LAB#7

Sorting

• Insertion sort• In the outer for loop, out starts at 1 and moves right. It marks the leftmost unsorted data.

• In the inner while loop, in starts at out and moves left, until either temp is smaller than the array element there, or it can’t go left any further.

• Each pass through the while loop shifts another sorted element one space right.

Insertion sort

Insertion sortExample #1: Show the steps of sorting the following array:

8 6 1 4

8 6 1 46 8 1 46 8 1 46 1 8 41 6 8 41 6 8 41 6 4 81 4 6 81 4 6 8

Insertion sortExample #2: Show the steps of sorting the following array:

3 -1 5 7

3 -1 5 2-1 3 5 2-1 3 5 2-1 3 5 2-1 3 2 5-1 2 3 5-1 2 3 5

Selection sort

• Selection Sort :1. Find the minimum value in the list

2. Swap it with the value in the first position

3. Repeat the steps above for the remainder of

the list (starting at the second position and

advancing each time)

Example #1: Show the steps of sorting the following array:

8 6 1 4

8 6 1 41 6 8 41 6 8 41 4 8 61 4 8 61 4 6 81 4 6 8

Selection sort

Example #2: Show the steps of sorting the following array:

3 -1 5 7

3 -1 5 2-1 3 5 2-1 3 5 2-1 2 5 3-1 2 5 3-1 2 3 5-1 2 3 5

Selection sort

• Bubble Sort :1. compares the first two elements

2. If the first is greater than the second, swaps

them

3. continues doing this for each pair of elements

4. Starts again with the first two elements,

repeating until no swaps have occurred on

the last pass

Bubble sort

Example #1: Show the steps of sorting the following array:

8 6 1 4

8 6 1 46 8 1 46 1 8 46 1 4 81 6 4 81 4 6 81 4 6 8

Bubble sort

Example #2: Show the steps of sorting the following array:

3 -1 5 7

3 -1 5 2-1 3 5 2-1 3 5 2-1 3 2 5-1 3 2 5-1 2 3 5-1 2 3 5

Bubble sort

Quick sort

Quick Sort :•Quick sort is a divide and conquer algorithm. Quick sort

first divides a large list into two smaller sub-lists: the low elements and the high elements. Quick sort can then recursively sort the sub-lists.

• A Quick sort works as follows:

1.Choose a pivot value: We take the value of the middle element , but it can be any value.

2.Partition.3. Sort both part: Apply quick sort algorithm recursively to the left and the right parts.

Example #1: Show the steps of sorting the following array:

3 -1 5 7

3 -1 5 23 -1 5 22 -1 5 32 -1 5 32 -1 5 32 -1 5 3-1 2 3 5

Quick sort

Example #2: Show the steps of sorting the following array:

8 6 1 5 9 4

Quick sort8 6 1 5 9 44 6 1 5 9 84 6 1 5 9 84 6 1 5 9 84 1 6 5 9 84 1 6 5 9 84 1 6 5 9 84 1 6 5 9 81 4 6 5 8 91 4 6 5 8 91 4 6 5 8 91 4 5 6 8 9

Merge Sort

Merge Sort :• Merge sort is a much more efficient sorting technique than the bubble Sort and the insertion Sort at least in terms of speed.

• A merge sort works as follows:1. Divide the unsorted list into two sub lists of

about half the size. Sort each sub list recursively by re-applying the merge sort.

2. Merge the two sub lists back into one sorted list.

Example #1: Show the steps of sorting the following array:

6 5 3 1 8 7 2 4

Merge Sort

Example #2: Show the steps of sorting the following array:

38 27 43 3 9 82 10

Merge Sort

LAB#7

Searching

Linear Search

Linear Search :• Linear Search : Search an array or list by checking items

one at a time.

• Linear search is usually very simple to implement, and is practical when the list has only a few elements, or when performing a single search in an unordered list.

Linear Search

Linear Search :

0 1 2 3 4 5 6 7 8 9 10 11

=?12 =?12 =?12 =?12

#include <iostream>using namespace std; int LinearSearch(int Array[],int Size,int ValToSearch) {

bool NotFound = true;int i = 0;while(i < Size && NotFound){ if(ValToSearch != Array[i])

i++;else NotFound = false; }

if( NotFound == false )return i;

else return -1;}

Linear Search

int main(){int Number[] = { 67, 278, 463, 2, 4683, 812, 236, 38 }; int Quantity = 8;int NumberToSearch = 0; cout << "Enter the number to search: ";cin >> NumberToSearch; int i = LinearSearch(Number, Quantity, NumberToSearch);if(i == -1) cout << NumberToSearch << " was not found in the collection\n\n";else { cout << NumberToSearch << " is at the index " << i<<endl;return 0; }

Linear Search

Binary Search

Binary Search :• Binary Search >>> sorted array.• Binary Search Algorithm :

1.get the middle element.2.If the middle element equals to the searched value, the

algorithm stops.3.Otherwise, two cases are possible: o searched value is less, than the middle element. Go to the

step 1 for the part of the array, before middle element. o searched value is greater, than the middle element. Go to

the step 1 for the part of the array, after middle element.

Binary Search

Example Binary Search :

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4

3 4

3

12

Binary Search#include <iostream>using namespace std;

int binarySearch(int arr[], int value, int left, int right) {

while (left <= right){

int middle = (left + right) / 2; // compute mid point.if (arr[middle] == value)// found it. return position

return middle;else if (arr[middle] > value) // repeat search in bottom half.

right = middle - 1;else

left = middle + 1; // repeat search in top half. }

return -1;}

Binary Search

void main(){int x=0;int myarray[10]={2,5,8,10,20,22,26,80,123,131};cout<<"Enter a searched value : ";cin>>x;if(binarySearch(myarray,x,0,9)!=-1)

cout<<"The searched value found at position : "<<binarySearch(myarray,x,0,9)<<endl;

elsecout<<"Not found"<<endl;

}

Binary Search

void main(){int x=0;int myarray[10]={2,5,8,10,20,22,26,80,123,131};cout<<"Enter a searched value : ";cin>>x;if(binarySearch(myarray,x,0,9)!=-1)

cout<<"The searched value found at position : "<<binarySearch(myarray,x,0,9)<<endl;

elsecout<<"Not found"<<endl;

}

Exercise

Exercise #1 :Write a C++ program that define an array myarray of type integer with the elements (10,30,5,1,90,14,50,2). Then the user can enter any number and found if it is in the array or not.

A. Use linear search.B. Edit the previous program and use binary search.