How to solve the frog jumps problem?

 



These days programmers are practicing a lot of DSA problems, so that they can get placed in famous tech companies. 

There are a lot of famous companies that are hiring candidates who have great knowledge of data structure. 

The Frog Jumpsproblem is one of the most asked DSA problems by different famous companies. However, the programmers get confused in solving this problem. 

The problem of Frog Jumps is based on Array and requires a dynamic programming approach to solve. Those who are not having the knowledge of the correct approach will be not able to solve it. 

 

Through this guide, you will be able to know about the concept which is required to solve the Frog Jumps. 

Once you understand the concept behind the Frog Jumps, then you will be able to solve the Zig Zag tree traversal question. 

 

What is the Frog Jumps Problem?

The Frog Jumps problem refers to the question where you will be given a frog that will jump through the stairs which will be given as the arrays. You have to jump in a way that the frog reaches its destination but with minimum energy loss. 

The concept of energy lost is whatever amount of energy has been wasted for jumping from one data element to another. You will have to do this for every jump, so that you can get to know how much energy was lost for crossing all the elements. 

However, an important thing that you should know is that the energy that will be calculated for the jump will be the difference between both elements. 

Therefore, we have to find all the arrays through which we will be able to cross the stairs or all the data elements with minimum energy loss. 

For solving this question, there are various ways available, however, their time complexity or space complexity is higher than the required. Therefore, we will learn about the concept through which we will solve this question with less time complexity and space complexity. 

 

So, now let’s get started with our next part: how we will get minimum energy loss for crossing the frog. 

 

How To Solve The Frog Jumps Problem

The Frog Jumps problem will require the approach of dynamic programming. However, there are different approaches available through which you can solve the problem, but you will not be able to get the correct answer from them. Now, take a look at the problem statement and what will be the approach that will be required to solve it. 

 

Problem Statement: Find the minimum energy loss from the given data elements for the Frog Jumps. 

[30, 10, 60, 10, 60, 55]

 

Approach: 

  • First of all, we will check all the elements of the given array. 
  • Now, we have to find the elements through which we will get minimum lost energy. 
  • So, we have to find such a combination whose difference is lesser than the others. 
  • When we found out that combination whose difference is lesser than the other along with traversing over all the arrays, then we will stop the recursive calls and will end the iteration. 
  • After it, we will calculate all the energy loss and will show the answer.

Dry Run

  • For the given question, we will start with iteration. 
  • Now, we will calculate the difference between the first two elements along with the values on which we are jumping. 
  • So, we will check for the values 30 - 10= 20 and the next one is 30 - 60= 30. So, we will choose the jump from 30 to 60 as it takes high energy loss but we reach the high value. 
  • Now, we will again jump to the next element and will calculate their differences. 
  • Therefore, the element that will be is 60 - 10 = 50, and 60 - 60 = 0. So, we will go with the second combination as the element is taking no energy loss, but for the first combination, it is taking 50 energy loss. 
  • Now, we will jump from 60 to 55 which will be 60-55 which equals 5. So, we have finally got all the energy loss. 
  • So, we will calculate all of the energy loss which will be the minimum loss. Therefore, it is 30 from the first jump which is (30-60) + 0 from the second jump which is from (60 – 60), and 5 from the (60-55). In addition, it will be 35 energy loss which is the minimum for the given elements. 
  • If we have taken the first jump of the 30-10, 10-10, 10-60, and 60-55, then the energy loss that we will be having will be 20+0+50+5= 75 which is much higher than the answer that we have got.....



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