Devised by John Von Neumann, the merge sort algorithm in programming languages is used to derive outputs by the principle of merging.

Professional programmers for Java and other languages might be acquainted with the fact that the merge sort algorithm is used for counting the number of inversions in a given list. This algorithm is employed for external sorting.

The prime rule to merge two sorted arrays using  the merge sort algorithm is to divide the input statement into two equal halves so that we can maintain uniformity after deriving the output.

Once the process has been initiated we can confirm the clarity of the output after considering the first and last occurrences in the sorted arrays.

This blog will iterate further on the concept so read till the end.

What do you mean by merging two sorted arrays?

Before understanding the concept of how you can merge two sorted arrays, let us understand what sort of output is generated after merging two sorted arrays.

The merge sort algorithm is based on the fundamentals of divide and conquer. This means that the algorithm will keep dividing two sets of strings until it cannot be divided any further.

The size of the merged array will represent the size of the two sorted arrays that were merged together. Consider the following example for reference:

There are two sorted arrays:

m- 4, 0, 4, 0

n- 0, 4, 0, 4

Output: 4, 0, 4, 0, 0, 4, 0, 4

Now, the computed output after merging the two sorted arrays will be written as follows:

4, 0, 4, 0, 0, 4, 0, 4

This way we can conclude that the algorithm for generating the output for merging two sorted arrays can be defined mathematically as: m+n

This formula also describes the size of the output array. This concludes that the given set of arrays have been merged using the divide and conquer technique. We would suggest to run this program in a compiler to understand further 

With that, we can proceed with our discussion for how many comparisons are required for merging two sorted arrays.

How many approaches can be employed for merging two sorted arrays?

Here are some of the most resourceful approaches that you can employ for merging two given sorted arrays.

Let us consider the former example and iterate on the basis of that:

m- 4, 0, 4, 0

n- 0, 4, 0, 4

Output: 4, 0, 4, 0, 0, 4, 0, 4

Using the Native Approach

The native approach which is also in other terms considered the brute force approach is definitely one of the lengthiest methods for deriving the outpur but it is by far the most efficient.

In the case of the brute force approach, the programmer has to derive all the possible outcomes or solutions for the problem and figure out the outcome that matches the output statement.

Time complexity: As discussed, the time constraint for this particular outcome is lengthier as compared to the other approaches that we shall be discussing shortly.

The time constraint is increased due to the fact that you have to derive all the possible outcomes.

Using the Time and Extra Space approach

This algorithm creates a third array combining the two right away. The third array is formulated using and adding the elements from the first and the third arrays.

The procedure for doing so is to traverse the first array and include the elements and then approach the second array and imply the same process.

Time complexity: In comparison to the brute force method, the time and space constraint is a relatively faster method for comparing and adding the two sorted arrays.

Using only the Extra Space constraint

This algorithm is similar to time and space but, this approach goes an extra mile to traverse both sets of arrays and figure out the smaller elements that are to be included first.

You can copy the smaller elements to the newly created array for generating the output and move further along to the greater elements.

Finally, if you find that there are any greater elements left in the two arrays you can add them afterwards. 

Time complexity: This approach minimises the time complexity to a much greater extent as compared to the other approaches.

Also in comparison to the last few algorithms that we discussed, this approach is definitely more thorough and less time consuming.

Using Maps

Maps in Java and other programming languages is a structural format where the programmer inputs the problem statement in order to derive the required output.

The structure of the map uses elements from the array. In this case the elements will be considered as keys. After inserting the elements from both the arrays, you can print the keys on your map.

Time complexity: Here the integers of the two given arrays, m and n have to be added using the log algorithm. This makes the process lengthier and more time consuming.

Those were all of the basic approaches that you can apply in order to merge two sorted arrays. 

In terms of comparison we can attest to the fact that the time and space algorithm is the best approach to consider thus far. Time constraint is not a problem if you employ this algorithm and you can generate the results fairly easily.

The first and last occurrences in both the arrays after deriving the input is basically what matters in terms of merging two sorted arrays.

If both the elements for the first and the last occurrence match with the given output, you can confirm that the generated outcome is correct.

Final Thoughts

The merge sort algorithm is one of the most efficient approaches for considering the implementation of equal elements in a tabular or data format.

If you want to confirm that by merging two sorted arrays will derive the right output, consider by matching the first and last occurrences of x the input and out statements.