Searching Arrays. COMP104 Array Sorting & Searching / Slide 2 Unordered Linear Search * Search an unordered array of integers for a value and save its.

Searching

Arrays

COMP104 Array Sorting & Searching / Slide 2

Unordered Linear Search Search an unordered array of integers for a

value and save its index if the value is found. Otherwise, set index to -1.

Algorithm:Assume value not in array and set index = -1Start with the first array element (index 0) WHILE(more elements in array){

If value found at current index, save indexTry next element (increment index)

}


Unordered Linear Searchvoid main() {

int A[8] = {10, 7, 9, 1, 17, 30, 5, 6};int x, n, index;

cout << "Enter search element: ";cin >> x;index = -1;for(n=0; n<8; n++)

if(A[n]==x)index = n;

if(index==-1)cout << "Not found!!" << endl;

elsecout << "Found at: " << index << endl;

}


Ordered Linear Search Search an ordered array of integers for a value and save

its index if the value is found. Otherwise, set index to -1.

The key difference in design is that this array is ordered. If we perform a linear search, and find that we have

already passed where the element might be found, we can quit early.


Ordered Linear Search

void main() {

int A[8] = { 1, 5, 6, 7, 9, 10, 17, 30};int x, n, index;

cout << "Enter search element: ";cin >> x;index = -1;for(n=0; n<8 && A[n]<=x; n++)

if(A[n] == x)index = n;

if(index==-1)cout << "Not found!!" << endl;

elsecout << "Found at: " << index << endl;

}


Binary Search

Search an ordered array of integers for a value and save its index if the value is found. Otherwise, set index to -1.

Binary search takes advantage of the sorting, to search the array efficiently.


Binary Search Binary search is based on a divide-and-

conquer strategy which works as follows: Start by looking at the middle element of the

array 1. If the value it holds is lower than the search

element, eliminate the first half of the array. 2. If the value it holds is higher than the search

element, eliminate the second half of the array.

Repeat this process until the element is found, or until the entire array is eliminated.


Binary Searchvoid main() {

int A[8] = {1, 5, 6, 7, 9, 10, 17, 30};int x, lower, middle, upper;

cout << "Enter search element: ";cin >> x;lower = 0;upper = 7; // array size - 1middle = (lower + upper)/2;while(A[middle]!=x && lower<upper){

if(x<A[middle])upper = middle - 1;

elselower = middle + 1;

middle = (lower + upper)/2;}if(A[middle]!=x)

cout << "Not found!!" << endl;else

cout << "Found at: " << middle << endl;}

Sorting

Arrays


Sorting To arrange a set of items in sequence. About 25~50% of all computing power is

used in sorting. Possible reasons:

Many applications require sorting Many applications perform sorting when they

don't have to Many applications use inefficient sorting

algorithms


Sorting Applications List of student ID names and numbers in a table

(sorted by name) List of scores before letter grade

assignment (sorted by students' scores) List of horses after a race (sorted by the

finishing times) To prepare an originally unsorted array for

ordered binary searching


Some Sorting Methods Selection sort

Bubble sort

Shell sort (a simple but faster sorting method)

Quick sort (a much faster sorting method for most applications)


Selection Sort Selection sort performs sorting by

repeatedly putting the largest element to the end of the unsorted part of the array until the whole array is sorted.

It is similar to the way that many people do their sorting.


Selection Sort Algorithm

1. Define the unsorted part of the array as the entire array

2. While the unsorted part of the array has more than one element:

Find its largest element

Swap with last element

Reduce unsorted part of the array by 1


Selection Sort// Selection Sort of integers into ascending orderint main(){

const int size = 9;int A[size] = { 10, 7, 9, 1, 9, 17, 30, 5, 6};int i, rightmost, temp, max_index;

for(rightmost=size-1; rightmost>0; rightmost--){// find largest itemmax_index = 0;for(i=1; i<=rightmost; i++)

if(A[i] > A[max_index]) max_index = i; // swap largest item with last item temp = A[max_index];

A[max_index] = A[rightmost];A[rightmost] = temp;

}cout << "The sorted array: ";for(i=0; i<size; i++)

cout << A[i] << " ";cout << endl;return 0;

}


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. It then repeats the process for the unsorted part of

the array until the whole array is sorted.


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.


Bubble Sort

Algorithm Define the unsorted part of the array to be

the entire array While the unsorted part of the array has

more than one element: 1. For every element in the unsorted part,

swap with the next neighbor if it is larger than the neighbor

2. Reduce the unprocessed part of the array by 1


Bubble Sort// Bubble Sort of integers into ascending orderint main(){

const int size = 9;int A[size] = { 10, 7, 9, 1, 9, 17, 30, 5, 6};int i, rightmost, temp;

for(rightmost=size-1; rightmost>0; rightmost--){for(i=0; i<rightmost; i++){

if(A[i] > A[i+1] ){ // swap if greatertemp = A[i];

A[i] = A[i+1]; A[i+1] = temp; }

}}cout << "The sorted array: ";for(i=0; i<size; i++)

cout << A[i] << " ";cout << endl;return 0;

}

Searching Arrays. COMP104 Array Sorting & Searching / Slide 2 Unordered Linear Search * Search an unordered array of integers for a value and save its.

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