The document discusses several properties of binary trees: - A binary tree has a single root node that connects to all other tree nodes. Each child node can only have one parent, but a parent node can have multiple children. - The maximum number of nodes in a binary tree with height H is 2H - 1. The minimum height of a binary tree with N nodes is log2N + 1. - Properties like the maximum nodes at each level, minimum number of levels for a given number of leaves, and relationships between the number of nodes, leaves, and edges are defined.

1. PROPERTIES OF
BINARY TREE
-RACKSAVI.R,
I M.Sc Information Technology,
V.V.Vanniaperumal college for women,
Virudhunagar.

2. PROPERTIES OF TREE?
Every tree has a specific
root node. A root node can
cross each tree node. Every
child has only one parent, but
the parent can have many
children.

3. The formula for the maximum number of
nodes is derived , that each node can
have only two descendents.
Given a height of the
binary tree “H” ,the maximum
number of nodes in the tree is
given as
Nmax = 2H - 1

4. The minimum height of a binary tree is
determined as:
Hmin = [ log2 N ] + 1
For instance,
If there are three nodes to be stored
in the binary tree (N = 3) then Hmin = 2.

5.  Maximum height of tree for N nodes:
Hmin = N
 Minimum height of a tree:
Nmin = H
 At each level i , max possible nodes
are
2i
 A tree with n nodes has exactly
( n – 1 ) edges or branches.

6. • Maximum number of nodes at level ‘l’ of
a binary tree is,
2l-1 .
• A binary tree with L leaves at least in
levels,
Log2L + 1 .
• A leaves are on same level.
• All internal nodes (except root node)
have at least [ (m/2) ] children.

7. • A Binary tree is a fairly well-balanced
tree since all leaf nodes must be at
the bottom .
• If height of the leaf node is 0,
log2 ( n+1 ) - 1

8.  Keys are arranged in a proper order
within a node.
 All keys in the sub tree to the left of
a key are Predecessors.
 All keys to the right of the key are
Successors.

9.  For any non-empty binary tree, if n
is the number of nodes and e is the
number of edges, then
n = e + 1 .
 For any non-empty binary tree T,
if n0 is the number of leaf nodes
( degree=0 ) & n2 is the number
of internal nodes( degree=2 ), then
n0 = n2 + 1 .

10. Thank
you