Tag: Tree in Data Structure PDF

Tree Data Structure | Tree Terminology

Tree Data Structure-

 

Tree data structure may be defined as-

 

Tree is a non-linear data structure which organizes data in a hierarchical structure and this is a recursive definition.

OR

A tree is a connected graph without any circuits.

OR

If in a graph, there is one and only one path between every pair of vertices, then graph is called as a tree.

 

Example-

 

 

Properties-

 

The important properties of tree data structure are-

  • There is one and only one path between every pair of vertices in a tree.
  • A tree with n vertices has exactly (n-1) edges.
  • A graph is a tree if and only if it is minimally connected.
  • Any connected graph with n vertices and (n-1) edges is a tree.

 

To gain better understanding about Tree Data Structure,

Watch this Video Lecture

 

Tree Terminology-

 

The important terms related to tree data structure are-

 

 

1. Root-

 

  • The first node from where the tree originates is called as a root node.
  • In any tree, there must be only one root node.
  • We can never have multiple root nodes in a tree data structure.

 

Example-

 

 

Here, node A is the only root node.

 

2. Edge-

 

  • The connecting link between any two nodes is called as an edge.
  • In a tree with n number of nodes, there are exactly (n-1) number of edges.

 

Example-

 

 

3. Parent-

 

  • The node which has a branch from it to any other node is called as a parent node.
  • In other words, the node which has one or more children is called as a parent node.
  • In a tree, a parent node can have any number of child nodes.

 

Example-

 

 

Here,

  • Node A is the parent of nodes B and C
  • Node B is the parent of nodes D, E and F
  • Node C is the parent of nodes G and H
  • Node E is the parent of nodes I and J
  • Node G is the parent of node K

 

4. Child-

 

  • The node which is a descendant of some node is called as a child node.
  • All the nodes except root node are child nodes.

 

Example-

 

 

Here,

  • Nodes B and C are the children of node A
  • Nodes D, E and F are the children of node B
  • Nodes G and H are the children of node C
  • Nodes I and J are the children of node E
  • Node K is the child of node G

 

5. Siblings-

 

  • Nodes which belong to the same parent are called as siblings.
  • In other words, nodes with the same parent are sibling nodes.

 

Example-

 

 

Here,

  • Nodes B and C are siblings
  • Nodes D, E and F are siblings
  • Nodes G and H are siblings
  • Nodes I and J are siblings

 

6. Degree-

 

  • Degree of a node is the total number of children of that node.
  • Degree of a tree is the highest degree of a node among all the nodes in the tree.

 

Example-

 

 

Here,

  • Degree of node A = 2
  • Degree of node B = 3
  • Degree of node C = 2
  • Degree of node D = 0
  • Degree of node E = 2
  • Degree of node F = 0
  • Degree of node G = 1
  • Degree of node H = 0
  • Degree of node I = 0
  • Degree of node J = 0
  • Degree of node K = 0

 

7. Internal Node-

 

  • The node which has at least one child is called as an internal node.
  • Internal nodes are also called as non-terminal nodes.
  • Every non-leaf node is an internal node.

 

Example-

 

 

Here, nodes A, B, C, E and G are internal nodes.

 

8. Leaf Node-

 

  • The node which does not have any child is called as a leaf node.
  • Leaf nodes are also called as external nodes or terminal nodes.

 

Example-

 

 

Here, nodes D, I, J, F, K and H are leaf nodes.

 

9. Level-

 

  • In a tree, each step from top to bottom is called as level of a tree.
  • The level count starts with 0 and increments by 1 at each level or step.

 

Example-

 

 

10. Height-

 

  • Total number of edges that lies on the longest path from any leaf node to a particular node is called as height of that node.
  • Height of a tree is the height of root node.
  • Height of all leaf nodes = 0

 

Example-

 

 

Here,

  • Height of node A = 3
  • Height of node B = 2
  • Height of node C = 2
  • Height of node D = 0
  • Height of node E = 1
  • Height of node F = 0
  • Height of node G = 1
  • Height of node H = 0
  • Height of node I = 0
  • Height of node J = 0
  • Height of node K = 0

 

11. Depth-

 

  • Total number of edges from root node to a particular node is called as depth of that node.
  • Depth of a tree is the total number of edges from root node to a leaf node in the longest path.
  • Depth of the root node = 0
  • The terms “level” and “depth” are used interchangeably.

 

Example-

 

 

Here,

  • Depth of node A = 0
  • Depth of node B = 1
  • Depth of node C = 1
  • Depth of node D = 2
  • Depth of node E = 2
  • Depth of node F = 2
  • Depth of node G = 2
  • Depth of node H = 2
  • Depth of node I = 3
  • Depth of node J = 3
  • Depth of node K = 3

 

12. Subtree-

 

  • In a tree, each child from a node forms a subtree recursively.
  • Every child node forms a subtree on its parent node.

 

Example-

 

 

13. Forest-

 

A forest is a set of disjoint trees.

 

Example-

 

 

To gain better understanding about Tree Terminology,

Watch this Video Lecture

 

Download Handwritten Notes Here-

 

 

Next Article- Binary Tree | Types of Binary Trees

 

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