Difference Between Complete Binary Tree and Full Binary Tree

A brief explanation about Complete Binary Tree and Full Binary Tree

A complete binary tree an unidirectional tree where all levels are filled completely with nodes, with the exception of the top level that fills from right to left. In the same way, a fully-integrated binary tree is one in which every node, except for the last one are each filled with nodes and nodes in the final level have been filled left-to-right.

A fully binary tree can be described as a tree in which each node has two or zero children. Also, every node of a full binary tree is either without kids (a leaf node) or has two children. A full binary tree can be often referred to as a true binary tree.

It is important to know the distinctions of Complete Binary Tree and Full Binary Tree

Knowing the difference between fully binary in comparison to full binary tree is vital due to a number of reasons, among them:

1. Design of algorithms: Different algorithms are more suitable for different kinds of trees. Understanding the features of full and complete binary trees will help selecting the best algorithm to solve a particular issue.
2. Data storage Binary trees are commonly employed for data storage and knowing the difference between full and complete binary trees can assist in the design of efficient structures for data storage.
3. search and traversal Effective search and traversal algorithms are based upon the structure and arrangement of binaries. Knowing the difference between full and complete binary trees can aid in the development of efficient algorithms for traversal and search.
4. Optimization of code: By understanding the properties of complete and fully tree of binary, developers are able to improve their codes to make use of these characteristics which results in more efficient and speedier code.
5. Education in computer science: Knowing the distinctions between full and complete binary trees is an essential idea in the field of computer science education It is a crucial concept for students to comprehend for them to be able to move on into more advanced subjects.

Complete Binary Trees

A fully-integrated binary tree is an unidirectional tree where every level of the tree are filled completely with nodes, with the exception of the final level that can be filled left-to-right. In terms of the term “complete” refers to one in which all nodes, excluding the final stage are filled by nodes and the nodes of the final level have been filled left-to-right.

Characteristics of fully Binary Trees:

1. The design of the complete binary tree: Complete binary trees are shaped in a specific way with each level fully filled, with the exception of the top level which fills from right to left.
2. Nodes in a full binary tree: The number of nodes in a Binary tree will always be a factor of 2 minus. For example, a full binary tree that has three levels would have 23 (i.e. 1 – 2 = 7) nodes.
3. Properties of fully binary trees Full binary tree possess a number of key properties such as being able to say that the size of the tree is logarithmic to number of branches and the root node always appears located at index 1 within the representation of an array in the tree.

Examples of complete binary tree:

Here are a few examples of fully-binary trees:

In each of these cases in these examples, all levels of tree are filled to the max except for the top level that fills from right to left.

Full Binary Trees

A fully Binary tree refers to a tree in which each node has one or 2 children. That is, each node in a fully binary tree is either without kids (a leaf node) or has two children. A fully binary tree is sometimes referred to as a proper binary tree.

Characteristics of fully tree of binary:

1. The form of fully tree of binary: Full binary trees are shaped in a certain way in which every node has one or two children. This means that each degree of the tree’s structure is fully full.
2. Nodes in a fully binary tree Nodes in a complete binary tree is calculated by using the equation 2^(h+1) + 1, in which h represents the tree’s height. For instance, a complete binary tree that has three levels would have 2^(3+1) (1 – 3 equals 15 different nodes.
3. Full binary tree properties: Full binary trees contain a number of significant properties such as its height, which is logarithmic in relation to nodes and that the number leaf nodes is the same as how many internal nodes, plus one.

Examples of complete tree of binary:

Here are a few instances of full binary tree:

In each of these instances each one, each node is home to two or zero children, and each stage of the tree has been full.

Difference Between Complete Binary Tree and Full Binary Tree

The primary difference between complete binary and complete trees lies in how they are filled with nodes.

In a fully binary tree each level in the tree have been full of nodes with the exception of maybe the top level that is completely filled by the left and right. Contrarily the case of a fully binary tree, each node is either one or two children and each level in the tree is full of nodes.

A key distinction between fully binary trees or full binaries is in the amount of nodes that they comprise. Nodes within a fully binary tree always is a function of 2 minus 1. however there are nodes within a complete binary tree can be determined by using this formula: 2^(h+1) 1 with h being the size that the tree is.

One of the major ramifications of these distinctions can be that the size of a full binary tree is logarithmic regard to nodes however, it is the same for a fully Binary tree also is logarithmic however, it has a different base.

Furthermore the root node in an entire binary tree will always be at index 1 within an array of representations for the tree however, the root node of the full binary tree does not have to be located at index 1.

Although both complete binary trees as well as full-binary trees are crucial concepts in the field of computer science and possess several similarities Their differences are in the manner they are packed with nodes as well as the amount of nodes they have.

Applications and Uses

Full binary trees are used in a variety of ways in the field of computer science. They are employed in many algorithmic and information structures.

Binary trees that are complete can be typically employed to represent heaps of data which are employed to facilitate efficient sorting and searching of data. In particular, complete binary tree can be used as the representation of binary heaps which are utilized to create priority queues. Priority queues are frequently employed in databases, operating systems and other programs which require effective resource management.

Full Binary Trees are utilized in many algorithms, including Huffman code which is utilized to compress data. In particular, full binary tree serve as Huffman trees that are used to create the Huffman codes for specific characters in text files. Huffman code is utilized in numerous applications, including image compression, data compression, speech coding and more.

Complete binary trees as well as full binary trees are utilized in a variety of tree traversal algorithms including depth-first searches and breadth-first searches, which are utilized for searching and sorting data within trees. These algorithms are utilized in a variety of applications, including graph theory and artificial intelligence and natural language processing.

Full binary trees are used in a variety of ways in computer science. They are employed in many methods and structures for data. These are crucial concepts that should be understood by anyone who is interested in programming or computer science.

Conclusion

Complete Binary Tree and Full Binary Tree are both binary tree forms, however they differ in their characteristic. A full binary tree is one that includes all levels filled, except maybe for the final level which fills from right to left while a full-length binary tree is a complete one, with each node having at least two children. These characteristics can be beneficial in many applications of binary trees in maths and computer science.