There are various types of binary tree in data structure. Below are mentioned and explained one of the most used once:

[one_half]Full Binary Tree: A binary tree is said to be full binary tree if each of its node has either two children or no child at all. Every level is completely filled up. Number of node at any level i in a full binary tree is given by 2 raised to i. A full binary tree is shown in the figure.[/one_half]
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[one_half_last]Complete Binary Tree: A complete Binary tree is defined as a binary tree where:

All leaf nodes are on level n or n-1.

Levels are filled from left to right.

An example of binary tree is shown in the figure.

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[one_half]A skewed binary tree could be skewed to the left or it could be skewed to the right . In a left skewed binary tree, most of the nodes have the left child without corresponding right child. Similarly, in a right skewed binary tree, most of the nodes have the right child without a corresponding left child.[/one_half]

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[one_half_last]Strictly Binary Tree: If every non-terminal node in a binary tree consist of a non-empty left sub tree and right sub tree, then such a tree is called as strictly binary tree. In other words, a node will have either two children or no child at all.[/one_half_last]