Difference Between Subarray, Subsequence, And Subset

If you are new to programming and arrays, you might get confused between the terms; subarrays, subsequences and subsets.

These terminologies resemble each other but may often confuse the users. Even though various terms associated with arrays sound similar, they have different concepts.

In this article, we will look closely at their differences BUT for this, you have to understand what an array is.

Arrays can be considered as a set or group of elements belonging to the same data type.

Many times we make some divisions or sets inside these arrays to access only a limited number of elements. These are usually called subarrays.

These elements can be chosen based on their index value, the data they hold, memory allocation, or any other parameter.

You must think about whether the zero-sum arrays will have zero sum subarrays as well. For this, you have to understand what subarrays are.

For example, say that we have a set of all the integers in an array. The code wants to check only the numbers that are divisible by 9 without leaving any remainder.

In such cases, having divisions of the whole array will help you to check and utilize the value easily.

But what are these divisions called? And is there only one way to divide an array? Can you divide an array into arrays?

If you are looking for answers to such questions, this article will help you:

You will also get to know how these concepts can help you fetch the grid's unique paths for an array.

So let’s start with the basics of this phenomenon.

In this article, we will describe what are subarrays, subsequences, and subsets in arrays to get answers to such questions and how they differ from one another.

Let’s begin with understanding these terms and the differences between them based on major parameters.

## What are arrays in Python? The array can be defined as a structure that holds a limited number of elements given the fact that the elements are of the exact nature. They mainly use arrays to execute their algorithms.

If you are new to the study, you must start with learning about the following two terms in the case of an array:

Element: These are basically every single component of an array that you have to sort while solving a problem. Index: In order to navigate the location of each and every single element the array follows a given index which makes the task a lot easier.

Let us take an example of an array to understand the concept of elements and index more definitively:

33 44 55 66 77 88 99 00

0 1 2 3 4 5 6 7

## Arriving to conclusions from the given array:

We can see here that the index of the above array extends till 7 which means that the array can only store 8 elements. The length of the above array is 8 starting from 0 which makes it capable of storing 8 elements in total. As we have discussed above in the definition of an index, it is basically used to navigate the exact location of an element in an array. For instance, in the case of the above array, we can say that the element "66" is located in the "3rd" index and so forth.

Now that we have figured out the basic terminologies of an array, let us take a look at some of the problems that are dealt with using the arrays.

## Basic Operations

Here is the list of operations that are executed using an array:

Update: As the term suggests you can update each element based on its given index. Search: In this function, you can search for any given element using its index location. Deletion: In this procedure, you can delete any required element by tracing its index location. Insertion: You can follow this procedure to add any required element in a given index. Traverse: This function allows you to print the elements one at a time by navigation through each index point.

This was the list of the basic operations that you can carry out using an array. For an additional piece of information, you can note that, while using the Python language you can create an array by transferring the array module into the program.

## Definition

What are Subarrays?

Subarrays are arrays that store only the contagious elements of an array. Make sure you note that subarrays will include only a continuous sequence of elements present in an array.

What is subsequence?

You can select any elements from an array given that you do not disturb the sequence of the elements throughout the array.

What is subset?

You can have several subsets of any array or set. The essential point is that the null set and the array itself will always be the subsets of a particular array.

## Sequence

The element's order/sequence in subarrays, subsequences, and subsets is very different from one another.

Say that we have stored an array of the first 3 integers.

Now if we have to make subarray of the array mentioned above, we will have to take the exact sequence of elements and put them in a separate array.

Subsequences can be formed even if you eliminate any element from within however, the order of elements must be intact.

However, the subsets do not consider order or continuity in the order of the elements. Hence, you will get more sets of groups as compared to subsequences or subarrays.

## Element ordered

Do you know that only subarrays follow the rule of sequence and order?

In subarrays, the groups are formed by putting the elements available in the same order and sequence as they are placed in the main array.

However, in the case of subsequence, the order of elements is not considered the same as the main array. It can change from the previous format.

Lastly, the subsets don’t follow the rules of order similar to subsequences.

Continuous

You can either select the elements available continuously in an array or shuffle them up. Do you know that you can not shuffle the elements in case of subarrays?

Subarrays are formed by selecting the continuous elements only. This case remains the same in the case of Subsequence as well.

‘Subsets don't follow the rule of continuity which means that you can shuffle all the elements easily.

Examples

Let’s make all the terms clear with a working example.

The array will look like {0,2, 4,}.

Possible subarrays of the given array include {}- a null or empty array {0, 2,4}- array itself {0, 2} {2, 4}

And that is it. You can not take {0, 4} as a subarray of the given array.

Did you notice something in the first two subarray and what does that mean?

The point to be noted here is that a null array and the array will always be a subarray for any provided array.

It means that the array will include a null array and the array itself inside its scope.

Let’s clarify this concept with the help of enlisting the possible subsequence of the array we took before (i.e. {0, 2,4})

The subsequence of this array can be:

{}- a null or empty array {0, 2,4}- array itself {0, 2} {2, 4} {0, 4}

Now you must be clear about what subsequence is and how it differs from subarrays.

The major point of difference between subarrays and subsequence is that subsequence doesn’t follow the rule of contagious element placement.

Let’s now have a look at the subset and see if you can establish the difference between the three more clearly.

Based on this definition let's enlist the subsets of the array we considered before.

The possible subsets of {0, 2,4} except null set and the array itself will be:

{0} {2} {4} {2,0} {0,2} {0,4} {4,0} {2,4} {4,2} {4,2,0} {2,0,4} {0,4,2}

You can see how the subsets differ from subsequences and subarrays at the same time.

Now you are aware of the major point of differences between these terms. Let’s move on to discuss zero sum subarray and grid unique path.

## What is zero sum array?

Zero sum subarray are the arrays if the sum of all the elements of an array return value “zero”. You can easily apply the sum technique on the array and get this checked. However, it is not important if an array is a zero sum subarray, the subarrays of this array will also be zero sum array.

## What is Grid unique paths?

If you are new to the term grid unique paths, Let us explain what it means. In the shortest way possible, it can be defined as the path that allows the robot (system) to reach the bottom left corner without any obstacles.

## Merging two sorted arrays - Bonus Topic

For Merging two sorted arrays, you have to implement the merge sort algorithm. This is one of the lengthiest algorithms that are available but it certainly makes it easier to solve the problem at hand.

The algorithm states that you have to divide the problem into equal sub-problems and figure out the solution to each. Afterward, we combine the solutions to find the final output for the problem.

Winding up

The subarrays, subsequences, and subsets can be easily distinguished if you know about the rules on which they run.

Establishing an understanding of these terms will help you to understand the grid's unique paths efficiently.

After understanding subarrays it becomes easy to understand the concept of zero sum subarray as well. Hopefully, all the terms are crystal clear for you now.