Find the longest substring with k unique characters in a given string

Did you know that navigating elements in a substring is much easier than an original string?

This is only made possible by using pointers. So, what is a pointer? 

Well, the pointers are essentially variables that are used for locating specific addresses of the elements stored within a string.

We can say that pointers are useful for navigating lengthy data structures and deriving outputs with much lesser time complexity than other approaches.

One such programming problem that we are going to be discussing in this blog is finding the longest substring with k unique characters.

Substrings are basically a subset of strings that are used for storing individual characters from the string that can be iterated within the program at any point of time using pointers.

Through this blog, we intend to discuss how you can achieve the longest substring including a unique character from a given string using different approaches.

What do you mean by a String?

In the context of computer programming, a string can be defined as a set of characters, numbers, alphabets or even spaces that are enclosed within quotations.

Essentially for a set of data to be considered as string, they must be enclosed in quotations for the computer program.

For instance, "Apple" and "The apple doesn't fall far from the tree" can be both considered as string since both of them are enclosed within quotations.

• Strings are basically used for storing a specific set of characters that may or may not be related to each other.

• An important fact to note about strings is that even though a character or number seems like it might be a string, it is always necessary to confirm.

Let's consider an example for reference:

String: '40'

Number: 40

Now once inserted in a computer program, the string '40' will be considered as 4 and 0, while the number 40 will be considered as a numerical.

This essentially means that using the quotations in a string is extremely important.

Similar to the concept of strings, we have yet another variable that is important for string. This is commonly referred to as the Substring.

A substring is basically a part of the string that represents a specific character within the string. 

Let's have a look at the concept of Substrings before we dive into the problem of finding the longest substring with k unique characters.

What is a Substring?

The Substrings are often referred to as a subset or a part of the original string. They are a contiguous series of characters that are found within a string.

For instance, if we consider our earlier example:

"The apple doesn't fall far from the tree"

Here, every individual character, such as "apple" is a substring of the entire line.

We commonly find the use of Substrings in Java where the function java.lang.String can be used within a program in order to create substrings from a new string.

There are two different variants available in a program using which we can obtain a substring in Java:

• int startIndex (Public String Substring)

This function can be used for generating a new string object that will already include a substring from a pre-specified startindex.

• int startIndex, int endIndex (Public String Substring)

This function is used for returning a new string object that will include substring from the indices lying between the startIndex and the endIndex.

Having a clear understanding of the properties of a substring is extremely essential for finding the longest substring with k unique characters. Let’s figure out how we can put different algorithms to use for solving this problem statement. 

How to find the longest substring with k unique characters in a given string problem?

Check out the following problem statement before we discuss the approaches for solving this problem.

Problem Statement

You have been given a string. The task is to print the longest possible substring within this sequence that will return k unique characters. If found that there are more substrings of longest possible lengths, you can print any of them.

Answer Key

We can essentially approach this problem by using two different methods.

Method 1: Using the Brute Force Approach

The Brute force is a commonly used algorithm that uses the exhaustive approach for solving a given problem.

When initialised in a program, it will find all the possible solutions until it reaches the desired output. This approach is efficient for finding the target sum in any given problem.

Now in the context of the given problem, if the length of the given string is considered as n, then we can find n*(n+1)/2 possible substrings.

Here is the algorithm for the Brute Force approach:

• We can start by generating all the substrings 

• Next up, we will check if any of them contain k unique characters

• Once we apply the Brute force approach, the time complexity would be O(n2) for generating all the substrings 

• Whereas, the time complexity would be O(n) to check all the generated substrings

Time Complexity for this approach:

O(n3)

Method 2: Using the Linear Time Approach

The general idea behind this approach is to maintain a window. This will be further utilised for storing all the elements until it contains less than or equal to k elements.

Here's the algorithm for the linear time approach:

• We will start by initiating a window where we will constantly keep adding elements

• This procedure will continue to follow until we have k number of elements left in the window

• We will also keep on updating the results as required by the program

• If the elements somehow start exceeding the capacity of the window, you can remove the excessive elements from the left corner

• Omce max substring is achieved, we will run the driver function by the end of the program

Time Complexity for this approach:

O(n)

Winding Up

Using brute force algorithms in a program is a highly efficient technique for solving any type of programming program. 

You can easily reach the target sum by simply iterating on the data and finding multiple solutions for the problem. Always remember to run the driver functiny the end of the program so that you are able to check the efficiency of your algorithm. 

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