Which technique is used for backtracking?

The world of programming is filled with algorithms and functions that exist to solve real time problems in the least possible time.

One such function that we shall be discussing in this blog is the backtracking problem.

In order to understand what backtracking essentially means, let us consider the example of an onion.

Notice how an onion has several layers that can be unfolded to reach its core? The backtracking algorithm follows a similar pattern.

It will recursively find all the possible solutions to a problem until it reaches the solution that exactly matches the required output.

Hence, you can certainly say that the backtracking algorithm is definitely one of the most useful solutions for solving a coding problem.

But, that is not all!

Apart from recursion, we also have the non-recursive technique that is also a part of backtracking. This is more commonly known as the iterative approach.

Learn all the details about backtracking by the help of this blog!

What is Backtracking?

Backtracking is basically one of the most optimal solutions for solving any coding based problem.

This is essentially an algorithmic technique that is used for solving technical problems in a recursive order.

So, what does it mean to solve a problem recursively?

Well, the recursive algorithm focuses on building the solution to a problem one step at a time. This means that the algorithm will continue to add cues and increase the value of the solution until it reaches the desired output for the solution.

Also based on this approach, the algorithm automatically removes certain parts of the solution that do not comply with the output.

This is done in order to remove the complexity and constraints of the program. Which is why, the Backtracking questions in the programming interviews are based on adapting solutions that ultimately add to the output.

If you are interested in appearing for the coding interviews, it would be best to have knowledge of the real-time uses of the backtracking algorithm.

What are the uses of Backtracking in real-time?

There are a few specific scenarios where the backtracking algorithm works the best for finding the optimal solution. Let's have a look at a few instances

• When faced with a decision making problem, the backtracking algorithm is better known to find the solution at a much faster pace than the other algorithms

• In order to optimise the solution of a problem, backtracking is found to be highly efficient and useful

• You can also find solutions to the enumeration based problems by using backtracking

• And, in case you are faced with a problem that does not have any limits, then the backtracking approach would certainly work the best for you

Backtracking essentially works on the principle of solving a problem recursively. If you are preparing for the technical or the coding interviews, such as Amazon, Microsoft or Google online test, you may have to solve a few problems based on backtracking in your technical rounds.

With that said, in our next segment, find the different categories of the backtracking algorithm and how they can be applied for solving a problem

What methods are used for Backtracking?

Did you know that the backtracking algorithm itself is classified into two different types?

These are namely the recursive and the non-recursive backtracking algorithms:

1. Recursive backtracking algorithm

Backtracking is basically a part of the binary tree traversal method that is optimal for finding solutions to the problems that have multiple possibilities.

Recursion refers to the process where a function calls itself in a repeated manner in order to split the solution into multiple sub-problems.

This way the task or backtracking problem at hand can be simplified making it more easier and efficient to reach the output.

The function that calls itself repeatedly within the program is referred to as the recursive function.

1. Non recursive backtracking algorithm

The non recursive backtracking algorithm in other terms is also known as iterative backtracking.

This form of backtracking focuses on exploring the solutions for performing a systematic search for any given problem, especially a binary tree based problem.

Iteration is essentially based on performing a set of functions on a regular basis using loops and a specific set of rules or instructions.

The program executes these sets of instructions till we reach the point where the loop turns out to be completely false.

This is done while keeping in mind that the control variable needs to be continuously updated so that we can make sure that the program will not enter an infinite loop.

Now, we would like to share an implementation of this approach in a backtracking problem so that you can see for yourself how the algorithm is used in a program.

Problem Statement

You have been given a set of all positive integers. Find all the possible subsets of these integers using backtracking.

Answer Key

The idea for solving this problem is quite simple. We will start by assuming that we have n number of elements within the array and the choices for each element is also n.

Hence, we will recursively call all the number of choices and insert the second element within the array.

Check out the algorithm for implementing the recursive function:

• Start by creating a recursive function using the input array and the current subset from the input

• Now, run a loop for the size of the input array and keep adding elements to your newly formed array

• Within this loop we will be calling the function for our next index and this process will be continued until we reach out final index

• Once we reach out final index, we will then backtrack to our last recursive call and finally remove our current index

The program will be finalized once our initial loop returns all the subsets for the given array.

Time Complexity for this approach:

O(n.2^n)

Wrapping Up

Backtracking is one of the common problems asked in coding interviews such as the Accenture assessment test, Microsoft codility test or the Google online test.

Hence if you are interested in ace your technical interviews, make sure to practice as many Backtracking problems as possible.