# Design and Analysis of Algorithm Lab 5 | Read Now

Design and Analysis of Algorithm Lab 5

5] Sort a given set of n integer elements using the merge sort method and compute its time complexity. Run the program for varied values of n>5000, and record the time taken to sort. Plot a graph of the time taken varses non-graph sheet. The elements can be read from a file or can be generated using the random number generator. Demonstrate using Java how the divide and conquer method works along with its time complexity analysis: worst case, average case, and best case.

5] Program code

```import java.util.Random;
import java.util.Scanner;

public class lab5
{
public static void main(String[] args)
{
int a[]= new int[100000];
Scanner in = new Scanner(System.in);
long start, end;

System.out.println("MERGE SORT PROGRAM");
System.out.println("Enter the number of elements to be sorted");
int n = in.nextInt();
Random rand= new Random();
for(int i=0;i<n;i++)
a[i]=rand.nextInt(100);

System.out.println("Array elements to be sorted are");
for(int i=0; i<n; i++)
System.out.print(a[i]+" ");

start=System.nanoTime();
mergesort(a,0,n-1);
end=System.nanoTime();
System.out.println("\nThe sorted elements are");
for(int i=0; i<n; i++)
System.out.print(a[i]+" ");

System.out.println("\nThe time taken to sort is "+(end-start)+"ns");
}

static void mergesort(int a[], int low, int high)
{
int mid;
if(low < high)
{
mid = (low+high)/2;
mergesort(a, low, mid);
mergesort(a, mid+1, high);
merge(a, low, mid, high);
}
}

static void merge(int a[], int low, int mid, int high)
{
int i, j, h, k, b[]= new int[100000];
h=low; i=low; j=mid+1;

while((h<=mid) && (j<=high))
{
if(a[h] < a[j])
{
b[i]=a[h];
h=h+1;
}
else
{
b[i] = a[j];
j=j+1;
}
i = i+1;
}

if(h > mid)
{
for(k=j; k<=high; k++)
{
b[i]=a[k];
i= i+1;
}
}
else
{
for(k=h;k<=mid;k++)
{
b[i]=a[k];
i= i+1;
}
}

for(k=low; k<= high; k++)
a[k] = b[k];
}
}```

Output