How do you find the number of Subarrays with sum 0?

Persistence and practice are the only keys for solving DSA problems especially for the beginners who are new to the field.

For people who are new to programming, it is enough to practice for two-three months for solving the DSA problems in order to crack your coding interviews.

But the question is, from where to begin?

DSA is certainly a vast concept and for what it's worth we have efficiently tried to simplify the learning curve for our readers.

That is why, we would recommend starting from the concept of Arrays and particularly the Subarray problem such as the one discussed in the blog!

Finding the largest Subarray with 0 sum value is our topic of discussion for this blog.

If this sounds interesting, you are free to check out the entire blog for solutions and algorithms for this coding problem!

What do you mean by Subarrays?

Have you ever heard of the term "An Array within an Array" in programming?

Well, these forms of arrays are essentially known as the Subarrays.

A Subarray is basically a section of the array that holds multiple variables of a single set of data. Hence, a Subarray is essentially an array by itself.

The Subarrays make it easier for the programmer to access data from different variables that are further used for declaring an Array. It is more versatile to store information within a Subarray due to the fact that we do not require creating separate variables for different values of the set of data.

Also, a fun fact about creating Subarrays is that the same amount of attention to detail is required for creating a Subarray as is required for an Array.

For instance, they have to constantly make sure the the values of the elements stored within the Subarray do not get interchanged due to the presence of bugs within the program.

Now, the problem of removing bugs is definitely not the only problem faced by programmers after implementing the Subarrays.

Another important aspect they have to look after is the fact that the Subarray must not be empty.

These sorts of Subarrays are more commonly known as the Zero Sum Subarrays. Evidently, as their name suggests the values contained within these arrays are essentially NULL hence, they are of no use for the data set.

Let's find out more about the Zero Sum Subarray in the next section.

What do you understand about the Zero Sum Subarray problem?

Before we get straight into discussing the problem, let us first understand what a Zero Sum Subarray essentially is.

The sum zero problem required the programmer to calculate the value of the elements stored within an Array in order to identify whether any of their values equals 0 or not.

This problem poses itself in the form of calculating the largest Subarray with 0 sum problem in a majority of technical and coding interviews.

For those who are interested in solving this DSA problem, the problem statement for a subarray with sum zero problem would look something as follows:

Problem Statement

You have been given an Array of the size "n". This array consists of both the positive and the negative integers. Your task is to figure out the length of the largest Subarray with 0 sum value within this Array.

Now, the problem description makes its intention extremely clear. We are only required to find the largest Subarray that contains a zero sum.

With effect to that, find the different approaches that can be applied for solving the zero Subarray problem in the following section.

How to solve a Zero Sum Subarray problem?

Starting off with our first method we have the Brute Force Algorithm where we shall be using three nested loops to traverse the Array.

Method 1: Using the Brute Force Algorithm

The idea here is to essentially use three nested loops within the programs. Using the loops we will be searching for the sum of all the Subarrays and finally storing the value of the largest Subarray with 0 sum in the given Array.

Here is the algorithm for how this function would work:

• Start by declaring the max length=0 function which can be used for storing the value of the largest Subarray containing a sum 0

• Next, we will traverse the Array from the beginning

• Now, initiate a nested loop from the "i" index of the array

• Start another loop from the "j" variable that will extend to the entire size of the array

• Also, initiate another function cursum=0 for storing the sum of all the Subarrays between the "ith" and the "jth" indices

• Finally, check for the largest Subarray with 0 sum in this function

• Once found, return the max_length of the given Array

Time Complexity for this approach:

O(n3)

Method 2: Initiating Efficient Brute Force

The key differences between this approach and the last approach that we have just discussed is the use of two nested loops in this approach.

The two nested loop approach is a more time efficient function that is used for solving a majority of other coding problems such as finding the longest palindrome subsequence.

Now, for finding the largest Subarray with a 0 sum value, you can use the following algorithms for this approach:

• Start by initiating the same max_length=0 function in the program

• Now, you may start the traversal along with initialising the cur_sum=0 function for storing the Subarray beginning from the ith index

• Start adding all the iterations of the elements to the list and similarly you will be able to find the largest Subarray consisting of the zero sum

• Keep updating the values of the Subarrays and you can finally return the max_length after the completion of the program

Time Complexity for this approach:

O(n2)

Final Thoughts

We all know that reducing the time complexity is the major reason for implementing Subarrays within an Array.

From iterating on the existing data to performing a function faster, Subarrays essentially help in optimising the performance of a program faster whilst consuming less amount of data.

Another common Subarray based problem you will find in programming is the longest palindrome subsequnce problem.

If you are interested in learning about more such Subarray problems, then our website can provide you with the best resources and information that is available out there.