Ways to Merge K sorted arrays

Did you know that merging the sorted arrays is considered one of the most basic level problems? 

This is because the concept of arrays is one of the first concepts taught to the beginners in programming.

So, you might be wondering what it means to merge two arrays? Well basically, when two arrays are merged their elements get combined together from beginning till the end of the list.

This means that two or more elements within the combined array will now have the same index position.

Also if any of the elements in these two arrays resemble each other, the system overwrites the elements and merges them as one!

If you are here to learn how to merge k sorted arrays in a program and print the final output then keep reading further.

What do you mean by merging an Array?

Before we learn how to merge an array, it is important that we learn the structure of arrays.

Well basically, an array is a collection of elements that are arranged in a lexical order such that the data can be retrieved whenever it is required by the user using pointers.

Now, since the elements in an array are arranged in a sequential order i.e beside each other, you can merge two arrays to form an output that would contain elements from both the arrays that were merged.

This action can be performed using multiple arrays at once. This is commonly known as the merge k sorted arrays problem that we are going to be discussing today.

In case both of these arrays contain similar keys or elements the system will overwrite the program and merge them as one as well!

So, now that we have a clear understanding of arrays, let's focus on learning about sorted arrays before we deal with the algorithms for merging the sorted arrays.

What do you mean by Sorted Arrays?

As the name suggests, the sorted arrays have all their elements aligned in a perfect order from ascending to descending.

Whether these elements are alphabets, integers or other numbers, they are always numerically and alphabetically arranged in a sorted array.

One of the common programming problems within this concept is the sort 0 1 2 problem where we have to arrange an array 0's, 1's and 2's in an ascending order.

Also, an important factor to note about the sorted arrays is that not only are the elements arranged systematically but, they are spaced equally. This means that the gap between the elements in a sorted array will be equidistant to each other.

Now, there are quite a few methods to merge k sorted arrays in a program. From the naive approach to min heap function the options are certainly not limited!

In the next section, let's find out how the process and algorithms work for merging any number of sorted arrays in a program. Meanwhile, we have also mentioned the time complexity for each of the approaches so that you can decide which one is the least time efficient by yourself.

What are the methods to merge k sorted arrays?

Now, before we discuss the methods to merge k sorted arrays, let's have a look at the problem statement first.

Problem Statement

You have been provided k sorted Arrays of size N for each of them. You are required to merge these arrays and print the output.

Answer Key

We can attempt to solve this problem by using the Naive Approach.

Method 1: Using the Naive Approach to merge k sorted arrays

The Naive Approach basically uses the sorting method for attempting the problem. This means that we will be creating an output array of the size (N*K) and then start copying the elements of the given arrays into the output array.

You can use the following algorithms to solve this problem:

• Start by creating an output of the size N*K 

• Next up, you are required to traverse the entire matrix from beginning till the end and start placing each of the element in the output array

• Finally, you need to sort the output array and print the derived result

Time Complexity for this approach:

O(N*K*log (N*K))

Method 2: Using the Merge Algorithm

The merge sort algorithm is also used for solving problems of sort O 1 2 in arrays. This process focuses on merging the given arrays in groups of two. 

After performing the first merge we will have K/2 arrays remaining. We have to further merge these arrays into two groups that will leave us with K/4 arrays.

This process is quite similar to the merge sort algorithm. We have to keep merging the arrays into equal halves until the two arrays are finally arranged in a group.

Finally, we will merge the remaining arrays from the bottom till top.

Here's how the algorithm for this approach would work:

• Start by creating a recursive function. This function will be used for the k arrays and it will return the output array

• Within the recursive function, if found that the value of K remains 1 you can return the array

If found that the value of K arrays is 2, you can proceed further and merge both of the arrays in a linear order. Finally, you may return the value of the array

• Also, if you find that the value of k arrays is greater than two then you are required to divide this group into equal halves and call the function recursively

For instance, 0 to K/2 would be one recursive function while K/2 to K will be the next recursive function 

• Finally, you can print the resulting array as the output

Time Complexity for this approach:

O(N*K*log K)

Final Thoughts

Did you know?

Sorting algorithm can be used for solving almost all of the array based problems?

From merging arrays to sort 0 1 2 problems, the list goes endless when it comes to using the sorting algorithm. 

Check out more programming problems and their solutions on our website.