How to solve ""Jumping numbers"" task?

Learning the Java programming language and getting acquainted with Arrays are basically the two important pillars of programming that every programmer should be a pro at!

Numbers and technical algorithms are secondary, but learning how to manipulate data especially by using arrays is absolutely necessary when it comes to coding and programming.

One such data concept is related to the jumping numbers. These are essentially numbers in a series of data where the difference between each of the adjacent pairs equals 1.

Hence, all the single digit numbers are commonly referred to as jumping numbers.

This is an arithmetic and logical problem that is often encountered in the technical interviews.

If you are interested in learning how to find the solution for a series of data containing the jumping numbers, read the entire blog for detailed information.

What are Jumping Numbers in programming?

Did you know?

The concept of jumping numbers in programming essentially refers to the adjacent digits in a given series of data that differ by the value of 1

Well, all of the single digit numbers in programming are known as the jumping numbers.

For instance, the numbers 7, 4343456 and 8987 are considered to be jumping numbers because of their natural numerical order.

Also, bear in mind that the difference between 9 and 0 cannot be considered to be a jumping number hence, only the single-digit numbers in programming are considered as jumping numbers.

That said, since you are here for a proper explanation on how to solve problems based on jumping numbers, let us discuss that in the next section of the blog.

What algorithms can be used for solving the "Jumping Numbers" task?

The jumping numbers problem is a pretty common question in technical interviews, here’s an overview of what the problem statement will look like for the jumping numbers problem.

Problem Statement:

You have been given a positive number i.e x. Your task is to print all the jumping numbers that are either smaller than this positive number or equal to it. You can print these numbers in any desired order.

Now, we would highly recommend trying out the algorithms and methods mentioned below on an online IDE so that you can see for yourself how they work in real-time.

But, in the meantime, here are some of the top methods for finding jumping numbers in a given sequence of data.

Method 1: Traversing the numbers right from 0 to x

Now, for people who already have been in the field of programming for quite a long time, they might consider using the Ninja Technique function for iterating but the process would be rather complex.

Computing the value of a third string generated by the program for calculating the value of two consecutive integers would simply consume a lot of time and space within the program.

Which is why, we are starting off with one of the easiest approach i.e traversing all the different characters between 0 to the given value (x) 

Here's how the algorithm for this method would work:

• Start by traversing right from the first digit of the given string i.e 0.

• Now, keep visiting each of the numbers without skipping any until you reach the given input number i.e "x".

• Keep in mind that you have to check for a "jumping number" for each of the characters that you have visited or traversed so far.

• You cannot skip any of the characters while following this approach hence this method requires you to be absolutely thorough with your implementation.

• For all the jumping numbers found, you may print yes, otherwise you can return no. 

Time Complexity for this approach:

O(x)

Method 2: Using Breadth First Search in a Graph

The Breadth First algorithm in programming starts visiting all the nodes implemented within a graph structure from the root of the graph. 

After visiting the root it will then move forward to the other nodes of the graph i.e its neighbouring nodes. Finally, by the end of the program it selects the nearest and the unvisited nodes and explores them before calling the program.

The breadth-first search analysis in the context of finding jumping numbers in a given data is said to improve the time complexity of the approach discussed earlier by O(k).

Here, "k" represents the jumping numbers that are evidently smaller than the value of "x" or are equal to its value.

Check out the algorithm for how the Breadth First Search will be implemented for this problem statement:

• Let us assume that we have implemented a graph for the provided data structure where the first node of the graph represents a 0 value. 

• Since we are using the BFS algorithm we will have to start right from the first node and try to reach all the attainable nodes within the graph.

• Finally, by doing so we should be able to print all characters that represent a jumping number for "x".

Time Complexity for this approach:

O(k)

Method 3: Using Depth First Traversal in Graph

In the Depth First Traversal method, you can essentially start from any of the nodes and it is not necessary to start from the root itself for the program.

That said, here's how the implementation of the Depth First Traversal would go:

• Firstly, you have to change the solution obtained by the former method into Depth First Search Traversal.

• Next up, you are required to extend this solution to be printed in a sorted order of numbers.

• Finally, you can extend the Sorted range of numbers to be printed given the required criteria.

Time Complexity for this approach:

O(k)

Final Thoughts

One of the biggest reasons why Java is preferred over other programming languages by the developers is that it enables quick and easy to perform functions that no other programming language offers over a single platform!

One such example is the Ninja Technique algorithm that is efficiently used for generating strings using only the digits.

For programmers who would like to see themselves at global developer positions, learning the concepts of Java can definitely help you succeed in your goal!

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