1. Sorting array
The bubblesort

2. Sorting An arrangement or permutation of data May be either:
ascending (non decreasing)
descending (non increasing)

3. Bubblesort

4. Bubblesort algorithm Compare adjacent pairs of array elements
Swap if necessary (out of order)
Repeat on next pair

5. Bubblesort example Given (D,B,E,C,A) We want (A,B,C,D,E) Pass 1:
Smallest to largest; ascending; non decreasing
Pass 1:
D,B,E,C,A start
D,B,E,C,A compare
B,D,E,C,A swap
B,D,E,C,A compare
B,D,E,C,A don’t swap
B,D,C,E,A swap
B,D,C,E,A compare
B,D,C,A,E swap
Note that at the end of pass 1, the last element (E above) is the largest.

6. Bubblesort example Pass 2: B,D,C,A,E start (from pass 1)
B,D,C,A,E compare
B,D,C,A,E don’t swap
B,C,D,A,E swap
B,C,D,A,E compare
B,C,A,D,E swap
Note that we don’t need to continue and compare D and E because E was the overall maximum.
Further note that D is the max of the sub array considered in pass 2.

7. Bubblesort example Pass 3: B,C,A,D,E start (from pass 2)
B,C,A,D,E compare
B,C,A,D,E don’t swap
B,A,C,D,E swap
Note that we don’t need to continue.

8. Bubblesort example Pass 4: B,A,C,D,E start (from pass 3)
B,A,C,D,E compare
A,B,C,D,E swap
Done!
In general, if the length of the list is N, we need to make N-1 passes.

9. Coding the bubblesort First, we need the swap operation:
1,2,4,3,5 becomes 1,2,3,4,5
Write a function that given the index i of an array elements swaps it with the element at index i+1.

10. Coding the bubblesort
public static void swap ( int start, int[] values ) { … }

11. Coding the bubblesort
public static void swap ( int start, int[] values ) {
int temp = values[ start ]; … }

12. Coding the bubblesort
public static void swap ( int start, int[] values ) {
int temp = values[ start ];
values[ start ] = values[ start + 1 ]; … }

13. Coding the bubblesort
public static void swap ( int start, int[] values ) {
int temp = values[ start ];
values[ start ] = values[ start + 1 ];
values[ start + 1 ] = temp; }

14. Coding the bubblesort
Now we need a function to call swap when that operation is necessary.
public static void bubblesort ( int[] values ) { … }
Recall: In general, if the length of the list is N, we need to make N-1 passes.

15. Coding the bubblesort
Recall: In general, if the length of the list is N, we need to make N-1 passes.
public static void bubblesort ( int[] values ) {
//perform one pass through the array
for (int i=0; i<values.length; i++) { … }
Recall from our example:
Pass 1:
D,B,E,C,A start
D,B,E,C,A compare
B,D,E,C,A swap
B,D,E,C,A compare
B,D,E,C,A don’t swap
B,D,C,E,A swap
B,D,C,E,A compare
B,D,C,A,E swap

16. Coding the bubblesort public static void bubblesort ( int[] values ) {
//perform one pass through the array
for (int i=0; i<values.length; i++) {
for (int j=0; j<values.length-1; j++) {
// swap if necessary … }
Recall from our example:
Pass 1:
D,B,E,C,A start
D,B,E,C,A compare
B,D,E,C,A swap
B,D,E,C,A compare
B,D,E,C,A don’t swap
B,D,C,E,A swap
B,D,C,E,A compare
B,D,C,A,E swap

17. Coding the bubblesort public static void bubblesort ( int[] values ) {
//perform one pass through the array
for (int i=0; i<values.length; i++) {
for (int j=0; j<values.length-1; j++) {
// swap if necessary
if (values[j] > values[j+1]) {
swap( j, values ); }
Recall from our example:
Pass 1:
D,B,E,C,A start
D,B,E,C,A compare
B,D,E,C,A swap
B,D,E,C,A compare
B,D,E,C,A don’t swap
B,D,C,E,A swap
B,D,C,E,A compare
B,D,C,A,E swap

18. Coding the bubblesort
But wait! The inner loop (j) always goes from start to end but we said that each pass ensures that the last element in the sub array is maximal and we don’t need to check so far each time.
public static void bubblesort ( int[] values ) {
//perform one pass through the array
for (int i=0; i<values.length; i++) {
for (int j=0; j<values.length-1; j++) {
// swap if necessary
if (values[j] > values[j+1]) {
swap( j, values ); }

19. Coding the bubblesort
But wait! The inner loop (j) always goes from start to end but we said that each pass ensures that the last element in the sub array is maximal and we don’t need to check so far each time.
public static void bubblesort ( int[] values ) {
//perform one pass through the array
for (int i=0; i<values.length; i++) {
for (int j=0; j<values.length-1-i; j++) {
// swap if necessary
if (values[j] > values[j+1]) {
swap( j, values ); }

20. Selection Sort

21. Selection sort
Based on the idea of repeated finding the minimal elements.
How can we find the (single, most) minimal element in an array?

22. Selection sort
How can we find the (single, most) minimal element in an array? …
//let 0 be the location of the smallest element so far
int whereSmallest = 0;
for (int i=1; i<A.length; i++) {
if (A[i]<A[whereSmallest]) {
whereSmallest = i; }
out.writeln( “the smallest is ” + A[whereSmallest]
+ “ which was located at position “ + whereSmallest + “.” );

23. Selection sort Idea: Find the smallest in A[0]..A[ A.length-1 ].
Put that in A[0].
Then find the smallest in A[1]..A[ A.length-1 ].
Put that in A[1]. …
But first, let’s develop a swapPairs function that swaps a pair of elements denoted by a and b in some array, A.
<-1, 2, 4, -5, 12>  <-5, 2, 4, -1, 12>

24. Selection sort public static void swapPair ( … ) { … }
What do we need in here to do the job (function parameters)?

25. Selection sort public static void swapPair ( int[] A, int a, int b ) {… }
What do we need in here to do the job (function parameters)?

26. Selection sort public static void swapPair ( int[] A, int a, int b ) {
int temp = A[a];
A[a] = A[b];
A[b] = temp; }

27. Selection sort Idea: Find the smallest in A[0]..A[ A.length-1 ].
Put that in A[0].
Then find the smallest in A[1]..A[ A.length-1 ].
Put that in A[1]. …
//let 0 be the location of the smallest element so far
int whereSmallest = 0;
for (int i=1; i<A.length; i++) {
if (A[i]<A[whereSmallest]) {
whereSmallest = i; }
swapPairs( A, 0, whereSmallest );

28. Selection sort Idea: Find the smallest in A[0]..A[ A.length-1 ].
Put that in A[0].
Then find the smallest in A[1]..A[ A.length-1 ].
Put that in A[1]. …
for (int j=0; j<A.length; j++) {
//let j be the location of the smallest element so far
int whereSmallest = j;
for (int i=j+1; i<A.length; i++) {
if (A[i]<A[whereSmallest]) {
whereSmallest = i; }
swap( A, j, whereSmallest );