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Tree Concepts

Tree Concepts. A tree are very flexible, versatile and powerful non-liner data structure that consists of finite set of elements, called nodes , and a finite set of directed lines called branches , that connect the nodes. A tree is a data structure. It is used for storing files

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Tree Concepts

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  1. Tree Concepts • A tree are very flexible, versatile and powerful non-liner data structure that consists of finite set of elements, called nodes, and a finite set of directed lines called branches, that connect the nodes. • A tree is a data structure. It is used for • storing files • compiler design • text processing • searching algorithms 1

  2. A starting node called root. • The rest of nodes can be split into T1, T2, -, Tn, which are subtrees of the root.

  3. Basic Terminology • Degree Of Node :- Number of sub trees for that node • A leaf :is any node with an outdegree of zero, that is, a node with no successors. • A node that is not a root or a leaf is known as an internal node. • A node is a parent if it has successors nodes; that is, if it has outdegree greater than zero. • A node with a predecessor is called a child. • A pathis a sequence of nodes in which each node is adjacent to the next node.

  4. A node 1 degree 3 children E C B siblings B, D D 2 E F H I J 3 G parent B ancestors A, D, H M 4 L K leaf height or depth tree = maximum level of any node in the tree = 4 degree of a tree = maximum of the degree of the nodes = 3

  5. When the branch is directed toward the node, it is indegreebranch. • When the branch is directed away from the node, it is an outdegreebranch. • If the tree is not empty, the first node is called the root. • Node degree=number of output paths for it. 6

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  7. Binary Trees • A binary tree is a finite set of nodes that is either empty or consists of a root and two disjoint binary trees called the left subtree and the right subtree. • A binary tree can have no more than two descendents. In this section we discuss the properties of binary trees, four different binary tree traversals • Properties • Binary Tree Traversals • Expression Trees 9

  8. Binary Trees • A binary tree is a tree in which no node can have more than two subtrees; the maximum outdegree for a node is two. • In other words, a node can have zero, one, or two subtrees. • These subtrees are designated as the left subtree and the right subtree. 10

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  10. A null tree is a tree with no nodes 12

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