To start with basics, it is very important to understand binary tree itself to understand different types of it.

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

– It has a root node , which may not have any child nodes (0 childnodes, NULL tree)

–Root node may have 1 or 2 child nodes . Each such node forms abinary tree itself

–Number of child nodes can be 0 ,1 ,2.......not more than 2

–There is a unique path from the root to every other node

Example :

```
X
/ \
X X
/ \
X X
```

Coming to your inquired terminologies:

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

Level 0 to h-1 represent a full binary tree of height h-1

– One or more nodes in level h-1 may have 0, or 1 child nodes

If j,k are nodes in level h-1, then j has more child nodes than k if and only if j is to the left of k , i.e. the last level (h) can be missing leaf nodes, however the ones present must be shifted to the left

Example :

```
X
/ \
/ \
/ \
X X
/ \ / \
X X X X
/ \ / \ / \ / \
X X X X X X X X
```

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

Each node has exactly two child nodes or no nodes

Example :

```
X
/ \
X X
/ \
X X
/ \ / \
X X X X
```

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

Each non leaf node has exactly two child nodes

All leaf nodes are at the same level

Example :

```
X
/ \
/ \
/ \
X X
/ \ / \
X X X X
/ \ / \ / \ / \
X X X X X X X X
/ \ / \ / \ / \ / \ / \ / \ / \
X X X X X X X X X X X X X X X X
```

You should also know what a perfect binary tree is?

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

– is a full binary tree

– All leaf nodes are at the same level

Example :

```
X
/ \
/ \
/ \
X X
/ \ / \
X X X X
/ \ / \ / \ / \
X X X X X X X X
/ \ / \ / \ / \ / \ / \ / \ / \
X X X X X X X X X X X X X X X X
```

Well, I am sorry I cannot post images as I do not have 10 reputation.
Hope this helps you and others!

1

Does http://en.wikipedia.org/wiki/Binary_tree#Types_of_binary_trees not answer your question?

– rodion – 2012-09-10T21:26:25.5803no its not ,a lot of confusion among these – kTiwari – 2012-09-10T21:28:32.270

Strict Binary Tree: Every node can have 2 child or no nodes at all – vikkyhacks – 2014-02-18T17:44:37.680