Arrays are a crucial programming concept asked in almost every coding interview!
If you are a programmer, you should be well-equipped with various arrays concepts such as maximum product subarray, sum pairs of arrays among others!
In this blog post, we are particularly discussing the maximum product of Subarray.
Wondering, what a maximum product subarray is ?
A contiguous subarray in an array that yields the maximum product is known as a maximum product of subarray. The objective of the maximum product of the subarray is to identify the subarray that has the highest product.
To improve your level of programming experience or your learning process, get to know a firm knowledge of how to approach this issue and enhance your computer science abilities.
Before digging deep into the topic, it’s wise to know about its basics.
Learn maximum product subarray problems and ways to find them.
What is a maximum product subarray problem?
A maximum product subarray is a problem that requires you to identify the contiguous subarray with the largest product in a set of numbers.
Consider the array [2, 3, -2, 4], for instance. Here, the greatest product 6 is in the subarray provided [2, 3, -2, 4].
Two variables must be maintained in order to determine the maximum product subarray: one for the maximum product seen thus far and another for the least product seen thus far (since the negative numbers can transform the minimum and maximum products).
One can determine the minimum and maximum products at each point by taking the minimum and maximum of the current number multiplied by the previous minimum and maximum products.
The subarray that yields the highest product after iterating through the array is the maximum product subarray.
The difficulty of this problem is O(n), where n represents the number of entries in the array.
Most asked maximum product subarray questions
To improve on your knowledge regarding this issue, you need to be aware of various questions that are frequently asked in the interview. So, here are some of the most asked maximum product of subarray questions:
- How to find the continuous subarray with the greatest product from an array of numbers is a common task.
You should use Kadane’s Algorithm (which is also used to solve reverse-level order traversal) to identify the contiguous subarray in an array of integers that has the largest product.
The greatest product of a subarray in the supplied array is determined by this algorithm, which employs a dynamic programming methodology.
The algorithm functions by recording the highest product at every index.
When a current index’s product is positive, the maximal output is the sum of that index’s current value and the prior maximum value. The maximal product is equal to the maximum of the present index and the preceding maximum product if the output at the present index is negative.
When the process is finished, the maximal product of each subarray in the input array will equal the sum of all the calculated maximum products.
- Find the subarray having the highest product given an array containing both negative and positive values.
The maximum and minimum products at each point are calculated by taking the minimum and maximum of the product of a current value with the previous minimum and maximum products, as well as the current number itself.
This method can be used to discover the subarray with the maximum result in an array of negative and positive values. The subarray that yields the highest computed result is the subarray with the maximum product.
- How to find the subarray having the highest product given a real number array.
A real number array’s maximum and minimum products are calculated at each place by taking the minimum and maximum of the product of the current value along with the preceding maximum and minimum products.
The subarray with the highest product is then returned.
- Determine the subarray’s length and initial index for the one with the maximum product provided an array of integers.
An integer array’s maximum and minimum products are calculated at each position by taking the minimum and maximum of the product of the initial maximum and minimum products and the current value.
The length and starting index of the subarray that produces the largest product is then tracked, and the length and starting index are returned.
- How can the greatest product and product value be determined with an array of integers?
In an array of integers, determine the contiguous subarray that yields the maximum product by multiplying the current value by the previous minimum and maximum products.
Note that the subarray yields the maximum product, and the program will return the subarray and the product value.
Ways to find maximum product subarray questions
There are two methods for determining the maximum product subarray:
- Using dynamic programming
The minimum and maximum output ending at each point are stored in an auxiliary array using dynamic programming.
The maximum product is calculated for each place by adding the maximum of the current value’s product with its preceding maximum product.
The minimum of the current value is multiplied by the preceding maximum product, and the current value itself is used to determine the minimum product.
The subarray that yields the maximum product contained in the auxiliary array is known as the maximum product subarray.
This method is used to solve other problems such as reverse-level order traversal, and minimum product subarray. etc.
- Constant Space
This method is similar to dynamic programming, but instead of using an additional array to hold the minimum and maximum products, it simply utilises two variables.
The min and max products are calculated for each place in a similar way to how dynamic programming is done.
The outcome is updated as we traverse through the array and is kept in the two variables.
Finding the largest product subarray can be accomplished using either of these methods, each of which has an O(n) time complexity, where n represents the number of members in the array.
Hope that you are clear on the maximum product subarray, and the different ways to solve its related problems!
Prepare this topic well while putting your hands on other essential topics like reverse-level order traversal!