Types of properties of binary tree in data structure

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Types of Properties of Binary Trees


  • Rooted binary tree: It has a root node and every node has atmost two children.
  • Full binary tree: It is a tree in which every node in the tree has either 0 or 2 children.
    Binary Trees

    • The number of nodes, n, in a full binary tree is atleast n = 2h – 1, and atmost n = 2h+1 – 1, where h is the height of the tree.
    • The number of leaf nodes l, in a full binary tree is number, L of internal nodes + 1, i.e, l = L+1.
  • Perfect binary tree: It is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level.
    Binary Trees

    • A perfect binary tree with l leaves has n = 2l-1nodes.
    • In perfect full binary tree, l = 2h and n = 2h+1 - 1 where, n is number of nod justes, h is height of tree and l is number of leaf nodes
  • Complete binary tree: It is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.
    Binary Trees

    • The number of internal nodes in a complete binary tree of n nodes is floor(n/2).
  • Balanced binary tree: A binary tree is height balanced if it satisfies the following constraints:
    1. The left and right subtrees' heights differ by at most one, AND
    2. The left subtree is balanced, AND
    3. The right subtree is balanced
    An empty tree is height balanced.
    Binary Trees

    • The height of a balanced binary tree is O(Log n) where n is number of nodes.
  • Degenarate tree: It is a tree is where each parent node has only one child node. It behaves like a linked list.

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