Those who are practicing the DSA problems must be aware of the topic of Tree Data Structure. Most well-known companies follow this data structure for their own products.
Programmers who are preparing for big IT companies will have to master the data structure and algorithm problems. It is a very important topic that is asked by the recruiter during the different rounds.
When you will start practicing the DSA, then you will get to know about all types of tricky questions through the online coding platforms.
There are a lot of questions that are asked by famous companies from the topic Tree and if you are not having all the knowledge of it, then you are going to miss a lot of opportunities.
To make you understand what a binary tree is and how to solve multiplication tree problems, here is what you need to read. You will find all the necessary information that will definitely help you in mastering the topic of Binary Tree.
## What is a Binary Tree?
The Binary Tree is a type of Tree Data Structure that comes with at most two children. As each element in a binary tree will have only two children, we classify it as a left child and a right child.
A binary tree is represented by the help of the pointer which is the topmost node. The node of the Binary Tree contains the element of data, a pointer that will point to the left child, and a pointer that will point to the right child.
As the Binary Tree is a part of the Tree data structure which is a type of non-linear data structure. So, the operations that we can perform on it are:
- Insertion of element
- Deletion of element
- Searching of element
- Traverse of element
An important thing that you should know. The root of the tree will be NULL if the tree is empty. It is an important point that you should remember because it is asked by most recruiters as a confusing question.
Some problems that are based on it are target sum, multiplication tree, finding height, and much more.
Through this, you will be able to get a better understanding of the Binary Tree.
What Is the Binary Tree Multiplication Problem?
The Binary Tree Multiplication Problem or Multiplication Tree problem is asked by a lot of recruiters or on the coding platforms in the daily contest section.
The problem statement of the Binary Tree Multiplication Problem is that you have to find the product of all the data elements that are in the right and left child of the binary tree.
So, for this, you will be given a tree that will be having the right child and left child, and you have to find the product of each element till the end.
For Example, A binary tree is having the data element 5,4,3,2,1,4,5,6,7, then you will have to make it and find the product of 543214567. But for doing this, you will need to have a better understanding of the basics of operations like traversing. Otherwise, you will find it very difficult to do.
How To Solve Binary Tree Multiplication Problem?
You will need to know the right approach, so that you will be able to solve the question properly in the most efficient way.
Therefore, to illustrate the approach and dry run of the Multiplication problem, here we are with the example that will be helping you very much. So, let’s take a look at the right approach and dry run for the multiplication tree problem.
Problem: Given a Binary Tree, find the product of all the nodes.
15
| |
2 3
| | | |
4 5 6 7
The elements are above which you can see. Now, let’s move with our approach first.
## Approach
We have to find the product of all the elements, so we have to traverse from the topmost node to the last element. But we will have to do it for the both left and the right child. If we traverse from the topmost to the left child, then we will have to ignore the topmost node in the second traverse.
Therefore, what we will be going to do here is we will traverse from the left subtree and find the product of all the elements. After it, we will again traverse to the right subtree and will find the product. Once we have found the product, then we will multiply them both to get the final product. To make this approach understandable to you, we will try to do it with the dry run. So, let’s get into that.
Dry Run
First of all, we will start from the topmost node which is 15. Now, we will traverse and will go to the next node which will be 2. We will multiply both elements. Again, we will traverse to the next node and it will be 4. Now, we have reached the end. But, we have an element left which is 5. So, we will traverse to that but there will be a condition, when we are traversing back, then we will not multiply that product of the location.
Now, we will traverse to element 5 and will multiply it. We are done with one of the children of the binary tree. Now, we will traverse to the next part. After traversing, we will get the product of all the elements. So, this is how we are gonna solve this problem. Now, the next part is on you, the Coding. Code the problem by following the same approach and the dry run that we have done.
Conclusion
Solving the problem gets easier if we are having the correct approach to it. There are a lot of programmers who start coding without writing the algorithm and doing a dry run. So, code the multiplication tree problem with the mentioned approach to solve it in the most effective way.