The document discusses different sorting algorithms like selection sort and bubble sort. It provides examples of how selection sort and bubble sort work on sample arrays. It also provides C++ code to implement selection sort and bubble sort to sort 5 random numbers entered by the user in ascending order. Selection sort works by selecting the smallest element from the unsorted part and swapping it with the element in the first index of unsorted array. Bubble sort works by repeatedly comparing adjacent elements and swapping them if they are in wrong order.

1. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012Lecture 01: Programming Fundamentals
Lecture 10
Sorting
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2. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
Sorting Arrays
• The process of arranging the values of an array
in particular order is called sorting.
• Two Types of sorting:
• Ascending Order: The smallest value is stored in the
first location of an array. The largest value is stored at
the last position of an array.
15 25 33 47 51
• Descending Order: The largest value is stored in the first
location of an array. The smallest value is stored at the
last position of an array.
51 47 33 25 15
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3. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
3
Given an array of length n,
– Search elements 0 through n-1 and select the smallest
• Swap it with the element in location 0
– Search elements 1 through n-1 and select the smallest
• Swap it with the element in location 1
– Search elements 2 through n-1 and select the smallest
• Swap it with the element in location 2
– Search elements 3 through n-1 and select the smallest
• Swap it with the element in location 3
– Continue in this fashion until there’s nothing left to
search

4. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
4
Example and analysis of selection sort
• The selection sort might swap an
array element with itself--this is
harmless, and not worth checking
for
• Analysis:
– The outer loop executes n-1 times
– The inner loop executes about n/2
times on average (from n to 2
times)
– Work done in the inner loop is
constant (swap two array
elements)
– Time required is roughly (n-
1)*(n/2)
– You should recognize this as O(n2)
7 2 8 5 4
2 7 8 5 4
2 4 8 5 7
2 4 5 8 7
2 4 5 7 8

5. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
Selection Sort
Program that take 5 random values from user
in an array and sort it in ascending order.
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6. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
int array[5], i, j, temp;
cout<< "Enter five integers" << endl;
for(i=0; i<5; i++)
{
cin>>array[i];
}
cout<<"The array in Actual Order n"<<endl;
for(i=0; i<5; i++)
{
cout<<array[i]<<" ";
}
for(i=0; i<5; i++)
for(j=i+1; j<5; j++)
if(array[i]>array[j])
{
temp = array[i];
array[i] = array[j];
array[j] = temp;
}
cout<<endl;
cout<<"The array in Sorted Ordern ";
for(i=0; i<5; i++)
{
cout<<array[i]<<" ";
}
getch();
}
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7. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
Bubble Sort
• In the bubble sort, as elements are sorted they
gradually "bubble" (or rise) to their proper
location in the array, like bubbles rising in a glass
of soda.
• The bubble sort repeatedly compares adjacent
elements of an array.
– The first and second elements are compared and swapped if out
of order.
– Then the second and third elements are compared and swapped
if out of order.
– This sorting process continues until the last two elements of the
array are compared and swapped if out of order.
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8. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
• When this first pass through the array is complete,
the bubble sort returns to elements one and two
and starts the process all over again.
• So, when does it stop?
• The bubble sort knows that it is finished when it examines
the entire array and no "swaps" are needed (thus the list is
in proper order).
• The bubble sort keeps track of occurring swaps by the use
of a flag.
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9. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
• The table below follows an array of numbers before,
during, and after a bubble sort for descending order.
• A "pass" is defined as one full trip through the array
comparing and if necessary, swapping, adjacent
elements.
• Several passes have to be made through the array
before it is finally sorted.
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Array at beginning: 84 69 76 86 94 91
After Pass #1: 84 76 86 94 91 69
After Pass #2: 84 86 94 91 76 69
After Pass #3: 86 94 91 84 76 69
After Pass #4: 94 91 86 84 76 69
After Pass #5 (done): 94 91 86 84 76 69

10. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
Program that take 5 random values from user
in an array and sort it in ascending order,
using bubble sort.
10

11. University Institute of Information Technology, PMAS-AAUR
Lecture 10: Programming Fundamentals:2012
main()
{
int array[5], i, j, temp;
cout<< "Enter five integers" << endl;
for(i=0; i<5; i++)
{
cin>>array[i];
}
cout<<"The array in Actual Order n"<<endl;
for(i=0; i<5; i++)
{
cout<<array[i]<<" ";
}
for(i=0; i<5; i++)
for(j=0; j<4; j++)
if(array[j]>array[j+1])
{
temp = array[j];
array[j] = array[j+1];
array[j+1] = temp;
}
cout<<endl;
cout<<"The array in Sorted Ordern ";
for(i=0; i<5; i++)
{
cout<<array[i]<<" ";
}
getch();
} 11