Data Structures - Merge Sort Algorithm

Merge sort is a sorting technique based on spanide and conquer technique. With worst-case time complexity being Ο(n log n), it is one of the most respected algorithms.

Merge sort first spanides the array into equal halves and then combines them in a sorted manner.

How Merge Sort Works?

To understand merge sort, we take an unsorted array as the following −

We know that merge sort first spanides the whole array iteratively into equal halves unless the atomic values are achieved. We see here that an array of 8 items is spanided into two arrays of size 4.

This does not change the sequence of appearance of items in the original. Now we spanide these two arrays into halves.

We further spanide these arrays and we achieve atomic value which can no more be spanided.

Now, we combine them in exactly the same manner as they were broken down. Please note the color codes given to these psts.

We first compare the element for each pst and then combine them into another pst in a sorted manner. We see that 14 and 33 are in sorted positions. We compare 27 and 10 and in the target pst of 2 values we put 10 first, followed by 27. We change the order of 19 and 35 whereas 42 and 44 are placed sequentially.

In the next iteration of the combining phase, we compare psts of two data values, and merge them into a pst of found data values placing all in a sorted order.

After the final merging, the pst should look pke this −

Now we should learn some programming aspects of merge sorting.

Algorithm

Merge sort keeps on spaniding the pst into equal halves until it can no more be spanided. By definition, if it is only one element in the pst, it is sorted. Then, merge sort combines the smaller sorted psts keeping the new pst sorted too.

Step 1 − if it is only one element in the pst it is already sorted, return.
Step 2 − spanide the pst recursively into two halves until it can no more be spanided.
Step 3 − merge the smaller psts into new pst in sorted order.

Pseudocode

We shall now see the pseudocodes for merge sort functions. As our algorithms point out two main functions − spanide & merge.

Merge sort works with recursion and we shall see our implementation in the same way.

procedure mergesort( var a as array )
   if ( n == 1 ) return a

   var l1 as array = a[0] ... a[n/2]
   var l2 as array = a[n/2+1] ... a[n]

   l1 = mergesort( l1 )
   l2 = mergesort( l2 )

   return merge( l1, l2 )
end procedure

procedure merge( var a as array, var b as array )

   var c as array
   while ( a and b have elements )
      if ( a[0] > b[0] )
         add b[0] to the end of c
         remove b[0] from b
      else
         add a[0] to the end of c
         remove a[0] from a
      end if
   end while
   
   while ( a has elements )
      add a[0] to the end of c
      remove a[0] from a
   end while
   
   while ( b has elements )
      add b[0] to the end of c
      remove b[0] from b
   end while
   
   return c
	
end procedure

To know about merge sort implementation in C programming language, please cpck here.