Merge sort algorithm

1. The Merge Sort
Merge sort is a recursive algorithm that continually splits a list in half. If the list is empty or has
one item, it is sorted by definition (the base case). If the list has more than one item, we split the
list and recursively invoke a merge sort on both halves. Once the two halves are sorted, the
fundamental operation, called a merge, is performed. Merging is the process of taking two smaller
sorted lists and combining them together into a single, sorted, new list.
Figure 1: Splitting the List in a Merge Sort
Figure 2: Lists as They Are Merged Together

2. Algorithm MergeSort(l,h)
{
if(l<h)
{
Mid=(l+h)/2;
MergeSort(l,mid);
MergeSort(Mid+1,h);
Merge(l,mid,h);
}
}
Algorithm Merge(A,B,m,n)
{
i=1,j=1,k=1;
while(i<=m && j<=n)
{
if(A[i]<B[j])
C[k++]=A[i++];
else
C[k++]=B[j++];
}
for(;i<=m;i++)
C[k++]=A[i];
for(;j<=n;j++)
C[k++]=B[j];
}
A B C
2=i 5=j 2=k
8 9 5
15 12 8
18 17 9
12
15
17
18
Size=m Size=n Size=m+n
1 2 3 4 5 6 7 8
9 3 7 5 6 4 8 2
1,8
1,4 5,8
1,2 3,4 5,6 7,8
1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8