Difference between Full Binary Tree, String Binary Tree, Full Binary Tree?

Question

I got confused in the terminology of the underlying trees, I studied the Tree, and I cannot distinguish between these trees:

a) Full binary tree

b) String binary tree

c) Full binary tree

Please help me split these trees. When and where are these trees used in the data structure?

Answer 1

Wikipedia gave

A complete binary tree (sometimes a regular binary tree or 2-tree or strictly binary tree) is a tree in which each node, except for the leaves, has two children.

Thus, you do not have nodes with one child. This seems to be the same as a string binary tree.

Here is a full / string binary tree image from google:

A complete binary tree is a binary tree in which each level, with the possible exception of the last one, is completely populated, and all nodes are as far away as possible.

It seems to be a balanced tree.

Here is the image of a complete binary tree, from google, the full part of the image is a bonus.

Answer 2

Perfect tree:

x / \ / \ xx / \ / \ xxxx / \ / \ / \ / \ xxxxxxxx 

Full tree:

  x / \ / \ xx / \ / \ xxxx / \ / xxx 

Strict / Full Tree:

  x / \ / \ xx / \ xx / \ xx 

Answer 3

There is a difference between STRICT and FULL BINARY TREE.

1) FULL BINARY TREE: A binary tree of height h containing exactly (2 ^ h) -1 is called a complete binary tree . (Ref: Pg 427, Data Structures, Algorithms, and Applications in C ++ [University Press], second edition of Sartaj Sahni).

or in other words

In FULL BINARY TREE, each node has exactly 0 or 2 children, and all leaf nodes are on the same level.

Example: The following is the FULL BINARY TREE:

  18 / \ 15 30 / \ / \ 40 50 100 40 

2) STRICT BINARY TREE: Each node has exactly 0 or 2 children.

For example: The following is a string binary tree:

  18 / \ 15 30 / \ 40 50 

I think there is no point in defining a complete binary tree, still for the sake of completeness, which I would like to tell you what a complete binary tree is.

3) FULL BINARY TREE: A binary tree is a complete binary tree if all levels are completely populated, with the possible exception of the last level, and the last level has all possible keys.

Example: The following is the FULL BINARY TREE:

  18 / \ 15 30 / \ / \ 40 50 100 40 / \ / 8 7 9 

Note: The following is also a complete binary tree:

  18 / \ 15 30 / \ / \ 40 50 100 40 

Answer 4

Disclaimer - The main source of some definitions is Wikipedia, any suggestions to improve my answer are welcome.

Although this post has an accepted answer and is a good one, I was still confused and would like to add a few more clarifications regarding the difference between these conditions.

(1) FULL BINARY TREE - . A full binary tree is a binary tree in which each node, except for the leaves, has two children. This is also called a strictly binary tree .

The above two are examples of a complete or strictly binary tree.

(2) FULL BINARY TREE - . Now the definition of a complete binary tree is rather ambiguous, it says: - A complete binary tree is a binary tree in which each level, except, possibly, the last one, is completely filled, and all nodes are as far as possible. It can have 1 to 2h nodes, as far as possible, at the last level h

Pay attention to the lines in italics.

The ambiguity lies in italics, “except possibly the last”, which means that the last level can also be completely filled, i.e. this exception does not always have to be met. If the exception is not thrown, then this is exactly the same as the second image that I wrote, which can also be called an ideal binary tree . Thus, an ideal binary tree is also full and complete, but not vice versa, which will be clear by another definition that I need to specify:

ALMOST FULL BINARY TREE - When an exception is thrown in the definition of a complete binary tree, it is called an almost complete binary tree or an almost complete binary tree. This is just a type of complete binary tree, but a clearer definition requires a separate definition.

Thus, an almost complete binary tree will look like this: you can see the nodes as far as possible in the image, so it looks more like a subset of a complete binary tree, to put it more strictly, each almost complete binary tree is a complete binary tree, but not vice versa.

Answer 5

Concluding from the above answers, Here is the exact difference between full / strictly, complete and perfect binary trees

• Full / strictly binary tree : - Each node, with the exception of leaf nodes, has two children

• Full binary tree : - Each level, with the exception of the last level, is completely populated, and all nodes remain valid.

