# Merge Sort ## Merge Sort

• Merging is the process of combining two or more sorted ﬁles into a third sorted file.
• Procedure: In merge sort, we divide the ﬁle into n subﬁles of size 1 and then merge adjacent pair of ﬁles. We then have n/2 files of size 2. We repeat this process until there is only one ﬁle remaining of size n.

### Efficiency of Merge Sort

• Let us assume that the file size n is a power of 2, say n=2m. Thus m=log2n.
• It is therefore obvious that there are no more than m or log2n passes in merge sort (since each pass divides the file into two parts), with each pass involving at most n comparisons.
• Thus, total number of comparisons in merge sort is at most = n*m = n*log2n.
• Hence the time complexity of merge sort = O (n Iog n).
• Average case complexity = Worst case complexity = Best case complexity = O(n log n).

### C Program For Merge Sort

```#include<stdio.h>

void mergesort(int a[],int i,int j);

void merge(int a[],int i1,int j1,int i2,int j2);

int main()

{

int a,n,i;

printf("Enter no of elements:");

scanf("%d",&n);

printf("Enter array elements:");

for(i=0;i<n;i++)

scanf("%d",&a[i]);

mergesort(a,0,n-1);

printf("\nSorted array is :");

for(i=0;i<n;i++)

printf("%d ",a[i]);

return 0;
}

void mergesort(int a[],int i,int j)

{
int mid;

if(i<j)

{

mid=(i+j)/2;

mergesort(a,i,mid);        //left

mergesort(a,mid+1,j);    //right

merge(a,i,mid,mid+1,j);    //merging of two sorted sub-arrays

}

}

void merge(int a[],int i1,int j1,int i2,int j2)

{

int temp;    //array used for merging

int i,j,k;

i=i1;    //beginning of the first list

j=i2;    //beginning of the second list

k=0;

while(i<=j1 && j<=j2)    //while elements in both lists

{

if(a[i]<a[j])

temp[k++]=a[i++];

else

temp[k++]=a[j++];

}

while(i<=j1)    //copy remaining elements of the first list

temp[k++]=a[i++];

while(j<=j2)    //copy remaining elements of the second list

temp[k++]=a[j++];

//Transfer elements from temp[] back to a[]

for(i=i1,j=0;i<=j2;i++,j++)

a[i]=temp[j];

}```

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