7 8 index 1 7 N 8 swap true Finished second Bubble Up

60 The Third Bubble Up 426144533672398 1 2 3 4 5 6 7 8 j index 2 1 A.length 8 swap false

61 The Third Bubble Up 426144533672398 1 2 3 4 5 6 7 8 j index 2 1 A.length 8 swap false Swap

62 The Third Bubble Up 426234533671498 1 2 3 4 5 6 7 8 j index 2 1 A.length 8 swap true Swap

63 The Third Bubble Up 426234533671498 1 2 3 4 5 6 7 8 j index 2 2 A.length 8 swap true

64 The Third Bubble Up 426234533671498 1 2 3 4 5 6 7 8 j index 2 2 A.lengt 8 swap true Swap

65 The Third Bubble Up 422364533671498 1 2 3 4 5 6 7 8 j index 2 2 A.lengt 8 swap true Swap

66 The Third Bubble Up 422364533671498 1 2 3 4 5 6 7 8 to_do index 2 3 N 8 did_swap true

67 The Third Bubble Up 422364533671498 1 2 3 4 5 6 7 8 j index 2 3 A.length 8 swap true No Swap

68 The Third Bubble Up 422364533671498 1 2 3 4 5 6 7 8 j index 2 4 A.length 8 did_swap true

69 The Third Bubble Up 422364533671498 1 2 3 4 5 6 7 8 j index 2 4 A.length 8 swap true Swap

70 The Third Bubble Up 422363345671498 1 2 3 4 5 6 7 8 j index 2 4 A.length 8 swap true Swap

71 The Third Bubble Up 422363345671498 1 2 3 4 5 6 7 8 j index 2 5 A.length 8 did_swap true

72 The Third Bubble Up 422363345671498 1 2 3 4 5 6 7 8 j index 2 5 A.length 8 swap true Swap

73 The Third Bubble Up 452363342671498 1 2 3 4 5 6 7 8 j index 2 5 A.length 8 did_swap true Swap

74 After Third Pass of Outer Loop 452363342671498 1 2 3 4 5 6 7 8 j index 2 6 A.length 8 did_swap true Finished third Bubble Up

75 The Fourth Bubble Up 452363342671498 1 2 3 4 5 6 7 8 j index 3 1 A.length 8 swap false

76 The Fourth Bubble Up 452363342671498 1 2 3 4 5 6 7 8 j index 3 1 A.length 8 swap false Swap

77 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 to_do index 3 1 N 8 did_swap true Swap

78 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 3 2 A.length 8 swap true

79 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 3 2 A.length 8 did_swap true No Swap

80 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 3 3 A.length 8 swap true

81 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 3 3 A.length 8 did_swap true No Swap

82 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 3 4 A.length 8 swap true

83 The Fourth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 3 4 A.length 8 did_swap true No Swap

84 After Fourth Pass of Outer Loop 452314334267698 1 2 3 4 5 6 7 8 j index 3 5 A.length 8 swap true Finished fourth Bubble Up

85 The Fifth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 4 1 A.length 8 swap false

86 The Fifth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 4 1 A.lenght 8 swap false No Swap

87 The Fifth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 4 2 A.length 8 swap false

88 The Fifth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 4 2 A.length 8 swap false No Swap

89 The Fifth Bubble Up 452314334267698 1 2 3 4 5 6 7 8 j index 4 3 A.length 8 swap false

90 Finished Early 452314334267698 1 2 3 4 5 6 7 8 j index 3 4 A.lengt 8 swap false We didnt do any swapping, so all of the other elements must be correctly placed. We can skip the last two passes of the outer loop.

91 Bubble sort Summary Bubble Up algorithm will move largest value to its correct location (to the right) Repeat Bubble Up until all elements are correctly placed: – Maximum of N-1 times – Can finish early if no swapping occurs We reduce the number of elements we compare each time one is correctly placed

92 Linear search Use linear to seach and value is contained in one array.

93 Searching for x in an array a for(int i = 0; i < a.length; ++ i) { if (a[i] == x) System.out.println(true); }

94 Finding the minimal value in array int minValue = a[0]; int minIndex = 0; for(int i = start + 1; i < end; i ++) { if (a[i] < minValue) { minValue = a[i]; minIndex = i; }

95 Finding the minimal value in array int maxValue = a[0]; int maxIndex = 0; for(int i = start + 1; i < end; i ++) { if (a[i] > maxValue) { maxValue = a[i]; maxIndex = i; }

96 Binary search for a value in array Searching if x is in array a. We assume a is sorted in ascending order. int start = 0; int end = a.length - 1; boulean found = flase while (start <= end) { int m = (start + end)/2; if (x == a[m]) {found =false;} else if (x < a[m]) { end = m - 1;} else { start = m + 1; }

97 summary Buble sort Learnear search Binary sort


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