What is the Maximum Product Subarray in an Array?

Arrays are the most vital components of programming!

Do you agree? Well, all the tech-geeks do!

This is because you can apply various functions, concepts, technical approaches, and others to resolve your problem statements through arrays.

Are you wondering what are the tasks you can carry out with arrays?

You can find subarrays, apply array rotation, search functions, and many others for arrays!

One of the many such concepts is finding the maximum product subarray for a given array. Even though it sounds simple and straight, this concept has a lot of in-depth technical concepts and approaches.

If you don't have any idea about what is the maximum product subarray or how you can find it in a set of elements, you have landed on the right page.

This article comprises in-depth information that you need to understand and grasp to ensure that you can find the maximum product subarray and use this concept in your problem statements.

But if you are a learner and do not know what subarrays exactly are, don't worry about that too!

We will start everything from scratch!

Starting from the basics, let's discuss what subarrays are!

What is a subarray?

An array of the neighboring parts of an array!

Subarrays are simply sets of elements in an array that are placed next to each other. Simply put, the subarrays are parts of an array of the elements present in a series.

Let's try to understand the concept of subarrays with an array as an example:

Arr[]= {1, 2,3,4}

The subarrays of the above-mentioned array include:

=> {1, 2} => {2, 3} => {3, 4}
=> {1, 2,3} => {2, 3,4} => {1} => {2} => {3} => {4} => {} => {1, 2,3,4}

Note that every array will be a subarray of itself. Also, a null array or empty array is always a subarray for any given array.

Given that subarrays are clear to you, it’s time to discuss the next important topic i.e. maximum product subarray.

What do you mean by maximum product subarray?

As the name suggests, the maximum product subarray is a particular subarray that contains elements of an array yielding maximum product.

Simply put, it is a subarray with a larger product value than the other coexisting subarrays.

During a problem statement, when you are asked to find the product of elements in a subarray, the set with the maximum output value is called the maximum product subarray.

Can you think of all the possible ways in which you can find the product of elements in a subarray?

Let us look at how you can resolve the issue of finding the maximum product subarray in a database.

Approaches to solving maximum subarray problem

Do you know that the products can lie in the negative and positive range as well?

If you think that product of elements in a subarray can only be positive, how about you try to find the sum of array A={0, 0,0} or array B {-2, -3, -1}?

How can you compare product values in such cases? Don't worry! There are two different approaches to resolving maximum product subarray . ProblemsLet's discuss them in detail.

Brute Force Approach

The simplest way to find out the maximum product subarray!

This method is the simplest way of finding a subarray with the maximum product! In this method, you only have to declare an array and obtain the product of its elements.

Once you obtain the products, maximize the product and fetch your output from the results!

The brute force method is ideally used for smaller arrays and databases. You can efficiently get the desired results with this method if the array is small and simple.

There are certain steps in which the brute force method helps you in finding out the subarray with the maximum product.

These steps are:

=> The first step in this method is to initialize Or declare a variable. Say, you declare a variable output=O[]. Since the result will be a subarray, you will have to declare a variable array here. This variable array will store the maximum product.

=> After this, you will have to implement two loops in a nested format. The first loop will run from the first value till the n-1 value. Along with this, the second loop of j will run from i+1 until it reaches the end or N

=> Find out the subarray and obtain the product of its elements.

=> Once the maximum product is found, assign the values to the variable and display the results.

This way, you can easily find it in a database. Since nested loops are at work, It may take longer to apply this method on larger database.

In such situations, we can always rely on dynamic programming! Let's understand how?

Dynamic Programming

The second method of finding out the Maximum product subarray is through dynamic programming. This method is based on the theory that the answer or the result subarray will lie on either end of the array.

You can also perform array rotation to find the subarray faster and in a simpler manner.

The algorithm for this method is described in the following steps:

=> First of all, you will have to declare a variable array. Let's name this array as arr A[0]

=> Once done, simply declare two more variables to store the maximum and minimum products found so far. For say, let's call them maximum_sofar and minimum_sofar respectively.

=> The next step is to traverse the array you obtained as input. Make sure you swap the variables maximum_sofar and minimum_sofar in case of a negative value. Can you think of a reason why these values are interchanged? The answer is that the maximum value is negative and will be the minimum in the code results and vice-versa!

=> Afterward, all you need to do is maximize the value of maximum_sofar and minimize the product of minimum_sofar

=> After obtaining these values perform:maximum_sofar*A[i] and obtain the result.

=> Return and display the result in the final step!

Winding up

Finding the maximum product subarray can be a difficult task. But, with the right technique and approach, you can perform array rotation and find your maximum product subarray faster!

You can easily find the maximum product subarray with the help of the right technique! Array rotation, sorting, and searching of an array can help you in speeding up the process. Make sure you use them efficiently!