Did you know?
Programming concepts are better understood on paper and apparently, even the interviewers for coding interviews think the same.
Well, according to Quora, about 1/4th of the applicants of coding interviews get selected because of their exceptional performance in their written coding exams.
While we cannot guess all of the concepts that are important for the coding interviews, we can surely confirm that the Arrays and Subarrays definitely top the list!
Many of you might already be familiar with the concept of arrays, but the subarrays are definitely a trickier concept to grasp.
Essentially, we can define the Subarrays as a part of the array that holds the individual value of the elements.
Sometimes these elements contain values while other times they don't! We are here to discuss just that.
Learn more about how to find the Subarrays with 0 sum in the blog and start preparing to give your best in the coding interviews today!
What is a Subarray with 0 sum?
Before we describe the definition for Subarray with 0 sum, let us discuss what is essentially a Subarray.
Well, a Subarray can be defined as a predetermined section of an array consisting of variables that can be declared within the program.
The Subarrays are created in order to merge data containing multiple variables into one, so that it would be easier to locate the source and the exact location of the values stored within the array
Now that it's clear that the Subarrays are used for storing variables for different values of data stored within the Arrays, a Subarray containing zero sum would essentially be an empty.
Meaning, that the value of the data stored within a Subarray would essentially amount to 0.
The major problem with having Subarrays with 0 sum in an array is that they consume unnecessary space and data.
So, how would you figure out the presence of such Subarrays in a given data structure?
Let's find out in the section below.
What methods are used for finding zero sum in Subarrays?
We know that you are here for the quick methods and algorithms but, without essentially knowing the problem statement it would lead to nowhere.
Let's start from the beginning and have a look at the problem statement concerning zero sum subarrays.
Problem Statement:
You have been given an array consisting of positive as well as negative integers. Your task is to figure out the presence of at least one Subarray in this lot (of size one) that holds a zero sum value.
Now, this problem statement can be solved by using a number of effective methods but we have chosen the ones that have the least amount of time complexity.
Here is a brief discussion on all of these methods:
Method 1: Using the Brute Force Algorithm
Otherwise known as the Naive Approach, the Brute Force Algorithm focuses on dividing the problem statement into equal sections and iterating them further one at a time.
The idea behind using the Naive Approach is to consider all the existing Sub Arrays within the program one at a time and check the sum of all them.
This way, we will be able to analyse the sum of all the Subarrays and it will be easier to identify the Subarrays with zero sum values.
For this particular approach, we will be using two nested loops.
Method 2: Using the Hashing Table
Another effective method that can be used for iterating over the given array would be implementing a Hashing Table.
The idea here is to iterate through all the elements of the array and evaluate the sum of these elements from 0 to a chosen “i” point within the array.
If you find that any of the sums are being repeated, then you may rest assured that the given array sequence consists of a Subarray with sum zero.
The hashing table is used for effectively storing data values quickly and efficiently so that it becomes easier to compare the sum values of the elements to the current value.
An additional piece of information that we would like to share regarding the Hashing Table in Java is that it can be effectively used for solving complex coding problems. For instance the Hash Table can be used for finding sum of given input arrays, finding duplicates in a string or finding isomorphic strings.
Now, we are heading to the important part of the blog. Here we will be describing the algorithms for both of these approaches and their respective time complexities. This way you can be the best judge on which time complexity is better.
How to apply the algorithms for finding if there is a Subarray with 0 sum?
Starting from the Naive Approach or the Brute Force Algorithm, here's how the algorithm for this method should be implemented in a program:
Method 1: Implementation of the Naive Approach
- Start by considering all the Subarrays one at a time in order to analyse the sum of every Subarray.
- Next up, we will be running two different loops for the array.
- The outer loop will pick a starting point from the element “i”.
- While at the same time, the inner loop will try all the Subarrays from i till all the elements of the array are traversed.
Time Complexity for this approach:
O(N2)
Method 2: Implementing Hash Table on the given data
- Start by declaring a variable sum for the data and store all the sum of all the prefix elements of the given data.
- Traverse the given array at each index level and move ahead by adding the elements of the sum to confirm if the sum has been found earlier.
- Now, insert the value of all the prefixes in the map so that you will be able to compare it with the current value in future.
- Finally, you can return false if no Subarrays with 0 sum are detected.
Time Complexity for this approach:
O(N)
Wrapping Up
Did you know that a Subarray can essentially be a whole array by itself?
Well, if we clearly think about it, Subarrays are a contiguous part of the array which means that every element of an array is a Subarray.
Which is why, the problem statement of finding Subarrays with 0 sum basically means finding an element within an array that has a zero sum value.
Such DSA problems are often asked in the coding interviews thus, it is better to learn in-depth details about some of the most common topics such as differences between BST and Tree or what are isomorphic strings.
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