Sorting

Programming

Sorting

Arrays

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.

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.

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.)

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.

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.

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

// 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;

}

}}

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;}

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.

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.

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.

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

//Example1b: Bobble sort// Sort an array of integers in ascending ordervoid bubble(int data[], // in/output: array int size){ // input: array size

int temp; // for swapfor(int outer=size-1; outer > 0; outer--){

for (int inner=0; inner < outer; inner++) {// traverse the nested loopsif ( 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

}

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;}

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

// Sort array of strings in ascending ordervoid 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 itemmax_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;

}}

}

// Sort an array of strings in ascending ordervoid bubble(char data[][string_size], // in/output:array int size){ // input: array sizechar temp[string_size]; // for swap for(int outer=size-1 ; outer>0; outer--){

for (int inner=0; inner < outer; inner++) {// traverse the nested loopsif ( 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}