Bubble Sort Example

5 1 4 2 8

1 5 4 2 8

1 4 5 2 8

1 4 2 5 8

1 4 2 5 8

1 4 2 5 8

1 2 4 5 8

1 2 4 5 8

1 2 4 5 8

Selection Sort63 25 12 22 11

63 25 12 22 11

11 25 12 22 63

void selectionSort(int[] a) {   for (int i = 0; i < a.length - 1; i++) {     int min = i;     for (int j = i + 1; j < a.length; j++) {       if (a[j] < a[min]) {         min = j;       }     }     if (i != min) {       int swap = a[i];       a[i] = a[min];       a[min] = swap;     }   } }

11 12 25 22 63

11 12 22 25 63

i

i min

i min

i min

i, min

11 12 22 25 63i, min

Insertion SortinsertionSort(array A) begin   for i := 1 to length[A] - 1 do   begin     value := A[ i ];     j := i - 1;     while j >= 0 and A[ j ] > value do     begin       A[ j + 1] := A[ j ];       j := j - 1;     end;     A[ j + 1] := value;   end; end;

63 25 12 22 11

25 63 12 22 11

12 25 63 22 11

12 22 25 63 11

11 12 22 25 63

Merge Sort – Partition Process

35 62 33 20 5 72 48 50

35 62 33 20 5 72 48 50

35 62 33 20 5 72 48 50

35 62 33 20 5 72 48 50

Merge Sort – Merge Process

35 62 33 20 5 72 48 50

40 20 10 80 60 50 7 30 100 90 70

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

Starting at the beginning of the array, we look for the first element that is greater than the pivot. (tooBigIndex)

Starting from the other end we look for the first value that is less than or euqal to the pivot. (tooSmallIndex)

After finding the two out-of-place elements, exchange them.

tooBigIndex++ tooSmallIndex—

Stop when tooBigIndex >= tooSmallIndex

tooBigIndex tooSmallIndexQuicksort

40 20 10 80 60 50 7 30 100 90 70

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

tooBigIndex tooSmallIndex

40 20 10 30 60 50 7 80 100 90 70

tooBigIndex tooSmallIndex

40 20 10 30 7 50 60 80 100 90 70

tooBigIndex

tooSmallIndex

40 20 10 30 7 50 60 80 100 90 70

tooBigIndextooSmallIndex

7 20 10 30 40 50 60 80 100 90 70

Heapsort

21

42

22

27

23

45

35

19 4 5

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

45 27 42 21 23 22 35 19 4 5[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

5 27 42 21 23 22 35 19 4 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

42 27 5 21 23 22 35 19 4 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

42 27 35 21 23 22 5 19 4 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

42 27 35 21 23 22 5 19 4 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

4 27 35 21 23 22 5 19 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

35 27 4 21 23 22 5 19 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

35 27 22 21 23 4 5 19 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

35 27 22 21 23 4 5 19 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

19 27 22 21 23 4 5 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

27 19 22 21 23 4 5 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

27 23 22 21 19 4 5 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

27 23 22 21 19 4 5 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

5 23 22 21 19 4 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

23 5 22 21 19 4 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

23 21 22 5 19 4 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

23 21 22 5 19 4 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

4 21 22 5 19 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

22 21 4 5 19 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

22 21 4 5 19 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

19 21 4 5 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

21 19 4 5 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

21 19 4 5 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

5 19 4 21 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

19 5 4 21 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]

19 5 4 21 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

4 5 19 21 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

4 5 19 21 22 23 27 35 42 45[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

• For an element in arr[i]: Parent[(i-1)/2]– Left child [2i+1]– Right child [2i+2]