Properties of binary tree

Properties of binary tree

• 1.
  PROPERTIES OF BINARY TREE -RACKSAVI.R, IM.Sc Information Technology, V.V.Vanniaperumal college for women, Virudhunagar.
• 2.
  PROPERTIES OF TREE? Everytree 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 forthe 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 heightof 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 heightof 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 numberof 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 Binarytree 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
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   Keys arearranged 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 anynon-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.
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