• An ideal binary tree : - Each node, with the exception of leaf nodes, has two children, and each level (last level too) is completely full.

Answer 6

Consider a binary tree whose nodes are drawn in the form of a tree. Now start numbering the nodes from top to bottom and from left to right. A full tree has the following properties:

If n has children, then all nodes with a number less than n have two children.

If n has one child, it must be a left child, and all nodes less than n have two children. In addition, a node with a number greater than n has children.

If n has no children, then no node with a number greater than n has children.

You can use the full binary tree to represent the heap. It can be easily represented in continuous memory without spaces (i.e., all elements of the array are used, with the exception of any space that may exist at the end).

Answer 7

A full binary tree is a complete binary tree, but vice versa is not possible, and if the depth of the binary is n. nodes in a complete binary tree (2 ^ n-1). The binary tree does not need to have two children, but in the full binary, each node did not have one or two children.

Answer 8

To start with the basics, it is very important to understand the binary tree in order to understand its various types.

A tree is a binary tree if and only if: -

- It has a root root, which may not have child nodes (0 child nodes, NULL tree)

-Root node can have 1 or 2 child nodes. Each such node forms the ebony itself

- The number of child nodes can be 0, 1, 2 ....... no more than 2

- there is a unique path from the root to any other node

Example:

  X / \ XX / \ XX 

Getting started with your requested terminology:

A binary tree is a complete binary tree (height h, we root node as 0) if and only if: -

Level 0 to h-1 is a complete binary tree of height h-1

- One or more nodes of level h-1 may have 0 or 1 child nodes

If j, k are nodes of level h-1, then j has more child nodes than k if and only if j is to the left of k, i.e. at the last level (h), there may be no nodes of the sheet, those present must be shifted to the left

Example:

  X / \ / \ / \ XX / \ / \ XXXX / \ / \ / \ / \ XXXXXXXX 

A binary tree is a strictly binary tree if and only if: -

Each node has exactly two child nodes or nodes

Example:

  X / \ XX / \ XX / \ / \ XXXX 

A binary tree is a complete binary tree if and only if: -

Each non-leaf node has exactly two child nodes

All leaf nodes are on the same level.

Example:

  X / \ / \ / \ XX / \ / \ XXXX / \ / \ / \ / \ XXXXXXXX / \ / \ / \ / \ / \ / \ / \ / \ XXXXXXXXXXXXXXXX 

You should also know what an ideal binary tree is?

A binary tree is an ideal binary tree if and only if: -

- full binary tree

- all leaf nodes are on the same level

Example:

  X / \ / \ / \ XX / \ / \ XXXX / \ / \ / \ / \ XXXXXXXX / \ / \ / \ / \ / \ / \ / \ / \ XXXXXXXXXXXXXXXX 

Well, sorry, I can’t post the images since I do not have 10 reputation. Hope this helps you and others!

Answer 9

In my limited experience with a binary tree, I think:

• String binary tree . Each node, except that leaf nodes have two children or only have the root root.
• Full binary tree . The binary tree H is strictly (or exactly) containing 2 ^ H -1 nodes , it is clear that each level has the largest number of nodes.
• Full binary tree . This is a binary tree in which each level, with the possible exception of the last, is completely filled, and all nodes are as far as possible.

Answer 10

A complete binary tree is a binary tree in which each node has 0 or 2 children. In other words, each node in the tree, except for the leaves, has exactly two children.

A Full binary tree is a binary tree in which each level of the tree is completely populated, with the exception of the last level. In addition, at the last level, the nodes must be attached, starting from the leftmost position. A complete binary tree must satisfy the following conditions:

• If a, b are two nodes of a level higher than the last level, then a has more children than b if and only if a is to the left of b.
• From the root of the node, the level above the last level is a complete binary tree of height h-1.
• One or more nodes of the last level can have 0 or 1 children.

Answer 11

Consider a binary tree of height 'h'. A binary tree is called a complete binary tree if all leaves are present at a height of "h" or "h-1" without missing numbers in the sequence.

  1 / \ 2 3 / \ 4 5 

This is a complete binary tree.

  1 / \ 2 3 / / 4 6 

This is not a complete binary tree, as node number 5 is missing in the sequence