What is the sum of its maximum subarray?


Were you trying to solve the maximum sum of contiguous subarray problems? Did you find It difficult and confusing?

You are on time to read this article! Here we will discuss everything from the concept of a subarray to the ways of finding its maximum contiguous sum. With the help of this article, you will be easily able to solve questions where you need to find the subarrays for a given array or the largest subarray with 0 sums.

In this article, we will discuss the following:

  • What is a subarray?
  • What are the methods of finding the maximum sum of a subarray?
  • What is Kadane’s Algorithm?
  • What is the Brute Force approach?
  • Tips to keep in mind while solving the question.
  • What is the first unique character in a string?

 

What is a Subarray?

Any subset of the original array’s indices can be used to define a subarray, and a contiguous subarray. A contiguous subarray is defined by an interval of indices, which includes the first and last elements as well as everything in between.

We all know that an Array is nothing but a contiguous memory block. Hence, a Subarray is simply a part of a slice of this contiguous Array. These parts or slices maintain the order of the elements. 

Remember that a sub-array can consist of a single element of the said Array, or it can also comprise the given Array as a whole.

To help you remember it even better, here is an example.

Let us consider that this is the given Array for which subarrays need to be found:

Arr= {1,2,3,4,5}

Now, for this Array, the following will be the sub-arrays. 

 

What are the methods of finding the maximum sum of a subarray?

There are 2 methods for finding the maximum sum of a subarray. They are called the Brute force approach and Kadane’s algorithm. Most people are familiar with Kadane’s Algorithm. 

These methods can help you to solve all problems related to sub-arrays, the sum of sub-arrays and also questions like finding the largest subarray with 0 sums.

Let us now dive into the details of these methods.


What is Kadane’s Algorithm?

Firstly, let us understand how Kadane’s algorithm was found.

In 1977, a programmer named Uif Grenander proposed the problem of finding a contiguous subarray with the largest sum. While everyone was working on it for years, Jay Kadane derived an O(n) algorithm to find a solution to this problem in 1984, and since then it is now called Kadane’s Algorithm. 

By definition, Kadane’s Algorithm is “An iterative algorithm....


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