data structure

1. Programming
Sorting
Arrays

2. COMP102 Prog. Fundamentals. Sorting I/ Slide 2
Sorting
 To arrange a set of items in sequence.
 It is estimated that 25~50% of all
computing power is used for sorting
activities.
 Possible reasons:
 Many applications require sorting;
 Many applications perform sorting when they
don't have to;
 Many applications use inefficient sorting
algorithms.

3. COMP102 Prog. Fundamentals. Sorting I/ Slide 3
Sorting Applications
 To prepare a list of student ID, names, and
scores in a table (sorted by ID or name) for easy
checking.
 To prepare a list of scores before letter grade
assignment.
 To produce a list of horses after a race (sorted
by the finishing times) for payoff calculation.
 To prepare an originally unsorted array for
ordered binary searching.

4. COMP102 Prog. Fundamentals. Sorting I/ Slide 4
Some Sorting Methods
 Selection sort
 Bubble sort
 Shell sort (a simple but faster sorting
method than above; see p.331 of
Numerical Recipes in C, 2nd ed., by
William H. Press et al, Cambridge
University Press, 1992)
 Quick sort (a very efficient sorting method
for most applications; p.332-336, ibid.)

5. COMP102 Prog. Fundamentals. Sorting I/ Slide 5
Ex. 1A: Selection Sort
 Selection sort performs sorting by
repeatedly putting the largest element in
the unsorted portion of the array to the end
of this unsorted portion until the whole
array is sorted.
 It is similar to the way that many people do
their sorting.

6. COMP102 Prog. Fundamentals. Sorting I/ Slide 6
Ex. 1A: Selection Sort
 Algorithm
1. Define the entire array as the unsorted
portion of the array
2. While the unsorted portion of the array
has more than one element:
 Find its largest element.
 Swap with last element (assuming their
values are different).
 Reduce the size of the unsorted
portion of the array by 1.

7. Before sorting 14 2 10 5 1 3 17 7
After pass 1 14 2 10 5 1 3 7 17
After pass 2 7 2 10 5 1 3 14 17
After pass 3 7 2 3 5 1 10 14 17
After pass 4 1 2 3 5 7 10 14 17

8. // Sort array of integers in ascending order
void select(int data[], // in/output: array
int size){ // input: array size
int temp; // for swap
int max_index; // index of max value
for (int rightmost=size-1; rightmost>0; rightmost--){
//find the largest item in the unsorted portion
//rightmost is the end point of the unsorted part of array
max_index = 0; //points the largest element
for ( int current=1; current<=rightmost; current++)
if (data[current] > data[max_index])
max_index = current;
//swap the largest item with last item if necessary
if (data[max_index] > data[rightmost]){
temp = data[max_index]; // swap
data[max_index] = data[rightmost];
data[rightmost] = temp;
}
}}

9. const int array_size = 8;
int main() {
int list[array_size] = {14, 2, 10, 5, 1,
3, 17, 7};
int index, ans;
cout << "Before sorting: ";
for (index = 0; index<array_size; index++)
cout << list[index] <<" ";
cout << endl;
cout << "Enter sorting method 1(select), 2(bubble):";
cin >> ans;
if (ans == 1) select(list, array_size);
else bubble(list, array_size);
cout << endl << "After sorting: ";
for (index = 0; index<array_size; index++)
cout << list[index] <<" ";
cout << endl;
return 0;
}

10. COMP102 Prog. Fundamentals. Sorting I/ Slide 10
Ex. 1B: Bubble Sort
 Bubble sort examines the array from start
to finish, comparing elements as it goes.
 Any time it finds a larger element before a smaller
element, it swaps the two.
 In this way, the larger elements are passed
towards the end.
 The largest element of the array therefore
"bubbles" to the end of the array.
 Then it repeats the process for the unsorted
portion of the array until the whole array is sorted.

11. COMP102 Prog. Fundamentals. Sorting I/ Slide 11
Ex. 1A: Bubble Sort
 Bubble sort works on the same general principle as
shaking a soft drink bottle.
 Right after shaking, the contents are a mixture of
bubbles and soft drink, distributed randomly.
 Because bubbles are lighter than the soft drink,
they rise to the surface, displacing the soft drink
downwards.
 This is how bubble sort got its name, because the
smaller elements "float" to the top, while
the larger elements "sink" to the bottom.

