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What is Merge Sort Algorithm?


1) When the input sequence has fewer than two elements, returns.

2) Partition this input sequence into two halves.

3) Sort two subsequences while using same algorithm.

4) Merge two sorted subsequences to create the output sequence.


Merge sort uses the following algorithm:


1) Divide the block into two subblock associated with 'equal' size

2) Merge sort every block recursively

3) Merge the two sorted sub blocks in order to provided the sorted block


The following is the merge sort algorithm to sort a sub array from index low to index high:


If (low < high){
split the sub array into two halves
merge sort the left half
merge sort the righ half
merge the two sorted halves into one sorted array
}


The above algorithm translates to the following pseudo code:


mergeSort( A, L, H )//
here array = A, low = L, high = H, mddle = M //
{
M = ( L + H )/2;
mergeSort ( A, L, M );
mergeSort ( A, M+1, H );
merge ( A, L, M, M+1, H );
}


Merge Sort Algorithm : Divide and conquer method:


1) It’s  algorithm divides a problem into simpler version of itself.

2) By breaking down a problem into smaller parts, they become easier to solve. Usually, the solution for the smaller sub-problems can be applied to the larger, complicated one.


Merge-Pseudocode


Algorithm: MERGE( M, u, v, w)

m1 <= v - u + 1

m2 <= w - v

array create L[1 .. m1 +1] and R[1 ..m2+1]

for j <= 1 to m1

do L[i] <= M[u+ j -1]

for k <= 1 to m2

do R[k] <= M[v+ k]

L[m1+1] <= infinity

R[m2+1] <= infinity

j <= 1

k <= 1

for k <= u to w

do if L[j] <= R[k]

then M[l] <= L[j]

j <= j+1

else M[l] <= R[k]

k <= k+1





Example:-

Example of Merge sort Algorithm


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