Binary trees are one of the most complex but important forms of data structures. They are used to store data in a hierarchical manner. In your career, have you encountered the term binary tree when storing and managing data? If yes, you must be curious about several views of a binary tree and how to print them.
A binary tree is a data structure in which data is stored in the form of nodes connected by branches. In a binary tree, each node has two children, which can be thought of as branches of the root.
The flow and accessibility of data is isolated from the binary tree in an organized manner.
In this article, we will discuss one of the main questions about binary trees, namely Bottom view of binary tree and how to calculate it by different methods.
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Before we discuss this particular view of a binary tree, let’s take a look at all the available views of a binary tree and summarize them.
What is the point of view of a binary tree?
Just like a physical tree, a binary tree has four main views. These views are:
- top view of binary tree
- Right view of binary tree
- Left view of binary tree
- and the bottom view of the binary tree
Each view of a binary tree shows a different element placed along its line of sight. These views are important for understanding the accessibility and availability of data in a data structure.
You can observe the different parameters through the view of the binary tree. These parameters include the horizontal distance of the node, the location of the node, the node address, the number of levels of the node, and so on.
These parameters can help you observe the exact value and position of the node.
Let’s discuss in detail one of the most common views of a binary tree, the bottom view of a binary tree.
What is the bottom view of a binary tree?
The bottom view of a binary tree shows the nodes that are seen when viewing a particular binary tree from the bottom.
By performing a pre-horizontal sorting on the elements, you can easily access all the nodes and elements that can be found in the bottom view of the binary tree.
Initially, level and node-to-root distance values are passed for each element to place them appropriately in the tree. After that, in the pre-landscape order, the nodes available on the end view will be displayed in this view.
But there are different ways to print the bottom view of a binary tree through code.
Let’s discuss the most efficient and accurate way to implement a bottom view of a binary tree.
How to see the bottom view of a binary tree
There are two ways to get the bottom view of the tree. These methods use hashmap and recursive methods as well as queue methods.
We’ll start by discussing hashmaps and recursive methods in detail.
Hashmap and recursion
In this approach, the technique is to add nodes to the map under different conditions based on horizontal distance. Also, the function will be called recursively unless all nodes at the bottom are visited.
The following is showing Hashmap and recursive method to access Bottom view of binary tree:
- The first step is to perform a pre-order horizontal. This will help you to calculate the appropriate levels of the different nodes of the entire binary tree from the root to the final node.
- Now, build a hashmap where you can store all the heights of the nodes.Accurately store distances in this map
- For hashgraphs, keep keys horizontal or just keep the horizontal distance of specific nodes. And the value of that map will be a pair (p, q). In this pair, p is the element value of the node and q represents the height or horizontal distance of a particular node.
- After that, just for each node of the binary tree, add that node to the resulting map. This node will only be added if it is the first node with the same horizontal distance as the current one.
- However, if the node is already available within the same distance, you can replace the previously placed node with the current node value. This will only be done if the horizontal distance of the current node is relatively greater than the previous node.
Finally, get the nodes available on the map. This will be the bottom view of the binary tree. Let’s discuss the Queue method and see how exactly it handles time complexity.
Also in this method, a preorder traversal of the nodes is performed and the result is stored in a queue. In addition to the queue, the horizontal distance is to be stored as a key in the map.
Let’s understand the algorithm for this approach:
- First, after traversing each node sequentially, make a queue to store all nodes
- Next, place the value at the root of the binary tree in the queue. This root will be placed at a distance of 0 from the root
- Push the left child of the binary tree into the queue one at a time with a horizontal distance of hd-1.
- And the child on the right will be horizontally separated by hd+1
- Just push elements with the corresponding horizontal distance from the queue to the map, unless the queue is found to be empty.
Finally, print will show the mapped value of the bottom view of the binary tree with the appropriate nodes.
Rinversion of array and Sequential horizontal are the two main topics you need to learn to print Bottom view of binary tree. You can use the method of your choice to get the bottom view of the binary tree or any of the four views depending on the amount of data in each array.