### Merge Sort Implementation in JAVA

Merge Sort  is a technique of sorting data with below steps:-

1) Divide the data recursively until it can not  divide more.

2)  Compare the data and sort it.

3) Merge the data again .

```/*
* Merge Sort is based on the concept below points:-
* 1) Divide array until it can not be divide.
* 2) Merge it again in sorted pattern
*
*
*/

public class MergeSort {

public static int[]  mergeSort(int arr[])
{

//check for size if it is one then already sorted
int size=arr.length;
if(size==1)
{
return arr;
}

//find middle (divide an array into two half)
int mid=size/2;

//first half
int[] fhalf=new int[mid];
//second half
int[] shalf=new int[size-mid];

// Copy first half of the array
for (int i = 0; i < mid; i++)
{ fhalf[i] = arr[i];
}
// Copy second half of the array
for (int i = mid; i < size; i++)
{ shalf[i - mid] = arr[i];
}

//recursive call fhalf and shalf
return merge(mergeSort(fhalf), mergeSort(shalf));

}

public static int[] merge(int[] firstHalfSorted,int[] secondHalfSorted)
{
// First, create a new array to store the answer.

int SortedArray[] = new int[firstHalfSorted.length + secondHalfSorted.length];

int m = 0;
int n = 0;
int count = 0;

System.out.println("first array");
printArray(firstHalfSorted);
System.out.println("second array");
printArray(secondHalfSorted);
//compare the elements in both arary
while (m<firstHalfSorted.length && n<secondHalfSorted.length)
{
if (firstHalfSorted[m]>secondHalfSorted[n])
{
SortedArray[count]=secondHalfSorted[n];
count++;
n++;
}
else if (firstHalfSorted[m]<secondHalfSorted[n])
{
SortedArray[count]=firstHalfSorted[m];
count++;
m++;
}
}

//append the remaining elements at the end
if (m!=firstHalfSorted.length)
{
while(m<firstHalfSorted.length){
SortedArray[count]=firstHalfSorted[m];
count++;
m++;
}
}

//append the remaining elements at the end
if (n!=secondHalfSorted.length)
{
while(n<secondHalfSorted.length){
SortedArray[count]=secondHalfSorted[n];
count++;
n++;
}
}
System.out.println("sorted array");
printArray(SortedArray);
// At last return the sorted array
return SortedArray;
}

public static void printArray(int[] arr)
{
//System.out.println("printing array");
for(int i=0;i<arr.length;i++)
{
System.out.print(arr[i]+" ");
}
System.out.println(" ");
}

public static void main(String[] args)
{
int arr[]={14,33,27,10,25,19,40,45};
printArray(arr);
//calling merge function
arr=mergeSort(arr);
printArray(arr);
}

}
```

Implementation Steps:-

```14 33 27 10 25 19 40 45
first array
14
second array
33
sorted array
14 33
first array
27
second array
10
sorted array
10 27
first array
14 33
second array
10 27
sorted array
10 14 27 33
first array
25
second array
19
sorted array
19 25
first array
40
second array
45
sorted array
40 45
first array
19 25
second array
40 45
sorted array
19 25 40 45
first array
10 14 27 33
second array
19 25 40 45
sorted array
10 14 19 25 27 33 40 45
10 14 19 25 27 33 40 45
```