Question

PLEASE DO BOTH #5 AND #6.

The purpose of the project is to perform a timing experiment. You are required to complete the following activities:

1. Write a computer program that prompts the user for a number, creates an array for that number of random integers, and then usees the bubble sort to order the array. The program should print out the array prior to the call to the sorting algorithm and afterwards. You can write the program in either Java, C++, C#, or whatever language you are most comfortable in. Do Not use an API from the language library. Write the program to perform the sort.
2. Repeat 1 but use selection sort this time. Again, write out the program for the selection sort. DO not use the language library.

1 and 2 are primarily intended to make sure that your algorithms work.

Once you are convinced your programs work, do the following

3. Write a computer program that prompts the user for one number, n for the number of items in the array to sort, and create and sort 1000 different arrays of this size timing the run to get an average time to sort an array of this size. Then do the following:

   Initiate a variable running_time to 0

   Create a for loop that iterates 1000 times.

   In the body of the loop,

   Create an array of n random integers (Make sure you make the range of the random numbers substantially bigger than the array, ie. if the array size is 500 have the random number generator pick numbers between 1 and 5000. For the largest array have the random number generator pick numbers between 1 and 50,000).

   Get the time and set this to start-time (notice the sort is started after each array is built. You want to time the srt process only). You will have to figure out what the appropriate command is in the programming language you are using to find the time (Important: Do not start the timer until after the array is created).

   Use bubble sort to sort the array

   Get the time and set this to end-time Subtract start-time from end-time and add the result to total_time

   Once the program has run, note

   The number of items sorted

   The average running time for each array (total_time/1000)

   Repeat the process using 500, 2500 and 5000 as the size of the array.

4. Repeat 3 using selection sort.

5.) You now have 6 data points ( the averages from the three array sizes for the two sort algorithms) Create a spreadsheet showing the results of 3 and 4 and create a graph to graphically represent the information. Show both sort algorithms on the same graph for comparison.

6.)Write a one page document explaining the results, bearing in mind that both algorithms have a complexity of O(n^2) and what you know about complexity analysis. Use your knowledge of complexity analysis to explain your results.

Answer 1

Below is the code which does all the sorting. I have named the file Test.java.
Here is the comparison data(You can recreate similar data by running the code and getting the data points):

Here are the key points to note when submitting the report:

Worst case time complexity: (n2)
Number of comparisons: (n2)

Best case time complexity :

Bubble sort: (n)
Selection sort: (n2)
Average case time complexity :

Bubble sort: (n2)
Selection sort: (n2)
In the bubble sort, each element and its adjacent element is compared and swapped if required. On the other hand, selection sort works by selecting the element and swapping that particular element with the last element. The selected element could be largest or smallest depending on the order i.e., ascending or descending.
The worst case complexity is same in both the algorithms, i.e., O(n2), but best complexity is different. Bubble sort takes an order of n time whereas selection sort consumes an order of n2 time.
Bubble sort is a stable algorithm, in contrast, selection sort is unstable.
Selection sort algorithm is fast and efficient as compared to bubble sort which is very slow and inefficient.
5. Selection sort swaps elements "n" times in worst case, but Bubble sort swaps almost n*(n-1) times.

6. If we have a system where write operations are extremely expensive and read operations are not, then Selection sort could be ideal.
Selection sort is good for sorting arrays of small size.

7. Selection sort is better than Bubble sort due to less swapping required.
8. In Bubble sort, we can identify whether list is sorted or not in 1st iteration but in Selection sort we can't able to identify that.
Compared to Selection sort, Bubble sort should be used when the given array is almost sorted.

The results were obtained on a Linux Machine with Intel i7 processor, 4 GB RAM.

If you want to change the number of arrays(500,2500,5000,etc), just change the value of variable number_of_iterations in Test.java.

The program asks the user for number of elements to sort.

Test.java:

import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.Random;

class Test
{
public static void main (String[] args) throws java.lang.Exception
{

Scanner in = new Scanner(System.in);
System.out.println("enter number of elements to sort");
int n = in.nextInt();
int number_of_iterations = 5000;
sort(n,number_of_iterations);

}
public static void sort(int n,int number_of_iterations){
Random r = new Random();
int c, d, swap;
long running_time = 0,total_time = 0;
int i=0;

for(i=0;i<number_of_iterations;i++){

int array[] = new int[n];

for (c = 0; c < n; c++)
array[c] = r.nextInt();

System.out.println("Unsorted array :");

for (c = 0; c < n; c++)
System.out.println(array[c]);
  
long startTime = System.nanoTime();   
bubble_sort(array);
long endTime = System.nanoTime();   
System.out.println("Bubble Sorted array :");

for (c = 0; c < n; c++)
System.out.println(array[c]);
  
running_time = endTime - startTime;
total_time = total_time + running_time;

}
long total_time1 = total_time;

total_time = 0;

for (i=0;i<number_of_iterations;i++){
int array1[] = new int[n];

for (c = 0; c < n; c++)
array1[c] = r.nextInt();

System.out.println("Unsorted array :");

for (c = 0; c < n; c++)
System.out.println(array1[c]);
long startTime1 = System.nanoTime();   

selection_sort(array1);
long endTime1 = System.nanoTime();   

System.out.println("Selection Sorted array :");
running_time = endTime1 - startTime1;
total_time = total_time + running_time;

for (c = 0; c < n; c++)
System.out.println(array1[c]);
}
System.out.println("total time for Bubble Sort= "+total_time1+" nanoseconds");
System.out.println("Average running time for each array in Bubble Sort = "+(total_time1/number_of_iterations)+" nanoseconds");

System.out.println("total time for Selection Sort= "+total_time+" nanoseconds");
System.out.println("Average running time for each array in Selection Sort= "+(total_time/number_of_iterations)+" nanoseconds");
  
}
public static void bubble_sort(int array[]){
int n = array.length;
int c=0,d=0,swap;
for (c = 0; c < ( n - 1 ); c++) {
for (d = 0; d < n - c - 1; d++) {
if (array[d] > array[d+1]) {
swap = array[d];
array[d] = array[d+1];
array[d+1] = swap;
}
}
}
}
public static void selection_sort(int arr[])
{
int n = arr.length;

// One by one move boundary of unsorted subarray
for (int i = 0; i < n-1; i++)
{
// Find the minimum element in unsorted array
int min_idx = i;
for (int j = i+1; j < n; j++)
if (arr[j] < arr[min_idx])
min_idx = j;

// Swap the found minimum element with the first
// element
int temp = arr[min_idx];
arr[min_idx] = arr[i];
arr[i] = temp;
}
}
}