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LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)<br />
For any non‐empty binary tree with n0 leaf nodes and n2 nodes of degree 2, n0 =<br />
n2 + <strong>1.</strong><br />
Definitions for rooted trees:<br />
A binary tree is a connected acyclic graph such that the degree of each vertex is<br />
not more than three. It can be shown that in any binary tree, there are exactly<br />
two or more nodes of degree one than there are of degree three, but there can<br />
be any number of nodes of degree two. A rooted binary tree is such a graph that<br />
has one of its vertices of degree not more than two singled out as the root.<br />
1) A directed edge refers to the link from the parent to the child (the<br />
arrows in the picture of the tree).<br />
2) The root node of a tree is the node with no parents. The is at the most<br />
one root node in a rooted tree.<br />
3) A leaf node has no children.<br />
4) The depth of a node n is the length of the path from the root to the<br />
node. The set of all nodes at a given depth is sometimes called a level<br />
of the tree. The root node is at depth zero.<br />
5) The height of a tree is the length of the path from the root to the<br />
deepest node in the tree. A (rooted) tree with only a node (the root)<br />
has a height of zero.<br />
6) Siblings are nodes that share the same parent node.<br />
7) In‐degree of a node is the number of edges arriving at that node.<br />
8) Out‐degree of a node is the number of edges leaving that node.<br />
Complete binary tree<br />
A tree consist of a finite set of elements called nodes and a finite set of directed<br />
lines called branches that connect the nodes.<br />
Prepared By :<br />
Er. Harvinder Singh<br />
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 179 ‐
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