**Introduction:**

- Trees are flexible,powerful non-linear data structure that can be used to represent data items which has hierarchical relationship
- Tree is an ideal data structure for representing hierarchical data.
- Tree can be defined as a finite set of one or more data items(ie nodes) such that

(a) There is a special node called the root of the tree

(b) The remaining nodes are partitioned in to n disjointed set of nodes each of which is a subtree. - Example of a tree(figure 1)

- Example of a structure that is not a tree

This also contains a set of nodes {A,B,C,D,G,H,I,E,F} with node A as a root node but this is not a tree because the node E is shared. so we cant subdivide the nodes in to disjointed sets.

__Tree Terminologies:__

__Node:__- Each data item in a tree is called a node.
- Node specifies the data information and links to other data items

__Root:__- Root is the first node in the tree
- Node A is the root node in the tree example

__Degree of a Node:__- Degree of a node is the
**number of subtrees of a node**in a given tree. - In figure1degree of node A is 3,degree of node B is 2,degree of node C is 2,degree of node D is 3 and degree of node j is 4

__Degree of a Tree:__- The Degree of a tree is the
**maximum degree of node**in a given tree. - In figure1 node j has maximum degree as 4,all the other nodes have less or equal degree so the degree of the tree in figure 1 is 4

__Leaf Node (or) Terminal Node:__- A node with degree 0 is called a leafnode
- ie a node with no subtrees or children is called leafnode.
- In figure1 nodes L,M,N,O,H,I,P,Q,R,S,K are leaf nodes
- Any node whose degree is non-zero is called non-terminal node

__Level of a Node:__- The tree is structured in different levels.
- The root node is always at level 0.Then its immediate children are at level 1and their immediate children are at level 2 and so on up to the terminal nodes
- ie If a node is at level n, then its children will be at level n+1.

__Depth of a tree (or)Height of a tree:__- Depth of a tree is the maximum level of any node in a given tree.
- The depth of a tree in figure 1 is 4.(including level 0)

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