12. COMP102 Prog. Fundamentals. Sorting I/ Slide 12
Ex. 1B: Bubble Sort
 Algorithm
Define the entire array as the unsorted
portion of the array.
While the unsorted portion of the array has
more than one element:
1. For every element in the unsorted portion,
swap with the next neighbor if it is larger than
the neighbor.
2. Reduce the size of the unsorted portion of the
array by 1.

13. Before sorting 14 2 10 5 1 3 17 7
outer=7, inner=0 2 14 10 5 1 3 17 7
outer=7, inner=1 2 10 14 5 1 3 17 7
outer=7, inner=2 2 10 5 14 1 3 17 7
outer=7, inner=3 2 10 5 1 14 3 17 7
outer=7, inner=4 2 10 5 1 3 14 17 7
outer=7, inner=6 2 10 5 1 3 14 7 17
outer=6, inner=1 2 5 10 1 3 14 7 17
outer=6, inner=2 2 5 1 10 3 14 7 17
outer=6, inner=3 2 5 1 3 10 14 7 17
outer=6, inner=5 2 5 1 3 10 7 14 17
outer=5, inner=1 2 1 5 3 10 7 14 17
outer=5, inner=2 2 1 3 5 10 7 14 17
outer=5, inner=4 2 1 3 5 7 10 14 17
outer=4, inner=0 1 2 3 5 7 10 14 17
---
outer=1, inner=0 1 2 3 5 7 10 14 17

14. //Example1b: Bobble sort
// Sort an array of integers in ascending order
void bubble(int data[], // in/output: array
int size){ // input: array size
int temp; // for swap
for(int outer=size-1; outer > 0; outer--){
for (int inner=0; inner < outer; inner++) {
// traverse the nested loops
if ( data[inner] > data[inner+1] ) {
// swap current element with next
// if the current element is greater
temp = data[inner];
data[inner] = data[inner+1];
data[inner+1] = temp;
}
} // inner for loop
} // outer for loop
}

15. const int array_size = 12, string_size = 11;
int main() {
char month[array_size][string_size] = {"January",
"February","March","April","May","June","July","August",
"September", "October", "November", "December"};
int index, ans;
cout << "Enter sorting method 1(select), 2(bubble): ";
cin >> ans;
if (ans == 1) select(month, array_size);
else bubble(month, array_size);
cout << endl << "After sorting: ";
for (index = 0; index<array_size; index++)
cout << month[index] <<" ";
cout << endl;
return 0;
}

16. 0 1 2 3 4 5 6 7 8 9 10
month[0] J a n u a r y 0
month[1] F e b r u a r y 0
month[2] M a r c h 0
month[3] A p r i l 0
month[4] M a y 0
month[5] J u n e 0
month[6] J u l y 0
month[7] A u g u s t 0
month[8] S e p t e m b e r 0
month[9] O c t c b e r 0
month[10] N o v e m b e r 0
month[11] D e c e m b e r 0

17. // Sort array of strings in ascending order
void select(char data[][string_size], // in/output: array
int size){ // input: array size
char temp[string_size]; // for swap
int max_index; // index of max value
for (int rightmost=size-1; rightmost>0; rightmost--){
// find the largest item
max_index = 0;
for(int current=1; current<=rightmost; current++)
if (strcmp(data[current], data[max_index]) >0)
max_index = current;
// swap with last item if necessary
if(strcmp(data[max_index], data[rightmost])>0){
strcpy(temp,data[max_index]); // swap
strcpy(data[max_index],data[rightmost]);
strcpy(data[rightmost], temp);
for (int index=0; index< size; index++)
cout << data[index] << " ";
cout<<endl;
}
}
}

18. // Sort an array of strings in ascending order
void bubble(char data[][string_size], // in/output:array
int size){ // input: array size
char temp[string_size]; // for swap
for(int outer=size-1 ; outer>0; outer--){
for (int inner=0; inner < outer; inner++) {
// traverse the nested loops
if ( strcmp(data[inner], data[inner+1])>0 )
{
// swap current element with next
// if the current element is greater
strcpy(temp, data[inner]);
strcpy(data[inner], data[inner+1]);
strcpy(data[inner+1], temp);
for (int index=0; index< size; index++)
cout << data[index] << " ";
cout<<endl;
}
} // inner for loop
} // outer for loop
}