**BINARY TREE**

**An important category of general tree is Binary Tree. A binary tree can be defined as a finite collection of nodes where each node is having the property that it can have 0,1 or 2 children.**

**A binary tree may be empty known as Null tree or it contains a special node called the root of the tree and remaining nodes in the tree form the left and right binary sub-trees.**

**Here, the node A is the root of the binary tree which is the top of the tree.**

**B and C are the left and right sub-trees of the root A, respectively.**

**The left sub-tree namely B, having single node D.**

**The right sub-tree namely C having two nodes E and F.**

**Similar Binary tree**

**Two trees are called similar if both are having same structure but the elements in both the tree can be different as shown in fig. b**

** fig. b similar binary tree**

**Equivalent Binary tree**

**Two trees are called equivalent if both are having same structure and having the same content in their respective nodes.**

**Complete binary Tree **

**A binary tree is called complete if it contains the maximum number of nodes it can have as shown in fig. c**

** fig. c complete binary tree**

**On the other hand, a binary tree is said to be almost complete binary tree if all its levels are full except the last one as shown in fig. d**

**fig. d almost complete binary tree**

**In fig. c , at level k, there can be maximum 2^k nodes. therefore,**

** level 0 can have 2^0=1 node.**

** ****level 1 can have 2^1=2 nodes. **

** level 2 can have 2^2=4 nodes and so on.**

**Strictly Binary tree**

**A binary is called Strictly binary tree if all the non leaf nodes of the tree contains exactly two children.**

**It means , every non-leaf nodes contains left and right sub-tree.**

**It is also known as 2- tree or full Binary tree or extended binary tree.**

**It contains exactly 2n-1 nodes.**

**CHECK PROPERTIES OF BINARY TREE WITH PROOF**