What is the time complexity of LCS?



Time complexity and LCS are both important topics you do not want to skip. But if you are even slightly unsure about them, it is difficult to find the right, desirable answers. 

Whether it be how to reverse a string in c, understanding the definition of time complexity or the longest common subsequence! Every concept becomes increasingly difficult to analyze and understand that are listed on the internet. So many questions but only limited answers are available!

But fortunately for you, we have suitable answers to all your questions regarding time complexity and LCS. Read till the end to get it all right.

What is time complexity?

The concept of time complexity is very complex in itself. If you missed that one lesson about time complexity, do not worry, we have got you. We will brief you on the topic in an understandable way.

Time complexity is a word used in the context of programming. It depicts the time taken to process and execute a code or an algorithm in relation to the size of the code or the algorithm.

The concept analyses the overall time taken to execute an algorithm. It also inclucates and studies the change in the time taken to successfully execute the process. 

Now that you know what time complexity is, let us move on to LCS.

What is LCS?

LCS stands for Longest Common Subsequence. It entails finding the longest subsequence that is shared by all the sequences in an array. The common elements that will compose the LCS do not have to be in consecutive order in their own sequence, but they have to be in the order of their position. For example, if ABC is the LCS of a string set, then ABC needs to appear in that order in the string.

Let us take a look at an example.

In a set of sequences, the string sequences are ABJYTF, YLTFRC, BYTFA and YTBJFK. YTF is the only subsequence present in all four sequences. The LCS of these sequences is thus 3 since the length of YTF is 3.

In most cases, they are only two sequences. You can also have a look at  reverse a string in c to make the strings more compatible whenever necessary.

Let us now move on to the time complexity of LCS.

What is the time complexity of LCS?

The time complexity of LCS depends solely on the approach you take to get to the solution. However, it must also be noted that sometimes the time complexity of a code or an algorithm could also depend on your computer, network, connectivity, speed and other such external factors.

Nevertheless, there are two approaches incorporated to find the Longest Common Subsequence of a set which have been identified below:

Recursive Approach

This approach deals with going through all the possible subsequences in a set to determine the common ones among them and then choose the longest one of them as the LCS.

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