Python Data Structure and Algorithm Tutorial – Full Binary Tree

Full Binary Tree


In this tutorial, you will learn about full binary tree and its different theorems. Also, you will find working examples to check full binary tree in Python.

A full Binary tree is a special type of binary tree in which every parent node/internal node has either two or no children.

It is also known as a proper binary tree.

full binary tree
Full Binary Tree

Full Binary Tree Theorems

Let, i = the number of internal nodes
       n = be the total number of nodes
       l = number of leaves
      λ = number of levels
  1. The number of leaves is i + 1.
  2. The total number of nodes is 2i + 1.
  3. The number of internal nodes is (n – 1) / 2.
  4. The number of leaves is (n + 1) / 2.
  5. The total number of nodes is 2l – 1.
  6. The number of internal nodes is l – 1.
  7. The number of leaves is at most 2λ - 1.


Python Examples

The following code is for checking if a tree is a full binary tree.

/* Checking if a binary tree is a full binary tree in Python */

/* Creating a node */
class Node:

    def __init__(self, item):
        self.item = item
        self.leftChild = None
        self.rightChild = None

/* Checking full binary tree */
def isFullTree(root):

    /* Tree empty case */
    if root is None:
        return True

    /* Checking whether child is present */
    if root.leftChild is None and root.rightChild is None:
        return True

    if root.leftChild is not None and root.rightChild is not None:
        return (isFullTree(root.leftChild) and isFullTree(root.rightChild))

    return False


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