we know that binary trees are the ones that we use frequently for storing the data. Trees are preferred to linked lists,arrays because of its time complexity of O(logn). which trees will satisfy this condition that we have to know it.

1. Also See more posts : www.comsciguide.blogspot.com
Difference between Complete binary tree, Balanced binary tree,
Ordered binary tree, Full binary tree, Perfect Binary tree
Binary Tree:
A Tree in which each node has a degree of atmost 2. i.e. it
can have either 0,1 or 2 children.
Here, leaves are H, I, J. Except these, remaining internal
nodes has atmost 2 nodes as their child.
Full Binary tree:

2. Also See more posts : www.comsciguide.blogspot.com
Every node should have exactly 2 nodes except the leaves. It
is also called as Strict Binary Tree or 2- Binary Tree or Proper
Binary Tree.
Complete Binary Tree:
It is a binary tree in which every level (except possibly the
last) is completely filled, and all nodes are as far left as possible.

3. Also See more posts : www.comsciguide.blogspot.com
The above 3 fig’s are Complete Binary Trees.
Fig1 fig2 fig3
fig 4 fig 5
These are not complete trees as in fig1 at level 1, the 0 node has
no children. In fig 2, nodes 2, 5, 9 doesn’t have left child. For a
tree to be complete tree, right child is not necessary but left child
is must if right child is present incase of last level. For fig 3, the
node 0 doesn’t have a left child.same as for fig 4 and fig 5.
Ordered Binary Tree :
It is a Binary Tree in which all the elements are arranged in
an order i.e. For a node, All elements of left sub-tree should be
smaller than the node and all elements of right sub-tree should
be larger than the node.

4. Also See more posts : www.comsciguide.blogspot.com
In the above fig, Every node has smaller element as left child and
larger element as right child.
 An Ordered Tree may or may not be balanced. It may have
time complexity of O(n) or O(logn).
In the above Tree, we see that even though it is an Ordered
Tree, it is not balanced. For adding,deleting and Searching
operations, it has time complexity of O(n) same as linked list.

5. Also See more posts : www.comsciguide.blogspot.com
Balanced Binary Tree:
It is a Binary tree in which the elements are ordered and no
leaf is at “much greater” depth than any other leaf. It will have
time complxity of O(logn).
Perfectly balanced binary tree:
It is a Balanced binary tree in which the difference in the left
and right tree nodes’ count of any node is at most one.
In the given fig, the left binary tree is ordered whereas right
binary tree is ordered and balanced.
To avoid imbalance in the tree to search, apply operations
that rearrange some elements of the tree when adding or
removing an item from it. These operations are called Rotations.
The type of rotation should be further specified and depends on
the implementation of the specific data structure. As examples
for structures like these we can give Red-Black tree, AVL-
tree, AA-tree, Splay-tree and others.

6. Also See more posts : www.comsciguide.blogspot.com
Non-binary balanced trees:
Non-binary balanced search trees also have multiple
implementations with different special properties. Examples
are B- Trees, B+ Trees and Interval Trees. All of them are
ordered, balanced, but not binary. Their nodes can typically hold
more than one key and can have more than two child nodes.
These trees also perform operations like insert / search / delete
very fast.
Perfect binary tree:
In this tree, Every node has exactly two nodes and all levels
are completely filled.
( or )
A perfect binary tree is a binary tree in which all leaves have
the same depth or same level.
 In general A perfect binary tree satisfies all the properties of
complete and full binary trees.

7. Also See more posts : www.comsciguide.blogspot.com
 For an Orderded perfect binary tree, time complexity for
search, insert and remove operations has O(logn).
SEE ALSO:
www.comsciguide.blogspot.com
For Graph Terminology : Click here
Why analysis of Algorithms : Click here
4 pillars of OOPS concept : Click here