Properties of binary tree

Properties of Binary tree in Data Structure

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 N max = 2 H - 1

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

5. Maximum height of tree for N nodes: H min = N Minimum height of a tree: N min = H At each level i , max possible nodes are 2 i 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, 2 l-1 . A binary tree with L leaves at least in levels, Log 2 L + 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 n = n 2 + 1 .

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